Daily Papers

Sparse matrices, more specifically SpGEMM kernels, are commonly found in a wide range of applications, spanning graph-based path-finding to machine learning algorithms (e.g., neural networks). A particular challenge in implementing SpGEMM kernels has been the pressure placed on DRAM memory. One approach to tackle this problem is to use an inner product method for the SpGEMM kernel implementation. While the inner product produces fewer intermediate results, it can end up saturating the memory bandwidth, given the high number of redundant fetches of the input matrix elements. Using an outer product-based SpGEMM kernel can reduce redundant fetches, but at the cost of increased overhead due to extra computation and memory accesses for producing/managing partial products. In this thesis, we introduce a novel SpGEMM kernel implementation based on the row-wise product approach. We leverage atomic instructions to merge intermediate partial products as they are generated. The use of atomic instructions eliminates the need to create partial product matrices. To evaluate our row-wise product approach, we map an optimized SpGEMM kernel to a custom accelerator designed to accelerate graph-based applications. The targeted accelerator is an experimental system named PIUMA, being developed by Intel. PIUMA provides several attractive features, including fast context switching, user-configurable caches, globally addressable memory, non-coherent caches, and asynchronous pipelines. We tailor our SpGEMM kernel to exploit many of the features of the PIUMA fabric. This thesis compares our SpGEMM implementation against prior solutions, all mapped to the PIUMA framework. We briefly describe some of the PIUMA architecture features and then delve into the details of our optimized SpGEMM kernel. Our SpGEMM kernel can achieve 9.4x speedup as compared to competing approaches.

The published MLP-based DRL in finance has difficulties in learning the dynamics of the environment when the action scale increases. If the buying and selling increase to one thousand shares, the MLP agent will not be able to effectively adapt to the environment. To address this, we designed a CNN agent that concatenates the data from the last ninety days of the daily feature vector to create the CNN input matrix. Our extensive experiments demonstrate that the MLP-based agent experiences a loss corresponding to the initial environment setup, while our designed CNN remains stable, effectively learns the environment, and leads to an increase in rewards.

This course, intended for undergraduates familiar with elementary calculus and linear algebra, introduces the extension of differential calculus to functions on more general vector spaces, such as functions that take as input a matrix and return a matrix inverse or factorization, derivatives of ODE solutions, and even stochastic derivatives of random functions. It emphasizes practical computational applications, such as large-scale optimization and machine learning, where derivatives must be re-imagined in order to be propagated through complicated calculations. The class also discusses efficiency concerns leading to "adjoint" or "reverse-mode" differentiation (a.k.a. "backpropagation"), and gives a gentle introduction to modern automatic differentiation (AD) techniques.

Near out-of-distribution detection (OODD) aims at discriminating semantically similar data points without the supervision required for classification. This paper puts forward an OODD use case for radar targets detection extensible to other kinds of sensors and detection scenarios. We emphasize the relevance of OODD and its specific supervision requirements for the detection of a multimodal, diverse targets class among other similar radar targets and clutter in real-life critical systems. We propose a comparison of deep and non-deep OODD methods on simulated low-resolution pulse radar micro-Doppler signatures, considering both a spectral and a covariance matrix input representation. The covariance representation aims at estimating whether dedicated second-order processing is appropriate to discriminate signatures. The potential contributions of labeled anomalies in training, self-supervised learning, contrastive learning insights and innovative training losses are discussed, and the impact of training set contamination caused by mislabelling is investigated.

Improving out-of-distribution (OOD) generalization during in-distribution (ID) adaptation is a primary goal of robust fine-tuning of zero-shot models beyond naive fine-tuning. However, despite decent OOD generalization performance from recent robust fine-tuning methods, confidence calibration for reliable model output has not been fully addressed. This work proposes a robust fine-tuning method that improves both OOD accuracy and confidence calibration simultaneously in vision language models. Firstly, we show that both OOD classification and OOD calibration errors have a shared upper bound consisting of two terms of ID data: 1) ID calibration error and 2) the smallest singular value of the ID input covariance matrix. Based on this insight, we design a novel framework that conducts fine-tuning with a constrained multimodal contrastive loss enforcing a larger smallest singular value, which is further guided by the self-distillation of a moving-averaged model to achieve calibrated prediction as well. Starting from empirical evidence supporting our theoretical statements, we provide extensive experimental results on ImageNet distribution shift benchmarks that demonstrate the effectiveness of our theorem and its practical implementation.

In recent studies, linear recurrent neural networks (LRNNs) have achieved Transformer-level performance in natural language and long-range modeling, while offering rapid parallel training and constant inference cost. With the resurgence of interest in LRNNs, we study whether they can learn the hidden rules in training sequences, such as the grammatical structures of regular language. We theoretically analyze some existing LRNNs and discover their limitations in modeling regular language. Motivated by this analysis, we propose a new LRNN equipped with a block-diagonal and input-dependent transition matrix. Experiments suggest that the proposed model is the only LRNN capable of performing length extrapolation on regular language tasks such as Sum, Even Pair, and Modular Arithmetic. The code is released at https://github.com/tinghanf/RegluarLRNN.

We introduce CrossWKV, a novel cross-attention mechanism for the state-based RWKV-7 model, designed to enhance the expressive power of text-to-image generation. Leveraging RWKV-7's linear-complexity Weighted Key-Value (WKV) architecture, CrossWKV integrates text and image modalities in a single pass, utilizing a generalized delta rule with vector-valued gating and low-rank adaptations (LoRA) to achieve superior cross-modal alignment. Unlike Transformer-based models, CrossWKV's non-diagonal, input-dependent transition matrix enables it to represent complex functions beyond the TC^0 complexity class, including all regular languages, as demonstrated by its ability to perform state-tracking tasks like S_5 permutation modeling. Evaluated within the Diffusion in RWKV-7 (DIR-7) on datasets such as LAION-5B and ImageNet, CrossWKV achieves a Frechet Inception Distance (FID) of 2.88 and a CLIP score of 0.33 on ImageNet 256x256, matching state-of-the-art performance while offering robust generalization across diverse prompts. The model's enhanced expressivity, combined with constant memory usage and linear scaling, positions it as a powerful solution for advanced cross-modal tasks, with potential applications in high-resolution generation and dynamic state manipulation.Code at https://github.com/TorchRWKV/flash-linear-attention

Linear transformation of the inputs alters the training performance of feed-forward networks that are otherwise equivalent. However, most linear transforms are viewed as a pre-processing operation separate from the actual training. Starting from equivalent networks, it is shown that pre-processing inputs using linear transformation are equivalent to multiplying the negative gradient matrix with an autocorrelation matrix per training iteration. Second order method is proposed to find the autocorrelation matrix that maximizes learning in a given iteration. When the autocorrelation matrix is diagonal, the method optimizes input gains. This optimal input gain (OIG) approach is used to improve two first-order two-stage training algorithms, namely back-propagation (BP) and hidden weight optimization (HWO), which alternately update the input weights and solve linear equations for output weights. Results show that the proposed OIG approach greatly enhances the performance of the first-order algorithms, often allowing them to rival the popular Levenberg-Marquardt approach with far less computation. It is shown that HWO is equivalent to BP with Whitening transformation applied to the inputs. HWO effectively combines Whitening transformation with learning. Thus, OIG improved HWO could be a significant building block to more complex deep learning architectures.

A central challenge of video prediction lies where the system has to reason the objects' future motions from image frames while simultaneously maintaining the consistency of their appearances across frames. This work introduces an end-to-end trainable two-stream video prediction framework, Motion-Matrix-based Video Prediction (MMVP), to tackle this challenge. Unlike previous methods that usually handle motion prediction and appearance maintenance within the same set of modules, MMVP decouples motion and appearance information by constructing appearance-agnostic motion matrices. The motion matrices represent the temporal similarity of each and every pair of feature patches in the input frames, and are the sole input of the motion prediction module in MMVP. This design improves video prediction in both accuracy and efficiency, and reduces the model size. Results of extensive experiments demonstrate that MMVP outperforms state-of-the-art systems on public data sets by non-negligible large margins (about 1 db in PSNR, UCF Sports) in significantly smaller model sizes (84% the size or smaller).

A wide array of sequence models are built on a framework modeled after Transformers, comprising alternating sequence mixer and channel mixer layers. This paper studies a unifying matrix mixer view of sequence mixers that can be conceptualized as a linear map on the input sequence. This framework encompasses a broad range of well-known sequence models, including the self-attention of Transformers as well as recent strong alternatives such as structured state space models (SSMs), and allows understanding downstream characteristics such as efficiency and expressivity through properties of their structured matrix class. We identify a key axis of matrix parameterizations termed sequence alignment, which increases the flexibility and performance of matrix mixers, providing insights into the strong performance of Transformers and recent SSMs such as Mamba. Furthermore, the matrix mixer framework offers a systematic approach to developing sequence mixers with desired properties, allowing us to develop several new sub-quadratic sequence models. In particular, we propose a natural bidirectional extension of the Mamba model (Hydra), parameterized as a quasiseparable matrix mixer, which demonstrates superior performance over other sequence models including Transformers on non-causal tasks. As a drop-in replacement for attention layers, Hydra outperforms BERT by 0.8 points on the GLUE benchmark and ViT by 2% Top-1 accuracy on ImageNet.

Vision-Language Models (VLMs) inherit adversarial vulnerabilities of Large Language Models (LLMs), which are further exacerbated by their multimodal nature. Existing defenses, including adversarial training, input transformations, and heuristic detection, are computationally expensive, architecture-dependent, and fragile against adaptive attacks. We introduce EigenShield, an inference-time defense leveraging Random Matrix Theory to quantify adversarial disruptions in high-dimensional VLM representations. Unlike prior methods that rely on empirical heuristics, EigenShield employs the spiked covariance model to detect structured spectral deviations. Using a Robustness-based Nonconformity Score (RbNS) and quantile-based thresholding, it separates causal eigenvectors, which encode semantic information, from correlational eigenvectors that are susceptible to adversarial artifacts. By projecting embeddings onto the causal subspace, EigenShield filters adversarial noise without modifying model parameters or requiring adversarial training. This architecture-independent, attack-agnostic approach significantly reduces the attack success rate, establishing spectral analysis as a principled alternative to conventional defenses. Our results demonstrate that EigenShield consistently outperforms all existing defenses, including adversarial training, UNIGUARD, and CIDER.

In the classical transformer attention scheme, we are given three n times d size matrices Q, K, V (the query, key, and value tokens), and the goal is to compute a new n times d size matrix D^{-1} exp(QK^top) V where D = diag( exp(QK^top) {bf 1}_n ). In this work, we study a generalization of attention which captures triple-wise correlations. This generalization is able to solve problems about detecting triple-wise connections that were shown to be impossible for transformers. The potential downside of this generalization is that it appears as though computations are even more difficult, since the straightforward algorithm requires cubic time in n. However, we show that in the bounded-entry setting (which arises in practice, and which is well-studied in both theory and practice), there is actually a near-linear time algorithm. More precisely, we show that bounded entries are both necessary and sufficient for quickly performing generalized computations: bullet On the positive side, if all entries of the input matrices are bounded above by o(sqrt[3]{log n}) then we show how to approximate the ``tensor-type'' attention matrix in n^{1+o(1)} time. bullet On the negative side, we show that if the entries of the input matrices may be as large as Omega(sqrt[3]{log n}), then there is no algorithm that runs faster than n^{3-o(1)} (assuming the Strong Exponential Time Hypothesis from fine-grained complexity theory). We also show that our construction, algorithms, and lower bounds naturally generalize to higher-order tensors and correlations. Interestingly, the higher the order of the tensors, the lower the bound on the entries needs to be for an efficient algorithm. Our results thus yield a natural tradeoff between the boundedness of the entries, and order of the tensor one may use for more expressive, efficient attention computation.

State-space models (SSMs) are a new class of foundation models that have emerged as a compelling alternative to Transformers and their attention mechanisms for sequence processing tasks. This paper provides a detailed theoretical analysis of selective SSMs, the core components of the Mamba and Mamba-2 architectures. We leverage the connection between selective SSMs and the self-attention mechanism to highlight the fundamental similarities between these models. Building on this connection, we establish a length independent covering number-based generalization bound for selective SSMs, providing a deeper understanding of their theoretical performance guarantees. We analyze the effects of state matrix stability and input-dependent discretization, shedding light on the critical role played by these factors in the generalization capabilities of selective SSMs. Finally, we empirically demonstrate the sequence length independence of the derived bounds on two tasks.

As language models grow ever larger, so do their vocabularies. This has shifted the memory footprint of LLMs during training disproportionately to one single layer: the cross-entropy in the loss computation. Cross-entropy builds up a logit matrix with entries for each pair of input tokens and vocabulary items and, for small models, consumes an order of magnitude more memory than the rest of the LLM combined. We propose Cut Cross-Entropy (CCE), a method that computes the cross-entropy loss without materializing the logits for all tokens into global memory. Rather, CCE only computes the logit for the correct token and evaluates the log-sum-exp over all logits on the fly. We implement a custom kernel that performs the matrix multiplications and the log-sum-exp reduction over the vocabulary in flash memory, making global memory consumption for the cross-entropy computation negligible. This has a dramatic effect. Taking the Gemma 2 (2B) model as an example, CCE reduces the memory footprint of the loss computation from 24 GB to 1 MB, and the total training-time memory consumption of the classifier head from 28 GB to 1 GB. To improve the throughput of CCE, we leverage the inherent sparsity of softmax and propose to skip elements of the gradient computation that have a negligible (i.e., below numerical precision) contribution to the gradient. Experiments demonstrate that the dramatic reduction in memory consumption is accomplished without sacrificing training speed or convergence.

Transformers evaluated in a single, fixed-depth pass are provably limited in expressive power to the constant-depth circuit class TC0. Running a Transformer autoregressively removes that ceiling -- first in next-token prediction and, more recently, in chain-of-thought reasoning. Both regimes rely on feedback loops that decode internal states into tokens only to re-encode them in subsequent steps. While this "thinking aloud" mirrors human reasoning, biological brains iterate without externalising intermediate states as language. To boost the expressive power of encoder Transformers without resorting to token-level autoregression, we introduce the SELF-Transformer: an encoder layer that iteratively refines its own attention weights to a fixed point. Instead of producing -- in one pass -- the alignment matrix that remixes the input sequence, the SELF-Transformer iteratively updates that matrix internally, scaling test-time computation with input difficulty. This adaptivity yields up to 20\% accuracy gains on encoder-style benchmarks without increasing parameter count, demonstrating that input-adaptive alignment at test time offers substantial benefits for only a modest extra compute budget. Self-Transformers thus recover much of the expressive power of iterative reasoning while preserving the simplicity of pure encoder architectures.

This study addresses the challenges of multi-label text classification. The difficulties arise from imbalanced data sets, varied text lengths, and numerous subjective feature labels. Existing solutions include traditional machine learning and deep neural networks for predictions. However, both approaches have their limitations. Traditional machine learning often overlooks the associations between words, while deep neural networks, despite their better classification performance, come with increased training complexity and time. This paper proposes a method utilizing the bag-of-words model approach based on the GloVe model and the CNN-BiLSTM network. The principle is to use the word vector matrix trained by the GloVe model as the input for the text embedding layer. Given that the GloVe model requires no further training, the neural network model can be trained more efficiently. The method achieves an accuracy rate of 87.26% on the test set and an F1 score of 0.8737, showcasing promising results.

Transformer models have been widely adopted in various domains over the last years, and especially large language models have advanced the field of AI significantly. Due to their size, the capability of these networks has increased tremendously, but this has come at the cost of a significant increase in necessary compute. Quantization is one of the most effective ways to reduce the computational time and memory consumption of neural networks. Many studies have shown, however, that modern transformer models tend to learn strong outliers in their activations, making them difficult to quantize. To retain acceptable performance, the existence of these outliers requires activations to be in higher bitwidth or the use of different numeric formats, extra fine-tuning, or other workarounds. We show that strong outliers are related to very specific behavior of attention heads that try to learn a "no-op" or just a partial update of the residual. To achieve the exact zeros needed in the attention matrix for a no-update, the input to the softmax is pushed to be larger and larger during training, causing outliers in other parts of the network. Based on these observations, we propose two simple (independent) modifications to the attention mechanism - clipped softmax and gated attention. We empirically show that models pre-trained using our methods learn significantly smaller outliers while maintaining and sometimes even improving the floating-point task performance. This enables us to quantize transformers to full INT8 quantization of the activations without any additional effort. We demonstrate the effectiveness of our methods on both language models (BERT, OPT) and vision transformers.

This paper presents a Bayesian nonparametric latent feature model specially suitable for exploratory analysis of high-dimensional count data. We perform a non-negative doubly sparse matrix factorization that has two main advantages: not only we are able to better approximate the row input distributions, but the inferred topics are also easier to interpret. By combining the three-parameter and restricted Indian buffet processes into a single prior, we increase the model flexibility, allowing for a full spectrum of sparse solutions in the latent space. We demonstrate the usefulness of our approach in the analysis of countries' economic structure. Compared to other approaches, empirical results show our model's ability to give easy-to-interpret information and better capture the underlying sparsity structure of data.

We look at the eigenvalues of the Hessian of a loss function before and after training. The eigenvalue distribution is seen to be composed of two parts, the bulk which is concentrated around zero, and the edges which are scattered away from zero. We present empirical evidence for the bulk indicating how over-parametrized the system is, and for the edges that depend on the input data.

Large Language Models (LLMs) have recently demonstrated a remarkable success across various tasks. However, efficiently serving LLMs has been a challenge due to its large memory bottleneck, specifically in small batch inference settings (e.g. mobile devices). Weight-only quantization can be a promising approach, but sub-4 bit quantization remains a challenge due to large-magnitude activation outliers. To mitigate the undesirable outlier effect, we first propose per-IC quantization, a simple yet effective method that creates quantization groups within each input channel (IC) rather than the conventional per-output channel (OC). Our method is motivated by the observation that activation outliers affect the input dimension of the weight matrix, so similarly grouping the weights in the IC direction can isolate outliers to be within a group. We also find that activation outliers do not dictate quantization difficulty, and inherent weight sensitivities also exist. With per-IC quantization as a new outlier-friendly scheme, we then propose Adaptive Dimensions (AdaDim), a versatile quantization framework that can adapt to various weight sensitivity patterns. We demonstrate the effectiveness of AdaDim by augmenting prior methods such as Round-To-Nearest and GPTQ, showing significant improvements across various language modeling benchmarks for both base (up to +4.7% on MMLU) and instruction-tuned (up to +10% on HumanEval) LLMs.

We analyze the DP (differential privacy) properties of the quantum recommendation algorithm and the quantum-inspired-classical recommendation algorithm. We discover that the quantum recommendation algorithm is a privacy curating mechanism on its own, requiring no external noise, which is different from traditional differential privacy mechanisms. In our analysis, a novel perturbation method tailored for SVD (singular value decomposition) and low-rank matrix approximation problems is introduced. Using the perturbation method and random matrix theory, we are able to derive that both the quantum and quantum-inspired-classical algorithms are big(mathcal{O}big(frac 1nbig),,, mathcal{O}big(1{min{m,n}}big)big)-DP under some reasonable restrictions, where m and n are numbers of users and products in the input preference database respectively. Nevertheless, a comparison shows that the quantum algorithm has better privacy preserving potential than the classical one.

Aligning large language models (LLMs) with human values is imperative to mitigate potential adverse effects resulting from their misuse. Drawing from the sociological insight that acknowledging all parties' concerns is a key factor in shaping human values, this paper proposes a novel direction to align LLMs by themselves: social scene simulation. To achieve this, we present MATRIX, a novel social scene simulator that emulates realistic scenes around a user's input query, enabling the LLM to take social consequences into account before responding. MATRIX serves as a virtual rehearsal space, akin to a Monopolylogue, where the LLM performs diverse roles related to the query and practice by itself. To inject this alignment, we fine-tune the LLM with MATRIX-simulated data, ensuring adherence to human values without compromising inference speed. We theoretically show that the LLM with MATRIX outperforms Constitutional AI under mild assumptions. Finally, extensive experiments validate that our method outperforms over 10 baselines across 4 benchmarks. As evidenced by 875 user ratings, our tuned 13B-size LLM exceeds GPT-4 in aligning with human values. Code is available at https://github.com/pangxianghe/MATRIX.

Despite Multi-modal Large Language Models (MM-LLMs) have made exciting strides recently, they are still struggling to efficiently model the interactions among multi-modal inputs and the generation in non-textual modalities. In this work, we propose TEAL (Tokenize and Embed ALl)}, an approach to treat the input from any modality as a token sequence and learn a joint embedding space for all modalities. Specifically, for the input from any modality, TEAL first discretizes it into a token sequence with the off-the-shelf tokenizer and embeds the token sequence into a joint embedding space with a learnable embedding matrix. MM-LLMs just need to predict the multi-modal tokens autoregressively as the textual LLMs do. Finally, the corresponding de-tokenizer is applied to generate the output in each modality based on the predicted token sequence. With the joint embedding space, TEAL enables the frozen LLMs to perform both understanding and generation tasks involving non-textual modalities, such as image and audio. Thus, the textual LLM can just work as an interface and maintain its high performance in textual understanding and generation. Experiments show that TEAL achieves substantial improvements in multi-modal understanding, and implements a simple scheme for multi-modal generations.

Recent works have demonstrated the effectiveness of retrieval augmentation in the Event Argument Extraction (EAE) task. However, existing retrieval-based EAE methods have two main limitations: (1) input length constraints and (2) the gap between the retriever and the inference model. These issues limit the diversity and quality of the retrieved information. In this paper, we propose a Compressive Memory-based Retrieval (CMR) mechanism for EAE, which addresses the two limitations mentioned above. Our compressive memory, designed as a dynamic matrix that effectively caches retrieved information and supports continuous updates, overcomes the limitations of the input length. Additionally, after pre-loading all candidate demonstrations into the compressive memory, the model further retrieves and filters relevant information from memory based on the input query, bridging the gap between the retriever and the inference model. Extensive experiments show that our method achieves new state-of-the-art performance on three public datasets (RAMS, WikiEvents, ACE05), significantly outperforming existing retrieval-based EAE methods.

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for partial differential equations. Algorithms for approximating the solution to these systems are often the bottleneck in problems that require their solution, particularly for modern applications that require many millions of unknowns. Indeed, numerical linear algebra techniques have been investigated for many decades to alleviate this computational burden. Recently, data-driven techniques have also shown promise for these problems. Motivated by the conjugate gradients algorithm that iteratively selects search directions for minimizing the matrix norm of the approximation error, we design an approach that utilizes a deep neural network to accelerate convergence via data-driven improvement of the search directions. Our method leverages a carefully chosen convolutional network to approximate the action of the inverse of the linear operator up to an arbitrary constant. We train the network using unsupervised learning with a loss function equal to the L^2 difference between an input and the system matrix times the network evaluation, where the unspecified constant in the approximate inverse is accounted for. We demonstrate the efficacy of our approach on spatially discretized Poisson equations with millions of degrees of freedom arising in computational fluid dynamics applications. Unlike state-of-the-art learning approaches, our algorithm is capable of reducing the linear system residual to a given tolerance in a small number of iterations, independent of the problem size. Moreover, our method generalizes effectively to various systems beyond those encountered during training.

Orthogonal finetuning (OFT) offers highly parameter-efficient adaptation while preventing catastrophic forgetting, but its high runtime and memory demands limit practical deployment. We identify the core computational bottleneck in OFT as its weight-centric implementation, which relies on costly matrix-matrix multiplications with cubic complexity. To overcome this, we propose OFTv2, an input-centric reformulation that instead uses matrix-vector multiplications (i.e., matrix-free computation), reducing the computational cost to quadratic. We further introduce the Cayley-Neumann parameterization, an efficient orthogonal parameterization that approximates the matrix inversion in Cayley transform via a truncated Neumann series. These modifications allow OFTv2 to achieve up to 10x faster training and 3x lower GPU memory usage without compromising performance. In addition, we extend OFTv2 to support finetuning quantized foundation models and show that it outperforms the popular QLoRA in training stability, efficiency, and memory usage.

Deep learning is widely used in wireless communications but struggles with fixed neural network sizes, which limit their adaptability in environments where the number of users and antennas varies. To overcome this, this paper introduced a generalization strategy for precoding and power allocation in scalable wireless networks. Initially, we employ an innovative approach to abstract the wireless network into a homogeneous graph. This primarily focuses on bypassing the heterogeneous features between transmitter (TX) and user entities to construct a virtual homogeneous graph serving optimization objectives, thereby enabling all nodes in the virtual graph to share the same neural network. This "TX entity" is known as a base station (BS) in cellular networks and an access point (AP) in cell-free networks. Subsequently, we design a universal graph neural network, termed the information carrying graph neural network (ICGNN), to capture and integrate information from this graph, maintaining permutation invariance. Lastly, using ICGNN as the core algorithm, we tailor the neural network's input and output for specific problem requirements and validate its performance in two scenarios: 1) in cellular networks, we develop a matrix-inverse-free multi-user multi-input multi-output (MU-MIMO) precoding scheme using the conjugate gradient (CG) method, adaptable to varying user and antenna numbers; 2) in a cell-free network, facing dynamic variations in the number of users served by APs, the number of APs serving each user, and the number of antennas per AP, we propose a universal power allocation scheme. Simulations demonstrate that the proposed approach not only significantly reduces computational complexity but also achieves, and potentially exceeds, the spectral efficiency (SE) of conventional algorithms.

Recent studies of two-view correspondence learning usually establish an end-to-end network to jointly predict correspondence reliability and relative pose. We improve such a framework from two aspects. First, we propose a Local Feature Consensus (LFC) plugin block to augment the features of existing models. Given a correspondence feature, the block augments its neighboring features with mutual neighborhood consensus and aggregates them to produce an enhanced feature. As inliers obey a uniform cross-view transformation and share more consistent learned features than outliers, feature consensus strengthens inlier correlation and suppresses outlier distraction, which makes output features more discriminative for classifying inliers/outliers. Second, existing approaches supervise network training with the ground truth correspondences and essential matrix projecting one image to the other for an input image pair, without considering the information from the reverse mapping. We extend existing models to a Siamese network with a reciprocal loss that exploits the supervision of mutual projection, which considerably promotes the matching performance without introducing additional model parameters. Building upon MSA-Net, we implement the two proposals and experimentally achieve state-of-the-art performance on benchmark datasets.

Recently, unsupervised exemplar-based image-to-image translation, conditioned on a given exemplar without the paired data, has accomplished substantial advancements. In order to transfer the information from an exemplar to an input image, existing methods often use a normalization technique, e.g., adaptive instance normalization, that controls the channel-wise statistics of an input activation map at a particular layer, such as the mean and the variance. Meanwhile, style transfer approaches similar task to image translation by nature, demonstrated superior performance by using the higher-order statistics such as covariance among channels in representing a style. In detail, it works via whitening (given a zero-mean input feature, transforming its covariance matrix into the identity). followed by coloring (changing the covariance matrix of the whitened feature to those of the style feature). However, applying this approach in image translation is computationally intensive and error-prone due to the expensive time complexity and its non-trivial backpropagation. In response, this paper proposes an end-to-end approach tailored for image translation that efficiently approximates this transformation with our novel regularization methods. We further extend our approach to a group-wise form for memory and time efficiency as well as image quality. Extensive qualitative and quantitative experiments demonstrate that our proposed method is fast, both in training and inference, and highly effective in reflecting the style of an exemplar. Finally, our code is available at https://github.com/WonwoongCho/GDWCT.

Low-rank adaptation is a popular parameter-efficient fine-tuning method for large language models. In this paper, we analyze the impact of low-rank updating, as implemented in LoRA. Our findings suggest that the low-rank updating mechanism may limit the ability of LLMs to effectively learn and memorize new knowledge. Inspired by this observation, we propose a new method called MoRA, which employs a square matrix to achieve high-rank updating while maintaining the same number of trainable parameters. To achieve it, we introduce the corresponding non-parameter operators to reduce the input dimension and increase the output dimension for the square matrix. Furthermore, these operators ensure that the weight can be merged back into LLMs, which makes our method can be deployed like LoRA. We perform a comprehensive evaluation of our method across five tasks: instruction tuning, mathematical reasoning, continual pretraining, memory and pretraining. Our method outperforms LoRA on memory-intensive tasks and achieves comparable performance on other tasks.

Current parameter-efficient fine-tuning (PEFT) methods build adapters without considering the context of downstream task to learn, or the context of important knowledge to maintain. As a result, there is often a performance gap compared to full-parameter finetuning, and meanwhile the finetuned model suffers from catastrophic forgetting of the pre-trained world knowledge. In this paper, we propose CorDA, a Context-oriented Decomposition Adaptation method that builds learnable adapters from weight decomposition oriented by the context of downstream task or world knowledge. Concretely, we collect a few data samples, and perform singular value decomposition for each linear layer of a pre-trained LLM multiplied by the covariance matrix of the input activation using these samples. By doing so, the context of the representative samples is captured through deciding the factorizing orientation. Our method enables two options, the knowledge-preserved adaptation and the instruction-previewed adaptation. For the former, we use question-answering samples to obtain the covariance matrices, and use the decomposed components with the smallest r singular values to initialize a learnable adapter, with the others frozen such that the world knowledge is better preserved. For the latter, we use the instruction data from the finetuning task, such as math or coding, to orientate the decomposition and train the largest r components that capture the main characteristics of the task to learn. We conduct extensive experiments on Math, Code, and Instruction Following tasks. Our knowledge-preserved adaptation not only achieves better performance than LoRA on finetuning tasks, but also mitigates the forgetting of world knowledge. Our instruction-previewed adaptation is able to further enhance the finetuning performance, surpassing full-parameter finetuning and the state-of-the-art PEFT methods.

While multi-modal large language models (MLLMs) have shown significant progress on many popular visual reasoning benchmarks, whether they possess abstract visual reasoning abilities remains an open question. Similar to the Sudoku puzzles, abstract visual reasoning (AVR) problems require finding high-level patterns (e.g., repetition constraints) that control the input shapes (e.g., digits) in a specific task configuration (e.g., matrix). However, existing AVR benchmarks only considered a limited set of patterns (addition, conjunction), input shapes (rectangle, square), and task configurations (3 by 3 matrices). To evaluate MLLMs' reasoning abilities comprehensively, we introduce MARVEL, a multidimensional AVR benchmark with 770 puzzles composed of six core knowledge patterns, geometric and abstract shapes, and five different task configurations. To inspect whether the model accuracy is grounded in perception and reasoning, MARVEL complements the general AVR question with perception questions in a hierarchical evaluation framework. We conduct comprehensive experiments on MARVEL with nine representative MLLMs in zero-shot and few-shot settings. Our experiments reveal that all models show near-random performance on the AVR question, with significant performance gaps (40%) compared to humans across all patterns and task configurations. Further analysis of perception questions reveals that MLLMs struggle to comprehend the visual features (near-random performance) and even count the panels in the puzzle ( <45%), hindering their ability for abstract reasoning. We release our entire code and dataset.

Large Language Models (LLMs) have demonstrated remarkable performance across various tasks but remain prone to hallucinations. Detecting hallucinations is essential for safety-critical applications, and recent methods leverage attention map properties to this end, though their effectiveness remains limited. In this work, we investigate the spectral features of attention maps by interpreting them as adjacency matrices of graph structures. We propose the LapEigvals method, which utilises the top-k eigenvalues of the Laplacian matrix derived from the attention maps as an input to hallucination detection probes. Empirical evaluations demonstrate that our approach achieves state-of-the-art hallucination detection performance among attention-based methods. Extensive ablation studies further highlight the robustness and generalisation of LapEigvals, paving the way for future advancements in the hallucination detection domain.

The total memory capacity (MC) of linear recurrent neural networks (RNNs) has been proven to be equal to the rank of the corresponding Kalman controllability matrix, and it is almost surely maximal for connectivity and input weight matrices drawn from regular distributions. This fact questions the usefulness of this metric in distinguishing the performance of linear RNNs in the processing of stochastic signals. This note shows that the MC of random nonlinear RNNs yields arbitrary values within established upper and lower bounds depending just on the input process scale. This confirms that the existing definition of MC in linear and nonlinear cases has no practical value.

We present a new methodology for detecting out-of-distribution (OOD) images by utilizing norms of the score estimates at multiple noise scales. A score is defined to be the gradient of the log density with respect to the input data. Our methodology is completely unsupervised and follows a straight forward training scheme. First, we train a deep network to estimate scores for levels of noise. Once trained, we calculate the noisy score estimates for N in-distribution samples and take the L2-norms across the input dimensions (resulting in an NxL matrix). Then we train an auxiliary model (such as a Gaussian Mixture Model) to learn the in-distribution spatial regions in this L-dimensional space. This auxiliary model can now be used to identify points that reside outside the learned space. Despite its simplicity, our experiments show that this methodology significantly outperforms the state-of-the-art in detecting out-of-distribution images. For example, our method can effectively separate CIFAR-10 (inlier) and SVHN (OOD) images, a setting which has been previously shown to be difficult for deep likelihood models.

We present a framework for using transformer networks as universal computers by programming them with specific weights and placing them in a loop. Our input sequence acts as a punchcard, consisting of instructions and memory for data read/writes. We demonstrate that a constant number of encoder layers can emulate basic computing blocks, including embedding edit operations, non-linear functions, function calls, program counters, and conditional branches. Using these building blocks, we emulate a small instruction-set computer. This allows us to map iterative algorithms to programs that can be executed by a looped, 13-layer transformer. We show how this transformer, instructed by its input, can emulate a basic calculator, a basic linear algebra library, and in-context learning algorithms that employ backpropagation. Our work highlights the versatility of the attention mechanism, and demonstrates that even shallow transformers can execute full-fledged, general-purpose programs.

Recommendation is the task of ranking items (e.g. movies or products) according to individual user needs. Current systems rely on collaborative filtering and content-based techniques, which both require structured training data. We propose a framework for recommendation with off-the-shelf pretrained language models (LM) that only used unstructured text corpora as training data. If a user u liked Matrix and Inception, we construct a textual prompt, e.g. "Movies like Matrix, Inception, {<m{>}"} to estimate the affinity between u and m with LM likelihood. We motivate our idea with a corpus analysis, evaluate several prompt structures, and we compare LM-based recommendation with standard matrix factorization trained on different data regimes. The code for our experiments is publicly available (https://colab.research.google.com/drive/1f1mlZ-FGaLGdo5rPzxf3vemKllbh2esT?usp=sharing).

State space models (SSM) have recently been shown to be very effective as a deep learning layer as a promising alternative to sequence models such as RNNs, CNNs, or Transformers. The first version to show this potential was the S4 model, which is particularly effective on tasks involving long-range dependencies by using a prescribed state matrix called the HiPPO matrix. While this has an interpretable mathematical mechanism for modeling long dependencies, it introduces a custom representation and algorithm that can be difficult to implement. On the other hand, a recent variant of S4 called DSS showed that restricting the state matrix to be fully diagonal can still preserve the performance of the original model when using a specific initialization based on approximating S4's matrix. This work seeks to systematically understand how to parameterize and initialize such diagonal state space models. While it follows from classical results that almost all SSMs have an equivalent diagonal form, we show that the initialization is critical for performance. We explain why DSS works mathematically, by showing that the diagonal restriction of S4's matrix surprisingly recovers the same kernel in the limit of infinite state dimension. We also systematically describe various design choices in parameterizing and computing diagonal SSMs, and perform a controlled empirical study ablating the effects of these choices. Our final model S4D is a simple diagonal version of S4 whose kernel computation requires just 2 lines of code and performs comparably to S4 in almost all settings, with state-of-the-art results for image, audio, and medical time-series domains, and averaging 85\% on the Long Range Arena benchmark.

This paper explores the relationship between matrix factorizations and linear matrix equations. It shows that every matrix factorization defines two hidden projectors, one for the column space and one for the row space of a matrix, and how to calculate them. The projectors can be applied to solve linear matrix equations, generate low-rank approximations, or design randomized matrix algorithms. But also, as demonstrated, they can be applied in cryptography to encrypt and decrypt messages. The paper discusses some of the security implications of this application and leaves some questions open for further investigation. The basic concepts are illustrated with source code listings. Finally, this work shares some personal reflections on the meaning and importance of understanding in the time of the artificial intelligence revolution.

This paper is an attempt to explain all the matrix calculus you need in order to understand the training of deep neural networks. We assume no math knowledge beyond what you learned in calculus 1, and provide links to help you refresh the necessary math where needed. Note that you do not need to understand this material before you start learning to train and use deep learning in practice; rather, this material is for those who are already familiar with the basics of neural networks, and wish to deepen their understanding of the underlying math. Don't worry if you get stuck at some point along the way---just go back and reread the previous section, and try writing down and working through some examples. And if you're still stuck, we're happy to answer your questions in the Theory category at forums.fast.ai. Note: There is a reference section at the end of the paper summarizing all the key matrix calculus rules and terminology discussed here. See related articles at http://explained.ai

Current foundation models exhibit impressive capabilities when prompted either with text only or with both image and text inputs. But do their capabilities change depending on the input modality? In this work, we propose IsoBench, a benchmark dataset containing problems from four major areas: math, science, algorithms, and games. Each example is presented with multiple isomorphic representations of inputs, such as visual, textual, and mathematical presentations. IsoBench provides fine-grained feedback to diagnose performance gaps caused by the form of the representation. Across various foundation models, we observe that on the same problem, models have a consistent preference towards textual representations. Most prominently, when evaluated on all IsoBench problems, Claude-3 Opus performs 28.7 points worse when provided with images instead of text; similarly, GPT-4 Turbo is 18.7 points worse and Gemini Pro is 14.9 points worse. Finally, we present two prompting techniques, IsoCombination and IsoScratchPad, which improve model performance by considering combinations of, and translations between, different input representations.

The weight matrix (WM) of a neural network (NN) is its program. The programs of many traditional NNs are learned through gradient descent in some error function, then remain fixed. The WM of a self-referential NN, however, can keep rapidly modifying all of itself during runtime. In principle, such NNs can meta-learn to learn, and meta-meta-learn to meta-learn to learn, and so on, in the sense of recursive self-improvement. While NN architectures potentially capable of implementing such behaviour have been proposed since the '90s, there have been few if any practical studies. Here we revisit such NNs, building upon recent successes of fast weight programmers and closely related linear Transformers. We propose a scalable self-referential WM (SRWM) that learns to use outer products and the delta update rule to modify itself. We evaluate our SRWM in supervised few-shot learning and in multi-task reinforcement learning with procedurally generated game environments. Our experiments demonstrate both practical applicability and competitive performance of the proposed SRWM. Our code is public.

A new class of affine scaling matrices for the interior point Newton-type methods is considered to solve the nonlinear systems with simple bounds. We review the essential properties of a scaling matrix and consider several well-known scaling matrices proposed in the literature. We define a new scaling matrix that is the convex combination of these matrices. The proposed scaling matrix inherits those interesting properties of the individual matrices and satisfies additional desired requirements. The numerical experiments demonstrate the superiority of the new scaling matrix in solving several important test problems.

Visual recognition of materials and their states is essential for understanding most aspects of the world, from determining whether food is cooked, metal is rusted, or a chemical reaction has occurred. However, current image recognition methods are limited to specific classes and properties and can't handle the vast number of material states in the world. To address this, we present MatSim: the first dataset and benchmark for computer vision-based recognition of similarities and transitions between materials and textures, focusing on identifying any material under any conditions using one or a few examples. The dataset contains synthetic and natural images. The synthetic images were rendered using giant collections of textures, objects, and environments generated by computer graphics artists. We use mixtures and gradual transitions between materials to allow the system to learn cases with smooth transitions between states (like gradually cooked food). We also render images with materials inside transparent containers to support beverage and chemistry lab use cases. We use this dataset to train a siamese net that identifies the same material in different objects, mixtures, and environments. The descriptor generated by this net can be used to identify the states of materials and their subclasses using a single image. We also present the first few-shot material recognition benchmark with images from a wide range of fields, including the state of foods and drinks, types of grounds, and many other use cases. We show that a net trained on the MatSim synthetic dataset outperforms state-of-the-art models like Clip on the benchmark and also achieves good results on other unsupervised material classification tasks.

We introduce ReALLM, a novel approach for compression and memory-efficient adaptation of pre-trained language models that encompasses most of the post-training quantization and fine-tuning methods for a budget of <4 bits. Pre-trained matrices are decomposed into a high-precision low-rank component and a vector-quantized latent representation (using an autoencoder). During the fine-tuning step, only the low-rank components are updated. Our results show that pre-trained matrices exhibit different patterns. ReALLM adapts the shape of the encoder (small/large embedding, high/low bit VQ, etc.) to each matrix. ReALLM proposes to represent each matrix with a small embedding on b bits and a neural decoder model D_phi with its weights on b_phi bits. The decompression of a matrix requires only one embedding and a single forward pass with the decoder. Our weight-only quantization algorithm yields the best results on language generation tasks (C4 and WikiText-2) for a budget of 3 bits without any training. With a budget of 2 bits, ReALLM achieves state-of-the art performance after fine-tuning on a small calibration dataset.

These handouts are designed for people who is just starting involved with the topic artificial neural networks. We show how it works a single artificial neuron (McCulloch & Pitt model), mathematically and graphically. We do explain the delta rule, a learning algorithm to find the neuron weights. We also present some examples in MATLAB/Octave. There are examples for classification task for lineal and non-lineal problems. At the end, we present an artificial neural network, a feed-forward neural network along its learning algorithm backpropagation. ----- Estos apuntes est\'an dise\~nados para personas que por primera vez se introducen en el tema de las redes neuronales artificiales. Se muestra el funcionamiento b\'asico de una neurona, matem\'aticamente y gr\'aficamente. Se explica la Regla Delta, algoritmo deaprendizaje para encontrar los pesos de una neurona. Tambi\'en se muestran ejemplos en MATLAB/Octave. Hay ejemplos para problemas de clasificaci\'on, para problemas lineales y no-lineales. En la parte final se muestra la arquitectura de red neuronal artificial conocida como backpropagation.

This work endeavors to juxtapose the efficacy of machine learning algorithms within classical and quantum computational paradigms. Particularly, by emphasizing on Support Vector Machines (SVM), we scrutinize the classification prowess of classical SVM and Quantum Support Vector Machines (QSVM) operational on quantum hardware over the Iris dataset. The methodology embraced encapsulates an extensive array of experiments orchestrated through the Qiskit library, alongside hyperparameter optimization. The findings unveil that in particular scenarios, QSVMs extend a level of accuracy that can vie with classical SVMs, albeit the execution times are presently protracted. Moreover, we underscore that augmenting quantum computational capacity and the magnitude of parallelism can markedly ameliorate the performance of quantum machine learning algorithms. This inquiry furnishes invaluable insights regarding the extant scenario and future potentiality of machine learning applications in the quantum epoch. Colab: https://t.ly/QKuz0

In this paper, we propose a new class of metric for table structure recognition (TSR) evaluation, called grid table similarity (GriTS). Unlike prior metrics, GriTS evaluates the correctness of a predicted table directly in its natural form as a matrix. To create a similarity measure between matrices, we generalize the two-dimensional largest common substructure (2D-LCS) problem, which is NP-hard, to the 2D most similar substructures (2D-MSS) problem and propose a polynomial-time heuristic for solving it. This algorithm produces both an upper and a lower bound on the true similarity between matrices. We show using evaluation on a large real-world dataset that in practice there is almost no difference between these bounds. We compare GriTS to other metrics and empirically validate that matrix similarity exhibits more desirable behavior than alternatives for TSR performance evaluation. Finally, GriTS unifies all three subtasks of cell topology recognition, cell location recognition, and cell content recognition within the same framework, which simplifies the evaluation and enables more meaningful comparisons across different types of TSR approaches. Code will be released at https://github.com/microsoft/table-transformer.

We present a system for automatic diacritization of Hebrew text. The system combines modern neural models with carefully curated declarative linguistic knowledge and comprehensive manually constructed tables and dictionaries. Besides providing state of the art diacritization accuracy, the system also supports an interface for manual editing and correction of the automatic output, and has several features which make it particularly useful for preparation of scientific editions of Hebrew texts. The system supports Modern Hebrew, Rabbinic Hebrew and Poetic Hebrew. The system is freely accessible for all use at http://nakdanpro.dicta.org.il.

Vector Symbolic Architectures (VSAs) give a way to represent a complex object as a single fixed-length vector, so that similar objects have similar vector representations. These vector representations then become easy to use for machine learning or nearest-neighbor search. We review a previously proposed VSA method, MBAT (Matrix Binding of Additive Terms), which uses multiplication by random matrices for binding related terms. However, multiplying by such matrices introduces instabilities which can harm performance. Making the random matrices be orthogonal matrices provably fixes this problem. With respect to larger scale applications, we see how to apply MBAT vector representations for any data expressed in JSON. JSON is used in numerous programming languages to express complex data, but its native format appears highly unsuited for machine learning. Expressing JSON as a fixed-length vector makes it readily usable for machine learning and nearest-neighbor search. Creating such JSON vectors also shows that a VSA needs to employ binding operations that are non-commutative. VSAs are now ready to try with full-scale practical applications, including healthcare, pharmaceuticals, and genomics. Keywords: MBAT (Matrix Binding of Additive Terms), VSA (Vector Symbolic Architecture), HDC (Hyperdimensional Computing), Distributed Representations, Binding, Orthogonal Matrices, Recurrent Connections, Machine Learning, Search, JSON, VSA Applications

Transformers can learn to perform numerical computations from examples only. I study nine problems of linear algebra, from basic matrix operations to eigenvalue decomposition and inversion, and introduce and discuss four encoding schemes to represent real numbers. On all problems, transformers trained on sets of random matrices achieve high accuracies (over 90%). The models are robust to noise, and can generalize out of their training distribution. In particular, models trained to predict Laplace-distributed eigenvalues generalize to different classes of matrices: Wigner matrices or matrices with positive eigenvalues. The reverse is not true.

We present Submatrix-wise Vector Embedding Learner (Swivel), a method for generating low-dimensional feature embeddings from a feature co-occurrence matrix. Swivel performs approximate factorization of the point-wise mutual information matrix via stochastic gradient descent. It uses a piecewise loss with special handling for unobserved co-occurrences, and thus makes use of all the information in the matrix. While this requires computation proportional to the size of the entire matrix, we make use of vectorized multiplication to process thousands of rows and columns at once to compute millions of predicted values. Furthermore, we partition the matrix into shards in order to parallelize the computation across many nodes. This approach results in more accurate embeddings than can be achieved with methods that consider only observed co-occurrences, and can scale to much larger corpora than can be handled with sampling methods.

Dense linear layers are the dominant computational bottleneck in foundation models. Identifying more efficient alternatives to dense matrices has enormous potential for building more compute-efficient models, as exemplified by the success of convolutional networks in the image domain. In this work, we systematically explore structured matrices as replacements for dense matrices. We show that different structures often require drastically different initialization scales and learning rates, which are crucial to performance, especially as models scale. Using insights from the Maximal Update Parameterization, we determine the optimal scaling for initialization and learning rates of these unconventional layers. Finally, we measure the scaling laws of different structures to compare how quickly their performance improves with compute. We propose a novel matrix family containing Monarch matrices, the Block Tensor-Train (BTT), which we show performs better than dense matrices for the same compute on multiple tasks. On CIFAR-10/100 with augmentation, BTT achieves exponentially lower training loss than dense when training MLPs and ViTs. BTT matches dense ViT-S/32 performance on ImageNet-1k with 3.8 times less compute and is more efficient than dense for training small GPT-2 language models.

Understanding how Transformer-based Language Models (LMs) learn and recall information is a key goal of the deep learning community. Recent interpretability methods project weights and hidden states obtained from the forward pass to the models' vocabularies, helping to uncover how information flows within LMs. In this work, we extend this methodology to LMs' backward pass and gradients. We first prove that a gradient matrix can be cast as a low-rank linear combination of its forward and backward passes' inputs. We then develop methods to project these gradients into vocabulary items and explore the mechanics of how new information is stored in the LMs' neurons.

Given a matrix Ain R^{ntimes d} and a vector bin R^n, we consider the regression problem with ell_infty guarantees: finding a vector x'in R^d such that |x'-x^*|_infty leq epsilon{d}cdot |Ax^*-b|_2cdot |A^dagger| where x^*=argmin_{xin R^d}|Ax-b|_2. One popular approach for solving such ell_2 regression problem is via sketching: picking a structured random matrix Sin R^{mtimes n} with mll n and SA can be quickly computed, solve the ``sketched'' regression problem argmin_{xin R^d} |SAx-Sb|_2. In this paper, we show that in order to obtain such ell_infty guarantee for ell_2 regression, one has to use sketching matrices that are dense. To the best of our knowledge, this is the first user case in which dense sketching matrices are necessary. On the algorithmic side, we prove that there exists a distribution of dense sketching matrices with m=epsilon^{-2}dlog^3(n/delta) such that solving the sketched regression problem gives the ell_infty guarantee, with probability at least 1-delta. Moreover, the matrix SA can be computed in time O(ndlog n). Our row count is nearly-optimal up to logarithmic factors, and significantly improves the result in [Price, Song and Woodruff, ICALP'17], in which a super-linear in d rows, m=Omega(epsilon^{-2}d^{1+gamma}) for gamma=Theta(frac{loglog n{log d}}) is required. We also develop a novel analytical framework for ell_infty guarantee regression that utilizes the Oblivious Coordinate-wise Embedding (OCE) property introduced in [Song and Yu, ICML'21]. Our analysis is arguably much simpler and more general than [Price, Song and Woodruff, ICALP'17], and it extends to dense sketches for tensor product of vectors.

Vision transformers have excelled in various computer vision tasks but mostly rely on rigid input sampling using a fixed-size grid of patches. This limits their applicability in real-world problems, such as in the field of robotics and UAVs, where one can utilize higher input elasticity to boost model performance and efficiency. Our paper addresses this limitation by formalizing the concept of input elasticity for vision transformers and introducing an evaluation protocol, including dedicated metrics for measuring input elasticity. Moreover, we propose modifications to the transformer architecture and training regime, which increase its elasticity. Through extensive experimentation, we spotlight opportunities and challenges associated with input sampling strategies.

We tackle the problem disentangling the latent space of an autoencoder in order to separate labelled attribute information from other characteristic information. This then allows us to change selected attributes while preserving other information. Our method, matrix subspace projection, is much simpler than previous approaches to latent space factorisation, for example not requiring multiple discriminators or a careful weighting among their loss functions. Furthermore our new model can be applied to autoencoders as a plugin, and works across diverse domains such as images or text. We demonstrate the utility of our method for attribute manipulation in autoencoders trained across varied domains, using both human evaluation and automated methods. The quality of generation of our new model (e.g. reconstruction, conditional generation) is highly competitive to a number of strong baselines.

Deep learning models like Transformers and Convolutional Neural Networks (CNNs) have revolutionized various domains, but their parameter-intensive nature hampers deployment in resource-constrained settings. In this paper, we introduce a novel concept utilizes column space and row space of weight matrices, which allows for a substantial reduction in model parameters without compromising performance. Leveraging this paradigm, we achieve parameter-efficient deep learning models.. Our approach applies to both Bottleneck and Attention layers, effectively halving the parameters while incurring only minor performance degradation. Extensive experiments conducted on the ImageNet dataset with ViT and ResNet50 demonstrate the effectiveness of our method, showcasing competitive performance when compared to traditional models. This approach not only addresses the pressing demand for parameter efficient deep learning solutions but also holds great promise for practical deployment in real-world scenarios.

We revisit the well-studied problem of approximating a matrix product, A^TB, based on small space sketches S(A) and S(B) of A in R^{n times d} and Bin R^{n times m}. We are interested in the setting where the sketches must be computed independently of each other, except for the use of a shared random seed. We prove that, when A and B are sparse, methods based on coordinated random sampling can outperform classical linear sketching approaches, like Johnson-Lindenstrauss Projection or CountSketch. For example, to obtain Frobenius norm error epsilon|A|_F|B|_F, coordinated sampling requires sketches of size O(s/epsilon^2) when A and B have at most s leq d,m non-zeros per row. In contrast, linear sketching leads to sketches of size O(d/epsilon^2) and O(m/epsilon^2) for A and B. We empirically evaluate our approach on two applications: 1) distributed linear regression in databases, a problem motivated by tasks like dataset discovery and augmentation, and 2) approximating attention matrices in transformer-based language models. In both cases, our sampling algorithms yield an order of magnitude improvement over linear sketching.

Recently, Visual Autoregressive (VAR) Models introduced a groundbreaking advancement in the field of image generation, offering a scalable approach through a coarse-to-fine "next-scale prediction" paradigm. However, the state-of-the-art algorithm of VAR models in [Tian, Jiang, Yuan, Peng and Wang, NeurIPS 2024] takes O(n^4) time, which is computationally inefficient. In this work, we analyze the computational limits and efficiency criteria of VAR Models through a fine-grained complexity lens. Our key contribution is identifying the conditions under which VAR computations can achieve sub-quadratic time complexity. Specifically, we establish a critical threshold for the norm of input matrices used in VAR attention mechanisms. Above this threshold, assuming the Strong Exponential Time Hypothesis (SETH) from fine-grained complexity theory, a sub-quartic time algorithm for VAR models is impossible. To substantiate our theoretical findings, we present efficient constructions leveraging low-rank approximations that align with the derived criteria. This work initiates the study of the computational efficiency of the VAR model from a theoretical perspective. Our technique will shed light on advancing scalable and efficient image generation in VAR frameworks.

We propose a deep learning methodology for multivariate regression that is based on pattern recognition that triggers fast learning over sensor data. We used a conversion of sensors-to-image which enables us to take advantage of Computer Vision architectures and training processes. In addition to this data preparation methodology, we explore the use of state-of-the-art architectures to generate regression outputs to predict agricultural crop continuous yield information. Finally, we compare with some of the top models reported in MLCAS2021. We found that using a straightforward training process, we were able to accomplish an MAE of 4.394, RMSE of 5.945, and R^2 of 0.861.

Neural networks have a reputation for being better at solving statistical or approximate problems than at performing calculations or working with symbolic data. In this paper, we show that they can be surprisingly good at more elaborated tasks in mathematics, such as symbolic integration and solving differential equations. We propose a syntax for representing mathematical problems, and methods for generating large datasets that can be used to train sequence-to-sequence models. We achieve results that outperform commercial Computer Algebra Systems such as Matlab or Mathematica.

Deep subspace clustering (DSC) networks based on self-expressive model learn representation matrix, often implemented in terms of fully connected network, in the embedded space. After the learning is finished, representation matrix is used by spectral clustering module to assign labels to clusters. However, such approach ignores complementary information that exist in other layers of the encoder (including the input data themselves). Herein, we apply selected linear subspace clustering algorithm to learn representation matrices from representations learned by all layers of encoder network including the input data. Afterward, we learn a multilayer graph that in a multi-view like manner integrates information from graph Laplacians of all used layers. That improves further performance of selected DSC network. Furthermore, we also provide formulation of our approach to cluster out-of-sample/test data points. We validate proposed approach on four well-known datasets with two DSC networks as baseline models. In almost all the cases, proposed approach achieved statistically significant improvement in three performance metrics. MATLAB code of proposed algorithm is posted on https://github.com/lovro-sinda/MLG-DSC.

This paper presents a new dataset of Peter the Great's manuscripts and describes a segmentation procedure that converts initial images of documents into the lines. The new dataset may be useful for researchers to train handwriting text recognition models as a benchmark for comparing different models. It consists of 9 694 images and text files corresponding to lines in historical documents. The open machine learning competition Digital Peter was held based on the considered dataset. The baseline solution for this competition as well as more advanced methods on handwritten text recognition are described in the article. Full dataset and all code are publicly available.

Personalized text-to-image generation has attracted unprecedented attention in the recent few years due to its unique capability of generating highly-personalized images via using the input concept dataset and novel textual prompt. However, previous methods solely focus on the performance of the reconstruction task, degrading its ability to combine with different textual prompt. Besides, optimizing in the high-dimensional embedding space usually leads to unnecessary time-consuming training process and slow convergence. To address these issues, we propose an efficient method to explore the target embedding in a textual subspace, drawing inspiration from the self-expressiveness property. Additionally, we propose an efficient selection strategy for determining the basis vectors of the textual subspace. The experimental evaluations demonstrate that the learned embedding can not only faithfully reconstruct input image, but also significantly improves its alignment with novel input textual prompt. Furthermore, we observe that optimizing in the textual subspace leads to an significant improvement of the robustness to the initial word, relaxing the constraint that requires users to input the most relevant initial word. Our method opens the door to more efficient representation learning for personalized text-to-image generation.

We provide a construction for categorical representation learning and introduce the foundations of "categorifier". The central theme in representation learning is the idea of everything to vector. Every object in a dataset S can be represented as a vector in R^n by an encoding map E: Obj(S)toR^n. More importantly, every morphism can be represented as a matrix E: Hom(S)toR^{n}_{n}. The encoding map E is generally modeled by a deep neural network. The goal of representation learning is to design appropriate tasks on the dataset to train the encoding map (assuming that an encoding is optimal if it universally optimizes the performance on various tasks). However, the latter is still a set-theoretic approach. The goal of the current article is to promote the representation learning to a new level via a category-theoretic approach. As a proof of concept, we provide an example of a text translator equipped with our technology, showing that our categorical learning model outperforms the current deep learning models by 17 times. The content of the current article is part of the recent US patent proposal (patent application number: 63110906).

Transformers are a widespread and successful model architecture, particularly in Natural Language Processing (NLP) and Computer Vision (CV). The essential innovation of this architecture is the Attention Mechanism, which solves the problem of extracting relevant context information from long sequences in NLP and realistic scenes in CV. A classical neural network component, a Multi-Layer Perceptron (MLP), complements the attention mechanism. Its necessity is frequently justified by its capability of modeling nonlinear relationships. However, the attention mechanism itself is nonlinear through its internal use of similarity measures. A possible hypothesis is that this nonlinearity is sufficient for modeling typical application problems. As the MLPs usually contain the most trainable parameters of the whole model, their omission would substantially reduce the parameter set size. Further components can also be reorganized to reduce the number of parameters. Under some conditions, query and key matrices can be collapsed into a single matrix of the same size. The same is true about value and projection matrices, which can also be omitted without eliminating the substance of the attention mechanism. Initially, the similarity measure was defined asymmetrically, with peculiar properties such as that a token is possibly dissimilar to itself. A possible symmetric definition requires only half of the parameters. We have laid the groundwork by testing widespread CV benchmarks: MNIST and CIFAR-10. The tests have shown that simplified transformer architectures (a) without MLP, (b) with collapsed matrices, and (c) symmetric similarity matrices exhibit similar performance as the original architecture, saving up to 90% of parameters without hurting the classification performance.

We introduce meta-factorization, a theory that describes matrix decompositions as solutions of linear matrix equations: the projector and the reconstruction equation. Meta-factorization reconstructs known factorizations, reveals their internal structures, and allows for introducing modifications, as illustrated with SVD, QR, and UTV factorizations. The prospect of meta-factorization also provides insights into computational aspects of generalized matrix inverses and randomized linear algebra algorithms. The relations between the Moore-Penrose pseudoinverse, generalized Nystr\"{o}m method, and the CUR decomposition are revealed here as an illustration. Finally, meta-factorization offers hints on the structure of new factorizations and provides the potential of creating them.

We study the topmost weight matrix of neural network language models. We show that this matrix constitutes a valid word embedding. When training language models, we recommend tying the input embedding and this output embedding. We analyze the resulting update rules and show that the tied embedding evolves in a more similar way to the output embedding than to the input embedding in the untied model. We also offer a new method of regularizing the output embedding. Our methods lead to a significant reduction in perplexity, as we are able to show on a variety of neural network language models. Finally, we show that weight tying can reduce the size of neural translation models to less than half of their original size without harming their performance.

We consider a deep matrix factorization model of covariance matrices trained with the Bures-Wasserstein distance. While recent works have made important advances in the study of the optimization problem for overparametrized low-rank matrix approximation, much emphasis has been placed on discriminative settings and the square loss. In contrast, our model considers another interesting type of loss and connects with the generative setting. We characterize the critical points and minimizers of the Bures-Wasserstein distance over the space of rank-bounded matrices. For low-rank matrices the Hessian of this loss can theoretically blow up, which creates challenges to analyze convergence of optimizaton methods. We establish convergence results for gradient flow using a smooth perturbative version of the loss and convergence results for finite step size gradient descent under certain assumptions on the initial weights.

Developing Intelligent Systems involves artificial intelligence approaches including artificial neural networks. Here, we present a tutorial of Deep Neural Networks (DNNs), and some insights about the origin of the term "deep"; references to deep learning are also given. Restricted Boltzmann Machines, which are the core of DNNs, are discussed in detail. An example of a simple two-layer network, performing unsupervised learning for unlabeled data, is shown. Deep Belief Networks (DBNs), which are used to build networks with more than two layers, are also described. Moreover, examples for supervised learning with DNNs performing simple prediction and classification tasks, are presented and explained. This tutorial includes two intelligent pattern recognition applications: hand- written digits (benchmark known as MNIST) and speech recognition.

In recent years, Transformers have become the de-facto architecture for sequence modeling on text and a variety of multi-dimensional data, such as images and video. However, the use of self-attention layers in a Transformer incurs prohibitive compute and memory complexity that scales quadratically w.r.t. the sequence length. A recent architecture, Mamba, based on state space models has been shown to achieve comparable performance for modeling text sequences, while scaling linearly with the sequence length. In this work, we present Mamba-ND, a generalized design extending the Mamba architecture to arbitrary multi-dimensional data. Our design alternatively unravels the input data across different dimensions following row-major orderings. We provide a systematic comparison of Mamba-ND with several other alternatives, based on prior multi-dimensional extensions such as Bi-directional LSTMs and S4ND. Empirically, we show that Mamba-ND demonstrates performance competitive with the state-of-the-art on a variety of multi-dimensional benchmarks, including ImageNet-1K classification, HMDB-51 action recognition, and ERA5 weather forecasting.

Pre-trained models have become the preferred backbone due to the expansion of model parameters, with techniques like Parameter-Efficient Fine-Tuning (PEFTs) typically fixing the parameters of these models. However, pre-trained models may not always be optimal, especially when there are discrepancies between training tasks and target tasks, potentially resulting in negative transfer. To address this, we introduce KIND, which performs Knowledge INtegration and Diversion in diffusion models. KIND first integrates knowledge by decomposing parameter matrices of models using U, Sigma, and V matrices, formally inspired by singular value decomposition (SVD). Then it explicitly partitions the components of these matrices into learngenes and tailors to condense common and class-specific knowledge, respectively, through a class gate. In this way, KIND redefines traditional pre-training methods by adjusting training objectives from maximizing model performance on current tasks to condensing transferable common knowledge, leveraging the Learngene framework. We conduct experiments on ImageNet-1K and compare KIND with PEFT and other learngene methods. Results indicate that KIND achieves state-of-the-art performance compared to other PEFT and learngene methods. Specifically, the images generated by KIND achieves more than 6.54 and 1.07 decrease in FID and sFID on DiT-L/2, utilizing only 45.4M trainable parameters and saving at least 35.4G FLOPs in computational cost.

Adapting pre-trained foundation models for various downstream tasks has been prevalent in artificial intelligence. Due to the vast number of tasks and high costs, adjusting all parameters becomes unfeasible. To mitigate this, several fine-tuning techniques have been developed to update the pre-trained model weights in a more resource-efficient manner, such as through low-rank adjustments. Yet, almost all of these methods focus on linear weights, neglecting the intricacies of parameter spaces in higher dimensions like 4D. Alternatively, some methods can be adapted for high-dimensional parameter space by compressing changes in the original space into two dimensions and then employing low-rank matrix decomposition. However, these approaches destructs the structural integrity of the involved high-dimensional spaces. To tackle the diversity of dimensional spaces across different foundation models and provide a more precise representation of the changes within these spaces, this paper introduces a generalized parameter-efficient fine-tuning framework, FLoRA, designed for various dimensional parameter space. Specifically, utilizing Tucker decomposition, FLoRA asserts that changes in each dimensional parameter space are based on a low-rank core space which maintains the consistent topological structure with the original space. It then models the changes through this core space alongside corresponding weights to reconstruct alterations in the original space. FLoRA effectively preserves the structural integrity of the change of original N-dimensional parameter space, meanwhile decomposes it via low-rank tensor decomposition. Extensive experiments on computer vision, natural language processing and multi-modal tasks validate FLoRA's effectiveness. Codes are available at https://github.com/SJTU-DeepVisionLab/FLoRA.

Practitioners prune neural networks for efficiency gains and generalization improvements, but few scrutinize the factors determining the prunability of a neural network the maximum fraction of weights that pruning can remove without compromising the model's test accuracy. In this work, we study the properties of input data that may contribute to the prunability of a neural network. For high dimensional input data such as images, text, and audio, the manifold hypothesis suggests that these high dimensional inputs approximately lie on or near a significantly lower dimensional manifold. Prior work demonstrates that the underlying low dimensional structure of the input data may affect the sample efficiency of learning. In this paper, we investigate whether the low dimensional structure of the input data affects the prunability of a neural network.

Given only a few observed entries from a low-rank matrix X, matrix completion is the problem of imputing the missing entries, and it formalizes a wide range of real-world settings that involve estimating missing data. However, when there are too few observed entries to complete the matrix, what other aspects of the underlying matrix can be reliably recovered? We study one such problem setting, that of "one-sided" matrix completion, where our goal is to recover the right singular vectors of X, even in the regime where recovering the left singular vectors is impossible, which arises when there are more rows than columns and very few observations. We propose a natural algorithm that involves imputing the missing values of the matrix X^TX and show that even with only two observations per row in X, we can provably recover X^TX as long as we have at least Omega(r^2 d log d) rows, where r is the rank and d is the number of columns. We evaluate our algorithm on one-sided recovery of synthetic data and low-coverage genome sequencing. In these settings, our algorithm substantially outperforms standard matrix completion and a variety of direct factorization methods.

Click-through rate (CTR) prediction, which aims to predict the probability of a user clicking on an ad or an item, is critical to many online applications such as online advertising and recommender systems. The problem is very challenging since (1) the input features (e.g., the user id, user age, item id, item category) are usually sparse and high-dimensional, and (2) an effective prediction relies on high-order combinatorial features (a.k.a. cross features), which are very time-consuming to hand-craft by domain experts and are impossible to be enumerated. Therefore, there have been efforts in finding low-dimensional representations of the sparse and high-dimensional raw features and their meaningful combinations. In this paper, we propose an effective and efficient method called the AutoInt to automatically learn the high-order feature interactions of input features. Our proposed algorithm is very general, which can be applied to both numerical and categorical input features. Specifically, we map both the numerical and categorical features into the same low-dimensional space. Afterwards, a multi-head self-attentive neural network with residual connections is proposed to explicitly model the feature interactions in the low-dimensional space. With different layers of the multi-head self-attentive neural networks, different orders of feature combinations of input features can be modeled. The whole model can be efficiently fit on large-scale raw data in an end-to-end fashion. Experimental results on four real-world datasets show that our proposed approach not only outperforms existing state-of-the-art approaches for prediction but also offers good explainability. Code is available at: https://github.com/DeepGraphLearning/RecommenderSystems.

Sparse Autoencoders (SAEs) have been proposed as an unsupervised approach to learn a decomposition of a model's latent space. This enables useful applications such as steering - influencing the output of a model towards a desired concept - without requiring labeled data. Current methods identify SAE features to steer by analyzing the input tokens that activate them. However, recent work has highlighted that activations alone do not fully describe the effect of a feature on the model's output. In this work, we draw a distinction between two types of features: input features, which mainly capture patterns in the model's input, and output features, which have a human-understandable effect on the model's output. We propose input and output scores to characterize and locate these types of features, and show that high values for both scores rarely co-occur in the same features. These findings have practical implications: after filtering out features with low output scores, we obtain 2-3x improvements when steering with SAEs, making them competitive with supervised methods.

The training process of neural networks usually optimize weights and bias parameters of linear transformations, while nonlinear activation functions are pre-specified and fixed. This work develops a systematic approach to constructing matrix activation functions whose entries are generalized from ReLU. The activation is based on matrix-vector multiplications using only scalar multiplications and comparisons. The proposed activation functions depend on parameters that are trained along with the weights and bias vectors. Neural networks based on this approach are simple and efficient and are shown to be robust in numerical experiments.

Large language models are now tuned to align with the goals of their creators, namely to be "helpful and harmless." These models should respond helpfully to user questions, but refuse to answer requests that could cause harm. However, adversarial users can construct inputs which circumvent attempts at alignment. In this work, we study to what extent these models remain aligned, even when interacting with an adversarial user who constructs worst-case inputs (adversarial examples). These inputs are designed to cause the model to emit harmful content that would otherwise be prohibited. We show that existing NLP-based optimization attacks are insufficiently powerful to reliably attack aligned text models: even when current NLP-based attacks fail, we can find adversarial inputs with brute force. As a result, the failure of current attacks should not be seen as proof that aligned text models remain aligned under adversarial inputs. However the recent trend in large-scale ML models is multimodal models that allow users to provide images that influence the text that is generated. We show these models can be easily attacked, i.e., induced to perform arbitrary un-aligned behavior through adversarial perturbation of the input image. We conjecture that improved NLP attacks may demonstrate this same level of adversarial control over text-only models.

We study the estimation of a planted signal hidden in a recently introduced nested matrix-tensor model, which is an extension of the classical spiked rank-one tensor model, motivated by multi-view clustering. Prior work has theoretically examined the performance of a tensor-based approach, which relies on finding a best rank-one approximation, a problem known to be computationally hard. A tractable alternative approach consists in computing instead the best rank-one (matrix) approximation of an unfolding of the observed tensor data, but its performance was hitherto unknown. We quantify here the performance gap between these two approaches, in particular by deriving the precise algorithmic threshold of the unfolding approach and demonstrating that it exhibits a BBP-type transition behavior. This work is therefore in line with recent contributions which deepen our understanding of why tensor-based methods surpass matrix-based methods in handling structured tensor data.

The ability of an architecture to realize permutations is quite fundamental. For example, Large Language Models need to be able to correctly copy (and perhaps rearrange) parts of the input prompt into the output. Classical universal approximation theorems guarantee the existence of parameter configurations that solve this task but offer no insights into whether gradient-based algorithms can find them. In this paper, we address this gap by focusing on two-layer fully connected feed-forward neural networks and the task of learning permutations on nonzero binary inputs. We show that in the infinite width Neural Tangent Kernel (NTK) regime, an ensemble of such networks independently trained with gradient descent on only the k standard basis vectors out of 2^k - 1 possible inputs successfully learns any fixed permutation of length k with arbitrarily high probability. By analyzing the exact training dynamics, we prove that the network's output converges to a Gaussian process whose mean captures the ground truth permutation via sign-based features. We then demonstrate how averaging these runs (an "ensemble" method) and applying a simple rounding step yields an arbitrarily accurate prediction on any possible input unseen during training. Notably, the number of models needed to achieve exact learning with high probability (which we refer to as ensemble complexity) exhibits a linearithmic dependence on the input size k for a single test input and a quadratic dependence when considering all test inputs simultaneously.

We consider in this work quantities that can be obtained as limits of powers of parametrized matrices, for instance the inverse matrix or the logarithm of the determinant. Under the assumption of affine dependence in the parameters, we use the Empirical Interpolation Method (EIM) to derive an approximation for powers of these matrices, from which we derive a nonintrusive approximation for the aforementioned limits. We derive upper bounds of the error made by the obtained formula. Finally, numerical comparisons with classical intrusive and nonintrusive approximation techniques are provided: in the considered test-cases, our algorithm performs well compared to the nonintrusive ones.

Linear Recurrent Neural Networks (linear RNNs) have emerged as competitive alternatives to Transformers for sequence modeling, offering efficient training and linear-time inference. However, existing architectures face a fundamental trade-off between expressivity and efficiency, dictated by the structure of their state-transition matrices. Diagonal matrices, used in models such as Mamba, GLA, or mLSTM, yield fast runtime but have limited expressivity. To address this, recent architectures such as DeltaNet and RWKV-7 adopted a diagonal plus rank-1 structure, which allows simultaneous token and channel mixing, improving associative recall and, as recently shown, state-tracking when allowing negative eigenvalues in the state-transition matrices. Building on the interpretation of DeltaNet's recurrence as performing one step of online gradient descent per token on an associative recall loss, we introduce DeltaProduct, which instead takes multiple (n_h) steps per token. This naturally leads to diagonal plus rank-n_h state-transition matrices, formed as products of n_h generalized Householder transformations, providing a tunable mechanism to balance expressivity and efficiency. We provide a detailed theoretical characterization of the state-tracking capability of DeltaProduct in finite precision, showing how it improves by increasing n_h. Our extensive experiments demonstrate that DeltaProduct outperforms DeltaNet in both state-tracking and language modeling, while also showing significantly improved length extrapolation capabilities.

This paper thoroughly analyses the effect of different input representations on polyphonic multi-instrument music transcription. We use our own GPU based spectrogram extraction tool, nnAudio, to investigate the influence of using a linear-frequency spectrogram, log-frequency spectrogram, Mel spectrogram, and constant-Q transform (CQT). Our results show that a 8.33% increase in transcription accuracy and a 9.39% reduction in error can be obtained by choosing the appropriate input representation (log-frequency spectrogram with STFT window length 4,096 and 2,048 frequency bins in the spectrogram) without changing the neural network design (single layer fully connected). Our experiments also show that Mel spectrogram is a compact representation for which we can reduce the number of frequency bins to only 512 while still keeping a relatively high music transcription accuracy.

Projection maintenance is one of the core data structure tasks. Efficient data structures for projection maintenance have led to recent breakthroughs in many convex programming algorithms. In this work, we further extend this framework to the Kronecker product structure. Given a constraint matrix {sf A} and a positive semi-definite matrix Win R^{ntimes n} with a sparse eigenbasis, we consider the task of maintaining the projection in the form of {sf B}^top({sf B}{sf B}^top)^{-1}{sf B}, where {sf B}={sf A}(Wotimes I) or {sf B}={sf A}(W^{1/2}otimes W^{1/2}). At each iteration, the weight matrix W receives a low rank change and we receive a new vector h. The goal is to maintain the projection matrix and answer the query {sf B}^top({sf B}{sf B}^top)^{-1}{sf B}h with good approximation guarantees. We design a fast dynamic data structure for this task and it is robust against an adaptive adversary. Following the beautiful and pioneering work of [Beimel, Kaplan, Mansour, Nissim, Saranurak and Stemmer, STOC'22], we use tools from differential privacy to reduce the randomness required by the data structure and further improve the running time.

Over the past few years, neural networks have re-emerged as powerful machine-learning models, yielding state-of-the-art results in fields such as image recognition and speech processing. More recently, neural network models started to be applied also to textual natural language signals, again with very promising results. This tutorial surveys neural network models from the perspective of natural language processing research, in an attempt to bring natural-language researchers up to speed with the neural techniques. The tutorial covers input encoding for natural language tasks, feed-forward networks, convolutional networks, recurrent networks and recursive networks, as well as the computation graph abstraction for automatic gradient computation.

We explore a class of adversarial attacks targeting the activations of language models. By manipulating a relatively small subset of model activations, a, we demonstrate the ability to control the exact prediction of a significant number (in some cases up to 1000) of subsequent tokens t. We empirically verify a scaling law where the maximum number of target tokens t_max predicted depends linearly on the number of tokens a whose activations the attacker controls as t_max = kappa a. We find that the number of bits of control in the input space needed to control a single bit in the output space (what we call attack resistance chi) is remarkably constant between approx 16 and approx 25 over 2 orders of magnitude of model sizes for different language models. Compared to attacks on tokens, attacks on activations are predictably much stronger, however, we identify a surprising regularity where one bit of input steered either via activations or via tokens is able to exert control over a similar amount of output bits. This gives support for the hypothesis that adversarial attacks are a consequence of dimensionality mismatch between the input and output spaces. A practical implication of the ease of attacking language model activations instead of tokens is for multi-modal and selected retrieval models, where additional data sources are added as activations directly, sidestepping the tokenized input. This opens up a new, broad attack surface. By using language models as a controllable test-bed to study adversarial attacks, we were able to experiment with input-output dimensions that are inaccessible in computer vision, especially where the output dimension dominates.

Large-scale foundation models have demonstrated exceptional performance in language and vision tasks. However, the numerous dense matrix-vector operations involved in these large networks pose significant computational challenges during inference. To address these challenges, we introduce the Block-Level Adaptive STructured (BLAST) matrix, designed to learn and leverage efficient structures prevalent in the weight matrices of linear layers within deep learning models. Compared to existing structured matrices, the BLAST matrix offers substantial flexibility, as it can represent various types of structures that are either learned from data or computed from pre-existing weight matrices. We demonstrate the efficiency of using the BLAST matrix for compressing both language and vision tasks, showing that (i) for medium-sized models such as ViT and GPT-2, training with BLAST weights boosts performance while reducing complexity by 70% and 40%, respectively; and (ii) for large foundation models such as Llama-7B and DiT-XL, the BLAST matrix achieves a 2x compression while exhibiting the lowest performance degradation among all tested structured matrices. Our code is available at https://github.com/changwoolee/BLAST.

This paper explores the scenarios under which an attacker can claim that 'Noise and access to the softmax layer of the model is all you need' to steal the weights of a convolutional neural network whose architecture is already known. We were able to achieve 96% test accuracy using the stolen MNIST model and 82% accuracy using the stolen KMNIST model learned using only i.i.d. Bernoulli noise inputs. We posit that this theft-susceptibility of the weights is indicative of the complexity of the dataset and propose a new metric that captures the same. The goal of this dissemination is to not just showcase how far knowing the architecture can take you in terms of model stealing, but to also draw attention to this rather idiosyncratic weight learnability aspects of CNNs spurred by i.i.d. noise input. We also disseminate some initial results obtained with using the Ising probability distribution in lieu of the i.i.d. Bernoulli distribution.

Latent factor models are the driving forces of the state-of-the-art recommender systems, with an important insight of vectorizing raw input features into dense embeddings. The dimensions of different feature embeddings are often set to a same value empirically, which limits the predictive performance of latent factor models. Existing works have proposed heuristic or reinforcement learning-based methods to search for mixed feature embedding dimensions. For efficiency concern, these methods typically choose embedding dimensions from a restricted set of candidate dimensions. However, this restriction will hurt the flexibility of dimension selection, leading to suboptimal performance of search results. In this paper, we propose Differentiable Neural Input Search (DNIS), a method that searches for mixed feature embedding dimensions in a more flexible space through continuous relaxation and differentiable optimization. The key idea is to introduce a soft selection layer that controls the significance of each embedding dimension, and optimize this layer according to model's validation performance. DNIS is model-agnostic and thus can be seamlessly incorporated with existing latent factor models for recommendation. We conduct experiments with various architectures of latent factor models on three public real-world datasets for rating prediction, Click-Through-Rate (CTR) prediction, and top-k item recommendation. The results demonstrate that our method achieves the best predictive performance compared with existing neural input search approaches with fewer embedding parameters and less time cost.

Model merging integrates the weights of multiple task-specific models into a single multi-task model. Despite recent interest in the problem, a significant performance gap between the combined and single-task models remains. In this paper, we investigate the key characteristics of task matrices -- weight update matrices applied to a pre-trained model -- that enable effective merging. We show that alignment between singular components of task-specific and merged matrices strongly correlates with performance improvement over the pre-trained model. Based on this, we propose an isotropic merging framework that flattens the singular value spectrum of task matrices, enhances alignment, and reduces the performance gap. Additionally, we incorporate both common and task-specific subspaces to further improve alignment and performance. Our proposed approach achieves state-of-the-art performance across multiple scenarios, including various sets of tasks and model scales. This work advances the understanding of model merging dynamics, offering an effective methodology to merge models without requiring additional training. Code is available at https://github.com/danielm1405/iso-merging .

Approximating nonlinear differential equations using a neural network provides a robust and efficient tool for various scientific computing tasks, including real-time predictions, inverse problems, optimal controls, and surrogate modeling. Previous works have focused on embedding dynamical systems into networks through two approaches: learning a single solution operator (i.e., the mapping from input parametrized functions to solutions) or learning the governing system of equations (i.e., the constitutive model relative to the state variables). Both of these approaches yield different representations for the same underlying data or function. Additionally, observing that families of differential equations often share key characteristics, we seek one network representation across a wide range of equations. Our method, called Predicting Operators and Symbolic Expressions (PROSE), learns maps from multimodal inputs to multimodal outputs, capable of generating both numerical predictions and mathematical equations. By using a transformer structure and a feature fusion approach, our network can simultaneously embed sets of solution operators for various parametric differential equations using a single trained network. Detailed experiments demonstrate that the network benefits from its multimodal nature, resulting in improved prediction accuracy and better generalization. The network is shown to be able to handle noise in the data and errors in the symbolic representation, including noisy numerical values, model misspecification, and erroneous addition or deletion of terms. PROSE provides a new neural network framework for differential equations which allows for more flexibility and generality in learning operators and governing equations from data.

Generative models are a class of machine learning models that aim to learn the underlying probability distribution of data. Unlike discriminative models, generative models focus on capturing the data's inherent structure, allowing them to generate new samples that resemble the original data. To fully exploit the potential of modeling probability distributions using quantum physics, a quantum-inspired generative model known as the Born machines have shown great advancements in learning classical and quantum data over matrix product state(MPS) framework. The Born machines support tractable log-likelihood, autoregressive and mask sampling, and have shown outstanding performance in various unsupervised learning tasks. However, much of the current research has been centered on improving the expressive power of MPS, predominantly embedding each token directly by a corresponding tensor index. In this study, we generalize the embedding method into trainable quantum measurement operators that can be simultaneously honed with MPS. Our study indicated that combined with trainable embedding, Born machines can exhibit better performance and learn deeper correlations from the dataset.

With 17,000 pairs of Sicilian-English translated sentences, Arba Sicula developed the first neural machine translator for the Sicilian language. Using small subword vocabularies, we trained small Transformer models with high dropout parameters and achieved BLEU scores in the upper 20s. Then we supplemented our dataset with backtranslation and multilingual translation and pushed our scores into the mid 30s. We also attribute our success to incorporating theoretical information in our dataset. Prior to training, we biased the subword vocabulary towards the desinences one finds in a textbook. And we included textbook exercises in our dataset.

We train a bilingual Arabic-Hebrew language model using a transliterated version of Arabic texts in Hebrew, to ensure both languages are represented in the same script. Given the morphological, structural similarities, and the extensive number of cognates shared among Arabic and Hebrew, we assess the performance of a language model that employs a unified script for both languages, on machine translation which requires cross-lingual knowledge. The results are promising: our model outperforms a contrasting model which keeps the Arabic texts in the Arabic script, demonstrating the efficacy of the transliteration step. Despite being trained on a dataset approximately 60% smaller than that of other existing language models, our model appears to deliver comparable performance in machine translation across both translation directions.

The utilization of Large Language Models (LLMs) for the construction of AI systems has garnered significant attention across diverse fields. The extension of LLMs to the domain of fashion holds substantial commercial potential but also inherent challenges due to the intricate semantic interactions in fashion-related generation. To address this issue, we developed a hierarchical AI system called Fashion Matrix dedicated to editing photos by just talking. This system facilitates diverse prompt-driven tasks, encompassing garment or accessory replacement, recoloring, addition, and removal. Specifically, Fashion Matrix employs LLM as its foundational support and engages in iterative interactions with users. It employs a range of Semantic Segmentation Models (e.g., Grounded-SAM, MattingAnything, etc.) to delineate the specific editing masks based on user instructions. Subsequently, Visual Foundation Models (e.g., Stable Diffusion, ControlNet, etc.) are leveraged to generate edited images from text prompts and masks, thereby facilitating the automation of fashion editing processes. Experiments demonstrate the outstanding ability of Fashion Matrix to explores the collaborative potential of functionally diverse pre-trained models in the domain of fashion editing.

Deep neural networks have achieved remarkable accomplishments in practice. The success of these networks hinges on effective initialization methods, which are vital for ensuring stable and rapid convergence during training. Recently, initialization methods that maintain identity transition within layers have shown good efficiency in network training. These techniques (e.g., Fixup) set specific weights to zero to achieve identity control. However, settings of remaining weight (e.g., Fixup uses random values to initialize non-zero weights) will affect the inductive bias that is achieved only by a zero weight, which may be harmful to training. Addressing this concern, we introduce fully identical initialization (IDInit), a novel method that preserves identity in both the main and sub-stem layers of residual networks. IDInit employs a padded identity-like matrix to overcome rank constraints in non-square weight matrices. Furthermore, we show the convergence problem of an identity matrix can be solved by stochastic gradient descent. Additionally, we enhance the universality of IDInit by processing higher-order weights and addressing dead neuron problems. IDInit is a straightforward yet effective initialization method, with improved convergence, stability, and performance across various settings, including large-scale datasets and deep models.

Input space reconstruction is an attractive representation learning paradigm. Despite interpretability of the reconstruction and generation, we identify a misalignment between learning by reconstruction, and learning for perception. We show that the former allocates a model's capacity towards a subspace of the data explaining the observed variance--a subspace with uninformative features for the latter. For example, the supervised TinyImagenet task with images projected onto the top subspace explaining 90\% of the pixel variance can be solved with 45\% test accuracy. Using the bottom subspace instead, accounting for only 20\% of the pixel variance, reaches 55\% test accuracy. The features for perception being learned last explains the need for long training time, e.g., with Masked Autoencoders. Learning by denoising is a popular strategy to alleviate that misalignment. We prove that while some noise strategies such as masking are indeed beneficial, others such as additive Gaussian noise are not. Yet, even in the case of masking, we find that the benefits vary as a function of the mask's shape, ratio, and the considered dataset. While tuning the noise strategy without knowledge of the perception task seems challenging, we provide first clues on how to detect if a noise strategy is never beneficial regardless of the perception task.

Parameter-efficient fine-tuning optimizes large, pre-trained foundation models by updating a subset of parameters; in this class, Low-Rank Adaptation (LoRA) is particularly effective. Inspired by an effort to investigate the different roles of LoRA matrices during fine-tuning, this paper characterizes and leverages unexpected asymmetry in the importance of low-rank adapter matrices. Specifically, when updating the parameter matrices of a neural network by adding a product BA, we observe that the B and A matrices have distinct functions: A extracts features from the input, while B uses these features to create the desired output. Based on this observation, we demonstrate that fine-tuning B is inherently more effective than fine-tuning A, and that a random untrained A should perform nearly as well as a fine-tuned one. Using an information-theoretic lens, we also bound the generalization of low-rank adapters, showing that the parameter savings of exclusively training B improves the bound. We support our conclusions with experiments on RoBERTa, BART-Large, LLaMA-2, and ViTs.

In recent years, multiple notions of algorithmic fairness have arisen. One such notion is individual fairness (IF), which requires that individuals who are similar receive similar treatment. In parallel, matrix estimation (ME) has emerged as a natural paradigm for handling noisy data with missing values. In this work, we connect the two concepts. We show that pre-processing data using ME can improve an algorithm's IF without sacrificing performance. Specifically, we show that using a popular ME method known as singular value thresholding (SVT) to pre-process the data provides a strong IF guarantee under appropriate conditions. We then show that, under analogous conditions, SVT pre-processing also yields estimates that are consistent and approximately minimax optimal. As such, the ME pre-processing step does not, under the stated conditions, increase the prediction error of the base algorithm, i.e., does not impose a fairness-performance trade-off. We verify these results on synthetic and real data.

The learnable, linear neural network layers between tensor power spaces of R^{n} that are equivariant to the orthogonal group, O(n), the special orthogonal group, SO(n), and the symplectic group, Sp(n), were characterised in arXiv:2212.08630. We present an algorithm for multiplying a vector by any weight matrix for each of these groups, using category theoretic constructions to implement the procedure. We achieve a significant reduction in computational cost compared with a naive implementation by making use of Kronecker product matrices to perform the multiplication. We show that our approach extends to the symmetric group, S_n, recovering the algorithm of arXiv:2303.06208 in the process.

Interpretability researchers have attempted to understand MLP neurons of language models based on both the contexts in which they activate and their output weight vectors. They have paid little attention to a complementary aspect: the interactions between input and output. For example, when neurons detect a direction in the input, they might add much the same direction to the residual stream ("enrichment neurons") or reduce its presence ("depletion neurons"). We address this aspect by examining the cosine similarity between input and output weights of a neuron. We apply our method to 12 models and find that enrichment neurons dominate in early-middle layers whereas later layers tend more towards depletion. To explain this finding, we argue that enrichment neurons are largely responsible for enriching concept representations, one of the first steps of factual recall. Our input-output perspective is a complement to activation-dependent analyses and to approaches that treat input and output separately.

This work builds upon previous efforts in online incremental learning, namely the Incremental Gaussian Mixture Network (IGMN). The IGMN is capable of learning from data streams in a single-pass by improving its model after analyzing each data point and discarding it thereafter. Nevertheless, it suffers from the scalability point-of-view, due to its asymptotic time complexity of Obigl(NKD^3bigr) for N data points, K Gaussian components and D dimensions, rendering it inadequate for high-dimensional data. In this paper, we manage to reduce this complexity to Obigl(NKD^2bigr) by deriving formulas for working directly with precision matrices instead of covariance matrices. The final result is a much faster and scalable algorithm which can be applied to high dimensional tasks. This is confirmed by applying the modified algorithm to high-dimensional classification datasets.

In this paper, we have shown a method of improving the quality of neural machine translation by translating/transliterating name entities as a preprocessing step. Through experiments we have shown the performance gain of our system. For evaluation we considered three types of name entities viz person names, location names and organization names. The system was able to correctly translate mostly all the name entities. For person names the accuracy was 99.86%, for location names the accuracy was 99.63% and for organization names the accuracy was 99.05%. Overall, the accuracy of the system was 99.52%

Modelling compositionality has been a longstanding area of research in the field of vector space semantics. The categorical approach to compositionality maps grammar onto vector spaces in a principled way, but comes under fire for requiring the formation of very high-dimensional matrices and tensors, and therefore being computationally infeasible. In this paper I show how a linear simplification of recursive neural tensor network models can be mapped directly onto the categorical approach, giving a way of computing the required matrices and tensors. This mapping suggests a number of lines of research for both categorical compositional vector space models of meaning and for recursive neural network models of compositionality.

One critical prerequisite for faithful text-to-image generation is the accurate understanding of text inputs. Existing methods leverage the text encoder of the CLIP model to represent input prompts. However, the pre-trained CLIP model can merely encode English with a maximum token length of 77. Moreover, the model capacity of the text encoder from CLIP is relatively limited compared to Large Language Models (LLMs), which offer multilingual input, accommodate longer context, and achieve superior text representation. In this paper, we investigate LLMs as the text encoder to improve the language understanding in text-to-image generation. Unfortunately, training text-to-image generative model with LLMs from scratch demands significant computational resources and data. To this end, we introduce a three-stage training pipeline that effectively and efficiently integrates the existing text-to-image model with LLMs. Specifically, we propose a lightweight adapter that enables fast training of the text-to-image model using the textual representations from LLMs. Extensive experiments demonstrate that our model supports not only multilingual but also longer input context with superior image generation quality.

Dictionary learning is a branch of signal processing and machine learning that aims at finding a frame (called dictionary) in which some training data admits a sparse representation. The sparser the representation, the better the dictionary. The resulting dictionary is in general a dense matrix, and its manipulation can be computationally costly both at the learning stage and later in the usage of this dictionary, for tasks such as sparse coding. Dictionary learning is thus limited to relatively small-scale problems. In this paper, inspired by usual fast transforms, we consider a general dictionary structure that allows cheaper manipulation, and propose an algorithm to learn such dictionaries --and their fast implementation-- over training data. The approach is demonstrated experimentally with the factorization of the Hadamard matrix and with synthetic dictionary learning experiments.

Modeling long range dependencies in sequential data is a fundamental step towards attaining human-level performance in many modalities such as text, vision, audio and video. While attention-based models are a popular and effective choice in modeling short-range interactions, their performance on tasks requiring long range reasoning has been largely inadequate. In an exciting result, Gu et al. (ICLR 2022) proposed the Structured State Space (S4) architecture delivering large gains over state-of-the-art models on several long-range tasks across various modalities. The core proposition of S4 is the parameterization of state matrices via a diagonal plus low rank structure, allowing efficient computation. In this work, we show that one can match the performance of S4 even without the low rank correction and thus assuming the state matrices to be diagonal. Our Diagonal State Space (DSS) model matches the performance of S4 on Long Range Arena tasks, speech classification on Speech Commands dataset, while being conceptually simpler and straightforward to implement.

Linear time-invariant state space models (SSM) are a classical model from engineering and statistics, that have recently been shown to be very promising in machine learning through the Structured State Space sequence model (S4). A core component of S4 involves initializing the SSM state matrix to a particular matrix called a HiPPO matrix, which was empirically important for S4's ability to handle long sequences. However, the specific matrix that S4 uses was actually derived in previous work for a particular time-varying dynamical system, and the use of this matrix as a time-invariant SSM had no known mathematical interpretation. Consequently, the theoretical mechanism by which S4 models long-range dependencies actually remains unexplained. We derive a more general and intuitive formulation of the HiPPO framework, which provides a simple mathematical interpretation of S4 as a decomposition onto exponentially-warped Legendre polynomials, explaining its ability to capture long dependencies. Our generalization introduces a theoretically rich class of SSMs that also lets us derive more intuitive S4 variants for other bases such as the Fourier basis, and explains other aspects of training S4, such as how to initialize the important timescale parameter. These insights improve S4's performance to 86% on the Long Range Arena benchmark, with 96% on the most difficult Path-X task.

In this work, we explore the use of a novel neural network architecture, the Kolmogorov-Arnold Networks (KANs) as feature extractors for sensor-based (specifically IMU) Human Activity Recognition (HAR). Where conventional networks perform a parameterized weighted sum of the inputs at each node and then feed the result into a statically defined nonlinearity, KANs perform non-linear computations represented by B-SPLINES on the edges leading to each node and then just sum up the inputs at the node. Instead of learning weights, the system learns the spline parameters. In the original work, such networks have been shown to be able to more efficiently and exactly learn sophisticated real valued functions e.g. in regression or PDE solution. We hypothesize that such an ability is also advantageous for computing low-level features for IMU-based HAR. To this end, we have implemented KAN as the feature extraction architecture for IMU-based human activity recognition tasks, including four architecture variations. We present an initial performance investigation of the KAN feature extractor on four public HAR datasets. It shows that the KAN-based feature extractor outperforms CNN-based extractors on all datasets while being more parameter efficient.

We present a Neural Network based Handwritten Text Recognition (HTR) model architecture that can be trained to recognize full pages of handwritten or printed text without image segmentation. Being based on Image to Sequence architecture, it can extract text present in an image and then sequence it correctly without imposing any constraints regarding orientation, layout and size of text and non-text. Further, it can also be trained to generate auxiliary markup related to formatting, layout and content. We use character level vocabulary, thereby enabling language and terminology of any subject. The model achieves a new state-of-art in paragraph level recognition on the IAM dataset. When evaluated on scans of real world handwritten free form test answers - beset with curved and slanted lines, drawings, tables, math, chemistry and other symbols - it performs better than all commercially available HTR cloud APIs. It is deployed in production as part of a commercial web application.

When dealing with electro or magnetoencephalography records, many supervised prediction tasks are solved by working with covariance matrices to summarize the signals. Learning with these matrices requires using Riemanian geometry to account for their structure. In this paper, we propose a new method to deal with distributions of covariance matrices and demonstrate its computational efficiency on M/EEG multivariate time series. More specifically, we define a Sliced-Wasserstein distance between measures of symmetric positive definite matrices that comes with strong theoretical guarantees. Then, we take advantage of its properties and kernel methods to apply this distance to brain-age prediction from MEG data and compare it to state-of-the-art algorithms based on Riemannian geometry. Finally, we show that it is an efficient surrogate to the Wasserstein distance in domain adaptation for Brain Computer Interface applications.

We propose SMMF (Square-Matricized Momentum Factorization), a memory-efficient optimizer that reduces the memory requirement of the widely used adaptive learning rate optimizers, such as Adam, by up to 96%. SMMF enables flexible and efficient factorization of an arbitrary rank (shape) of the first and second momentum tensors during optimization, based on the proposed square-matricization and one-time single matrix factorization. From this, it becomes effectively applicable to any rank (shape) of momentum tensors, i.e., bias, matrix, and any rank-d tensors, prevalent in various deep model architectures, such as CNNs (high rank) and Transformers (low rank), in contrast to existing memory-efficient optimizers that applies only to a particular (rank-2) momentum tensor, e.g., linear layers. We conduct a regret bound analysis of SMMF, which shows that it converges similarly to non-memory-efficient adaptive learning rate optimizers, such as AdamNC, providing a theoretical basis for its competitive optimization capability. In our experiment, SMMF takes up to 96% less memory compared to state-of-the-art memory efficient optimizers, e.g., Adafactor, CAME, and SM3, while achieving comparable model performance on various CNN and Transformer tasks.

Training deep neural networks on images represented as grids of pixels has brought to light an interesting phenomenon known as adversarial examples. Inspired by how humans reconstruct abstract concepts, we attempt to codify the input bitmap image into a set of compact, interpretable elements to avoid being fooled by the adversarial structures. We take the first step in this direction by experimenting with image vectorization as an input transformation step to map the adversarial examples back into the natural manifold of MNIST handwritten digits. We compare our method vs. state-of-the-art input transformations and further discuss the trade-offs between a hand-designed and a learned transformation defense.

In this study, we propose a simple method for fault-tolerant Strassen-like matrix multiplications. The proposed method is based on using two distinct Strassen-like algorithms instead of replicating a given one. We have realized that using two different algorithms, new check relations arise resulting in more local computations. These local computations are found using computer aided search. To improve performance, special parity (extra) sub-matrix multiplications (PSMMs) are generated (two of them) at the expense of increasing communication/computation cost of the system. Our preliminary results demonstrate that the proposed method outperforms a Strassen-like algorithm with two copies and secures a very close performance to three copy version using only 2 PSMMs, reducing the total number of compute nodes by around 24\% i.e., from 21 to 16.

We propose spatially-adaptive normalization, a simple but effective layer for synthesizing photorealistic images given an input semantic layout. Previous methods directly feed the semantic layout as input to the deep network, which is then processed through stacks of convolution, normalization, and nonlinearity layers. We show that this is suboptimal as the normalization layers tend to ``wash away'' semantic information. To address the issue, we propose using the input layout for modulating the activations in normalization layers through a spatially-adaptive, learned transformation. Experiments on several challenging datasets demonstrate the advantage of the proposed method over existing approaches, regarding both visual fidelity and alignment with input layouts. Finally, our model allows user control over both semantic and style. Code is available at https://github.com/NVlabs/SPADE .

A capsule is a group of neurons whose activity vector represents the instantiation parameters of a specific type of entity such as an object or an object part. We use the length of the activity vector to represent the probability that the entity exists and its orientation to represent the instantiation parameters. Active capsules at one level make predictions, via transformation matrices, for the instantiation parameters of higher-level capsules. When multiple predictions agree, a higher level capsule becomes active. We show that a discrimininatively trained, multi-layer capsule system achieves state-of-the-art performance on MNIST and is considerably better than a convolutional net at recognizing highly overlapping digits. To achieve these results we use an iterative routing-by-agreement mechanism: A lower-level capsule prefers to send its output to higher level capsules whose activity vectors have a big scalar product with the prediction coming from the lower-level capsule.

Previous work on augmenting large multimodal models (LMMs) for text-to-image (T2I) generation has focused on enriching the input space of in-context learning (ICL). This includes providing a few demonstrations and optimizing image descriptions to be more detailed and logical. However, as demand for more complex and flexible image descriptions grows, enhancing comprehension of input text within the ICL paradigm remains a critical yet underexplored area. In this work, we extend this line of research by constructing parallel multilingual prompts aimed at harnessing the multilingual capabilities of LMMs. More specifically, we translate the input text into several languages and provide the models with both the original text and the translations. Experiments on two LMMs across 3 benchmarks show that our method, PMT2I, achieves superior performance in general, compositional, and fine-grained assessments, especially in human preference alignment. Additionally, with its advantage of generating more diverse images, PMT2I significantly outperforms baseline prompts when incorporated with reranking methods. Our code and parallel multilingual data can be found at https://github.com/takagi97/PMT2I.

This short note is written for rapid communication of long context training and to share the idea of how to train it with low memory usage. In the note, we generalize the attention algorithm and neural network of Generative Pre-Trained Transformers and reinterpret it in Path integral formalism. First, the role of the transformer is understood as the time evolution of the token state and second, it is suggested that the all key-token states in the same time as the query-token can attend to the attention with the query token states. As a result of the repetitive time evolution, it is discussed that the token states in the past sequence meats the token states in the present sequence so that the attention between separated sequences becomes possible for maintaining infinite contextual information just by using low memory for limited size of sequence. For the experiment, the 12 input token window size was taken and one GPU with 24GB memory was used for the pre-training. It was confirmed that more than 150 length context is preserved. The sampling result of the training, the code and the other details will be included in the revised version of this note later.

We present Recurrent Fitting (ReFit), a neural network architecture for single-image, parametric 3D human reconstruction. ReFit learns a feedback-update loop that mirrors the strategy of solving an inverse problem through optimization. At each iterative step, it reprojects keypoints from the human model to feature maps to query feedback, and uses a recurrent-based updater to adjust the model to fit the image better. Because ReFit encodes strong knowledge of the inverse problem, it is faster to train than previous regression models. At the same time, ReFit improves state-of-the-art performance on standard benchmarks. Moreover, ReFit applies to other optimization settings, such as multi-view fitting and single-view shape fitting. Project website: https://yufu-wang.github.io/refit_humans/

Fast approximations to matrix multiplication have the potential to dramatically reduce the cost of neural network inference. Recent work on approximate matrix multiplication proposed to replace costly multiplications with table-lookups by fitting a fast hash function from training data. In this work, we propose improvements to this previous work, targeted to the deep learning inference setting, where one has access to both training data and fixed (already learned) model weight matrices. We further propose a fine-tuning procedure for accelerating entire neural networks while minimizing loss in accuracy. Finally, we analyze the proposed method on a simple image classification task. While we show improvements to prior work, overall classification accuracy remains substantially diminished compared to exact matrix multiplication. Our work, despite this negative result, points the way towards future efforts to accelerate inner products with fast nonlinear hashing methods.

Neural networks efficiently encode learned information within their parameters. Consequently, many tasks can be unified by treating neural networks themselves as input data. When doing so, recent studies demonstrated the importance of accounting for the symmetries and geometry of parameter spaces. However, those works developed architectures tailored to specific networks such as MLPs and CNNs without normalization layers, and generalizing such architectures to other types of networks can be challenging. In this work, we overcome these challenges by building new metanetworks - neural networks that take weights from other neural networks as input. Put simply, we carefully build graphs representing the input neural networks and process the graphs using graph neural networks. Our approach, Graph Metanetworks (GMNs), generalizes to neural architectures where competing methods struggle, such as multi-head attention layers, normalization layers, convolutional layers, ResNet blocks, and group-equivariant linear layers. We prove that GMNs are expressive and equivariant to parameter permutation symmetries that leave the input neural network functions unchanged. We validate the effectiveness of our method on several metanetwork tasks over diverse neural network architectures.

The image-to-image translation abilities of generative learning models have recently made significant progress in the estimation of complex (steered) mappings between image distributions. While appearance based tasks like image in-painting or style transfer have been studied at length, we propose to investigate the potential of generative models in the context of physical simulations. Providing a dataset of 300k image-pairs and baseline evaluations for three different physical simulation tasks, we propose a benchmark to investigate the following research questions: i) are generative models able to learn complex physical relations from input-output image pairs? ii) what speedups can be achieved by replacing differential equation based simulations? While baseline evaluations of different current models show the potential for high speedups (ii), these results also show strong limitations toward the physical correctness (i). This underlines the need for new methods to enforce physical correctness. Data, baseline models and evaluation code http://www.physics-gen.org.

In order to make the foundation model more efficient and effective, our idea is combining sequence transformation and state transformation. First, we prove the availability of rotary position embedding in the state space duality algorithm, which reduces the perplexity of the hybrid quadratic causal self-attention and state space duality by more than 4%, to ensure that the combining sequence transformation unifies position encoding. Second, we propose dynamic mask attention, which maintains 100% accuracy in the more challenging multi-query associative recall task, improving by more than 150% compared to quadratic causal self-attention and state space duality, to ensure that the combining sequence transformation selectively filters relevant information. Third, we design cross domain mixture of experts, which makes the computational speed of expert retrieval with more than 1024 experts 8 to 10 times faster than the mixture of experts, to ensure that the combining state transformation quickly retrieval mixture. Finally, we summarize these matrix algorithms that can form the foundation model: Wonderful Matrices, which can be a competitor to popular model architectures.

We present ClothesNet: a large-scale dataset of 3D clothes objects with information-rich annotations. Our dataset consists of around 4400 models covering 11 categories annotated with clothes features, boundary lines, and keypoints. ClothesNet can be used to facilitate a variety of computer vision and robot interaction tasks. Using our dataset, we establish benchmark tasks for clothes perception, including classification, boundary line segmentation, and keypoint detection, and develop simulated clothes environments for robotic interaction tasks, including rearranging, folding, hanging, and dressing. We also demonstrate the efficacy of our ClothesNet in real-world experiments. Supplemental materials and dataset are available on our project webpage.

AdamW has long been the dominant optimizer in language model pretraining, despite numerous claims that alternative optimizers offer 1.4 to 2x speedup. We posit that two methodological shortcomings have obscured fair comparisons and hindered practical adoption: (i) unequal hyperparameter tuning and (ii) limited or misleading evaluation setups. To address these two issues, we conduct a systematic study of ten deep learning optimizers across four model scales (0.1B-1.2B parameters) and data-to-model ratios (1-8x the Chinchilla optimum). We find that fair and informative comparisons require rigorous hyperparameter tuning and evaluations across a range of model scales and data-to-model ratios, performed at the end of training. First, optimal hyperparameters for one optimizer may be suboptimal for another, making blind hyperparameter transfer unfair. Second, the actual speedup of many proposed optimizers over well-tuned baselines is lower than claimed and decreases with model size to only 1.1x for 1.2B parameter models. Thirdly, comparing intermediate checkpoints before reaching the target training budgets can be misleading, as rankings between two optimizers can flip during training due to learning rate decay. Through our thorough investigation, we find that all the fastest optimizers such as Muon and Soap, use matrices as preconditioners -- multiplying gradients with matrices rather than entry-wise scalars. However, the speedup of matrix-based optimizers is inversely proportional to model scale, decreasing from 1.4x over AdamW for 0.1B parameter models to merely 1.1x for 1.2B parameter models.

We identify incremental learning dynamics in transformers, where the difference between trained and initial weights progressively increases in rank. We rigorously prove this occurs under the simplifying assumptions of diagonal weight matrices and small initialization. Our experiments support the theory and also show that phenomenon can occur in practice without the simplifying assumptions.

Much of machine learning research focuses on producing models which perform well on benchmark tasks, in turn improving our understanding of the challenges associated with those tasks. From the perspective of ML researchers, the content of the task itself is largely irrelevant, and thus there have increasingly been calls for benchmark tasks to more heavily focus on problems which are of social or cultural relevance. In this work, we introduce Kuzushiji-MNIST, a dataset which focuses on Kuzushiji (cursive Japanese), as well as two larger, more challenging datasets, Kuzushiji-49 and Kuzushiji-Kanji. Through these datasets, we wish to engage the machine learning community into the world of classical Japanese literature. Dataset available at https://github.com/rois-codh/kmnist

California is a global leader in agricultural production, contributing 12.5% of the United States total output and ranking as the fifth-largest food and cotton supplier in the world. Despite the availability of extensive historical yield data from the USDA National Agricultural Statistics Service, accurate and timely crop yield forecasting remains a challenge due to the complex interplay of environmental, climatic, and soil-related factors. In this study, we introduce a comprehensive crop yield benchmark dataset covering over 70 crops across all California counties from 2008 to 2022. The benchmark integrates diverse data sources, including Landsat satellite imagery, daily climate records, monthly evapotranspiration, and high-resolution soil properties. To effectively learn from these heterogeneous inputs, we develop a multi-modal deep learning model tailored for county-level, crop-specific yield forecasting. The model employs stratified feature extraction and a timeseries encoder to capture spatial and temporal dynamics during the growing season. Static inputs such as soil characteristics and crop identity inform long-term variability. Our approach achieves an overall R2 score of 0.76 across all crops of unseen test dataset, highlighting strong predictive performance across California diverse agricultural regions. This benchmark and modeling framework offer a valuable foundation for advancing agricultural forecasting, climate adaptation, and precision farming. The full dataset and codebase are publicly available at our GitHub repository.

Neural machine translation (NMT) methods developed for natural language processing have been shown to be highly successful in automating translation from one natural language to another. Recently, these NMT methods have been adapted to the generation of program code. In NMT for code generation, the task is to generate output source code that satisfies constraints expressed in the input. In the literature, a variety of different input scenarios have been explored, including generating code based on natural language description, lower-level representations such as binary or assembly (neural decompilation), partial representations of source code (code completion and repair), and source code in another language (code translation). In this paper we survey the NMT for code generation literature, cataloging the variety of methods that have been explored according to input and output representations, model architectures, optimization techniques used, data sets, and evaluation methods. We discuss the limitations of existing methods and future research directions

In this reproduction study, we revisit recent claims that self-attention implements kernel principal component analysis (KPCA) (Teo et al., 2024), positing that (i) value vectors V capture the eigenvectors of the Gram matrix of the keys, and (ii) that self-attention projects queries onto the principal component axes of the key matrix K in a feature space. Our analysis reveals three critical inconsistencies: (1) No alignment exists between learned self-attention value vectors and what is proposed in the KPCA perspective, with average similarity metrics (optimal cosine similarity leq 0.32, linear CKA (Centered Kernel Alignment) leq 0.11, kernel CKA leq 0.32) indicating negligible correspondence; (2) Reported decreases in reconstruction loss J_proj, arguably justifying the claim that the self-attention minimizes the projection error of KPCA, are misinterpreted, as the quantities involved differ by orders of magnitude (sim!10^3); (3) Gram matrix eigenvalue statistics, introduced to justify that V captures the eigenvector of the gram matrix, are irreproducible without undocumented implementation-specific adjustments. Across 10 transformer architectures, we conclude that the KPCA interpretation of self-attention lacks empirical support.

We present time vectors, a simple tool to customize language models to new time periods. Time vectors are created by finetuning a language model on data from a single time (e.g., a year or month), and then subtracting the weights of the original pretrained model. This vector specifies a direction in weight space that, as our experiments show, improves performance on text from that time period. Time vectors specialized to adjacent time periods appear to be positioned closer together in a manifold. Using this structure, we interpolate between time vectors to induce new models that perform better on intervening and future time periods, without any additional training. We demonstrate the consistency of our findings across different tasks, domains, model sizes, and time scales. Our results suggest that time is encoded in the weight space of finetuned models.

Large language models have led to state-of-the-art accuracies across a range of tasks. However,training large language model needs massive computing resource, as more and more open source pre-training models are available, it is worthy to study how to take full advantage of available model. We find a method to save training time and resource cost by changing the small well-trained model to large model. We initialize a larger target model from a smaller source model by copy weight values from source model and padding with zeros or small initialization values on it to make the source and target model have approximate outputs, which is valid due to block matrix multiplication and residual connection in transformer structure. We test the target model on several data sets and find it is still comparable with the source model. When we continue training the target model, the training loss can start from a smaller value.

We propose a novel interpretation technique to explain the behavior of structured output models, which learn mappings between an input vector to a set of output variables simultaneously. Because of the complex relationship between the computational path of output variables in structured models, a feature can affect the value of output through other ones. We focus on one of the outputs as the target and try to find the most important features utilized by the structured model to decide on the target in each locality of the input space. In this paper, we assume an arbitrary structured output model is available as a black box and argue how considering the correlations between output variables can improve the explanation performance. The goal is to train a function as an interpreter for the target output variable over the input space. We introduce an energy-based training process for the interpreter function, which effectively considers the structural information incorporated into the model to be explained. The effectiveness of the proposed method is confirmed using a variety of simulated and real data sets.

We present DictaBERT, a new state-of-the-art pre-trained BERT model for modern Hebrew, outperforming existing models on most benchmarks. Additionally, we release two fine-tuned versions of the model, designed to perform two specific foundational tasks in the analysis of Hebrew texts: prefix segmentation and morphological tagging. These fine-tuned models allow any developer to perform prefix segmentation and morphological tagging of a Hebrew sentence with a single call to a HuggingFace model, without the need to integrate any additional libraries or code. In this paper we describe the details of the training as well and the results on the different benchmarks. We release the models to the community, along with sample code demonstrating their use. We release these models as part of our goal to help further research and development in Hebrew NLP.

In this paper, we present a new comparative study on automatic essay scoring (AES). The current state-of-the-art natural language processing (NLP) neural network architectures are used in this work to achieve above human-level accuracy on the publicly available Kaggle AES dataset. We compare two powerful language models, BERT and XLNet, and describe all the layers and network architectures in these models. We elucidate the network architectures of BERT and XLNet using clear notation and diagrams and explain the advantages of transformer architectures over traditional recurrent neural network architectures. Linear algebra notation is used to clarify the functions of transformers and attention mechanisms. We compare the results with more traditional methods, such as bag of words (BOW) and long short term memory (LSTM) networks.

Second-order optimizers, maintaining a matrix termed a preconditioner, are superior to first-order optimizers in both theory and practice. The states forming the preconditioner and its inverse root restrict the maximum size of models trained by second-order optimizers. To address this, compressing 32-bit optimizer states to lower bitwidths has shown promise in reducing memory usage. However, current approaches only pertain to first-order optimizers. In this paper, we propose the first 4-bit second-order optimizers, exemplified by 4-bit Shampoo, maintaining performance similar to that of 32-bit ones. We show that quantizing the eigenvector matrix of the preconditioner in 4-bit Shampoo is remarkably better than quantizing the preconditioner itself both theoretically and experimentally. By rectifying the orthogonality of the quantized eigenvector matrix, we enhance the approximation of the preconditioner's eigenvector matrix, which also benefits the computation of its inverse 4-th root. Besides, we find that linear square quantization slightly outperforms dynamic tree quantization when quantizing second-order optimizer states. Evaluation on various networks for image classification demonstrates that our 4-bit Shampoo achieves comparable test accuracy to its 32-bit counterpart while being more memory-efficient. The source code will be made available.

The lottery ticket hypothesis (LTH) has increased attention to pruning neural networks at initialization. We study this problem in the linear setting. We show that finding a sparse mask at initialization is equivalent to the sketching problem introduced for efficient matrix multiplication. This gives us tools to analyze the LTH problem and gain insights into it. Specifically, using the mask found at initialization, we bound the approximation error of the pruned linear model at the end of training. We theoretically justify previous empirical evidence that the search for sparse networks may be data independent. By using the sketching perspective, we suggest a generic improvement to existing algorithms for pruning at initialization, which we show to be beneficial in the data-independent case.

Various visual foundation models have distinct strengths and weaknesses, both of which can be improved through heterogeneous multi-teacher knowledge distillation without labels, termed "agglomerative models." We build upon this body of work by studying the effect of the teachers' activation statistics, particularly the impact of the loss function on the resulting student model quality. We explore a standard toolkit of statistical normalization techniques to better align the different distributions and assess their effects. Further, we examine the impact on downstream teacher-matching metrics, which motivates the use of Hadamard matrices. With these matrices, we demonstrate useful properties, showing how they can be used for isotropic standardization, where each dimension of a multivariate distribution is standardized using the same scale. We call this technique "PHI Standardization" (PHI-S) and empirically demonstrate that it produces the best student model across the suite of methods studied.

Shampoo, a second-order optimization algorithm which uses a Kronecker product preconditioner, has recently garnered increasing attention from the machine learning community. The preconditioner used by Shampoo can be viewed either as an approximation of the Gauss--Newton component of the Hessian or the covariance matrix of the gradients maintained by Adagrad. We provide an explicit and novel connection between the optimal Kronecker product approximation of these matrices and the approximation made by Shampoo. Our connection highlights a subtle but common misconception about Shampoo's approximation. In particular, the square of the approximation used by the Shampoo optimizer is equivalent to a single step of the power iteration algorithm for computing the aforementioned optimal Kronecker product approximation. Across a variety of datasets and architectures we empirically demonstrate that this is close to the optimal Kronecker product approximation. Additionally, for the Hessian approximation viewpoint, we empirically study the impact of various practical tricks to make Shampoo more computationally efficient (such as using the batch gradient and the empirical Fisher) on the quality of Hessian approximation.

This paper investigates efficient deep neural networks (DNNs) to replace dense unstructured weight matrices with structured ones that possess desired properties. The challenge arises because the optimal weight matrix structure in popular neural network models is obscure in most cases and may vary from layer to layer even in the same network. Prior structured matrices proposed for efficient DNNs were mostly hand-crafted without a generalized framework to systematically learn them. To address this issue, we propose a generalized and differentiable framework to learn efficient structures of weight matrices by gradient descent. We first define a new class of structured matrices that covers a wide range of structured matrices in the literature by adjusting the structural parameters. Then, the frequency-domain differentiable parameterization scheme based on the Gaussian-Dirichlet kernel is adopted to learn the structural parameters by proximal gradient descent. On the image and language tasks, our method learns efficient DNNs with structured matrices, achieving lower complexity and/or higher performance than prior approaches that employ low-rank, block-sparse, or block-low-rank matrices.

Textual label names (descriptions) are typically semantically rich in many natural language understanding (NLU) tasks. In this paper, we incorporate the prompting methodology, which is widely used to enrich model input, into the label side for the first time. Specifically, we propose a Mask Matching method, which equips an input with a prompt and its label with another, and then makes predictions by matching their mask representations. We evaluate our method extensively on 8 NLU tasks with 14 datasets. The experimental results show that Mask Matching significantly outperforms its counterparts of fine-tuning and conventional prompt-tuning, setting up state-of-the-art performances in several datasets. Mask Matching is particularly good at handling NLU tasks with large label counts and informative label names. As pioneering efforts that investigate the label-side prompt, we also discuss open issues for future study.

Linear Recurrent Neural Networks (LRNNs) such as Mamba, RWKV, GLA, mLSTM, and DeltaNet have emerged as efficient alternatives to Transformers for long sequences. However, both Transformers and LRNNs struggle to perform state-tracking, which may impair performance in tasks such as code evaluation. In one forward pass, current architectures are unable to solve even parity, the simplest state-tracking task, which non-linear RNNs can handle effectively. Recently, Sarrof et al. (2024) demonstrated that the failure of LRNNs like Mamba to solve parity stems from restricting the value range of their diagonal state-transition matrices to [0, 1] and that incorporating negative values can resolve this issue. We extend this result to non-diagonal LRNNs such as DeltaNet. We prove that finite precision LRNNs with state-transition matrices having only positive eigenvalues cannot solve parity, while non-triangular matrices are needed to count modulo 3. Notably, we also prove that LRNNs can learn any regular language when their state-transition matrices are products of identity minus vector outer product matrices, each with eigenvalues in the range [-1, 1]. Our experiments confirm that extending the eigenvalue range of Mamba and DeltaNet to include negative values not only enables them to solve parity but consistently improves their performance on state-tracking tasks. We also show that state-tracking enabled LRNNs can be pretrained stably and efficiently at scale (1.3B parameters), achieving competitive performance on language modeling and showing promise on code and math tasks.

To fully understand the behavior of a large language model (LLM) requires our understanding of its input space. If this input space differs from our assumption, our understanding of and conclusions about the LLM is likely flawed, regardless of its architecture. Here, we elucidate the structure of the token embeddings, the input domain for LLMs, both empirically and theoretically. We present a generalized and statistically testable model where the neighborhood of each token splits into well-defined signal and noise dimensions. This model is based on a generalization of a manifold called a fiber bundle, so we denote our hypothesis test as the ``fiber bundle null.'' Failing to reject the null is uninformative, but rejecting it at a specific token indicates that token has a statistically significant local structure, and so is of interest to us. By running our test over several open-source LLMs, each with unique token embeddings, we find that the null is frequently rejected, and so the token subspace is provably not a fiber bundle and hence also not a manifold. As a consequence of our findings, when an LLM is presented with two semantically equivalent prompts, and if one prompt contains a token implicated by our test, that prompt will likely exhibit more output variability proportional to the local signal dimension of the token.

We report the effects of replacing the scaled dot-product (within softmax) attention with the negative-log of Euclidean distance. This form of attention simplifies to inverse distance weighting interpolation. Used in simple one hidden layer networks and trained with vanilla cross-entropy loss on classification problems, it tends to produce a key matrix containing prototypes and a value matrix with corresponding logits. We also show that the resulting interpretable networks can be augmented with manually-constructed prototypes to perform low-impact handling of special cases.

We consider the problem of linear estimation, and establish an extension of the Gauss-Markov theorem, in which the bias operator is allowed to be non-zero but bounded with respect to a matrix norm of Schatten type. We derive simple and explicit formulas for the optimal estimator in the cases of Nuclear and Spectral norms (with the Frobenius case recovering ridge regression). Additionally, we analytically derive the generalization error in multiple random matrix ensembles, and compare with Ridge regression. Finally, we conduct an extensive simulation study, in which we show that the cross-validated Nuclear and Spectral regressors can outperform Ridge in several circumstances.

We demonstrate that it is feasible to diacritize Hebrew script without any human-curated resources other than plain diacritized text. We present NAKDIMON, a two-layer character level LSTM, that performs on par with much more complicated curation-dependent systems, across a diverse array of modern Hebrew sources.

Deep neural networks are a promising tool for Audio Event Classification. In contrast to other data like natural images, there are many sensible and non-obvious representations for audio data, which could serve as input to these models. Due to their black-box nature, the effect of different input representations has so far mostly been investigated by measuring classification performance. In this work, we leverage eXplainable AI (XAI), to understand the underlying classification strategies of models trained on different input representations. Specifically, we compare two model architectures with regard to relevant input features used for Audio Event Detection: one directly processes the signal as the raw waveform, and the other takes in its time-frequency spectrogram representation. We show how relevance heatmaps obtained via "Siren"{Layer-wise Relevance Propagation} uncover representation-dependent decision strategies. With these insights, we can make a well-informed decision about the best input representation in terms of robustness and representativity and confirm that the model's classification strategies align with human requirements.

Vectors are universal mathematical objects that can represent text, images, speech, or a mix of these data modalities. That happens regardless of whether data is represented by hand-crafted features or learnt embeddings. Collect a large enough quantity of such vectors and the question of retrieval becomes urgently relevant: Finding vectors that are more similar to a query vector. This monograph is concerned with the question above and covers fundamental concepts along with advanced data structures and algorithms for vector retrieval. In doing so, it recaps this fascinating topic and lowers barriers of entry into this rich area of research.

As deep neural networks include a high number of parameters and operations, it can be a challenge to implement these models on devices with limited computational resources. Despite the development of novel pruning methods toward resource-efficient models, it has become evident that these models are not capable of handling "imbalanced" and "limited number of data points". We proposed a novel filter pruning method by considering the input and output of filters along with the values of the filters that deal with imbalanced datasets better than others. Our pruning method considers the fact that all information about the importance of a filter may not be reflected in the value of the filter. Instead, it is reflected in the changes made to the data after the filter is applied to it. In this work, three methods are compared with the same training conditions except for the ranking values of each method, and 14 methods are compared from other papers. We demonstrated that our model performed significantly better than other methods for imbalanced medical datasets. For example, when we removed up to 58% of FLOPs for the IDRID dataset and up to 45% for the ISIC dataset, our model was able to yield an equivalent (or even superior) result to the baseline model. To evaluate FLOP and parameter reduction using our model in real-world settings, we built a smartphone app, where we demonstrated a reduction of up to 79% in memory usage and 72% in prediction time. All codes and parameters for training different models are available at https://github.com/mohofar/Beta-Rank

This paper introduces a novel training methodology that enables a small Transformer model to generalize the addition of two-digit numbers to numbers with unseen lengths of digits. The proposed approach employs an autoregressive generation technique, processing from right to left, which mimics a common manual method for adding large numbers. To the best of my knowledge, this methodology has not been previously explored in the literature. All results are reproducible, and the corresponding R code is available at: https://github.com/AGPatriota/ALGA-R/.

This paper studies the problem of training a two-layer ReLU network for binary classification using gradient flow with small initialization. We consider a training dataset with well-separated input vectors: Any pair of input data with the same label are positively correlated, and any pair with different labels are negatively correlated. Our analysis shows that, during the early phase of training, neurons in the first layer try to align with either the positive data or the negative data, depending on its corresponding weight on the second layer. A careful analysis of the neurons' directional dynamics allows us to provide an O(log n{mu}) upper bound on the time it takes for all neurons to achieve good alignment with the input data, where n is the number of data points and mu measures how well the data are separated. After the early alignment phase, the loss converges to zero at a O(1{t}) rate, and the weight matrix on the first layer is approximately low-rank. Numerical experiments on the MNIST dataset illustrate our theoretical findings.

While GPT has become the de-facto method for text generation tasks, its application to pinyin input method remains unexplored. In this work, we make the first exploration to leverage Chinese GPT for pinyin input method. We find that a frozen GPT achieves state-of-the-art performance on perfect pinyin. However, the performance drops dramatically when the input includes abbreviated pinyin. A reason is that an abbreviated pinyin can be mapped to many perfect pinyin, which links to even larger number of Chinese characters. We mitigate this issue with two strategies, including enriching the context with pinyin and optimizing the training process to help distinguish homophones. To further facilitate the evaluation of pinyin input method, we create a dataset consisting of 270K instances from 15 domains. Results show that our approach improves performance on abbreviated pinyin across all domains. Model analysis demonstrates that both strategies contribute to the performance boost.

Via thousands of papers in Explainable AI (XAI), attention maps vaswani2017attention and feature attribution maps bansal2020sam have been established as a common means for explaining the input features that are important to AI's decisions. It is an interesting but unexplored question whether allowing users to edit the importance scores of input features at test time would improve the human-AI team's accuracy on downstream tasks. In this paper, we address this question by taking CHM-Corr, a state-of-the-art, ante-hoc explanation method taesiri2022visual that first predicts patch-wise correspondences between the input and the training-set images, and then uses them to make classification decisions. We build an interactive interface on top of CHM-Corr, enabling users to directly edit the initial feature attribution map provided by CHM-Corr. Via our CHM-Corr++ interface, users gain insights into if, when, and how the model changes its outputs, enhancing understanding beyond static explanations. Our user study with 18 machine learning researchers who performed sim1,400 decisions shows that our interactive approach does not improve user accuracy on CUB-200 bird image classification over static explanations. This challenges the belief that interactivity inherently boosts XAI effectiveness~sokol2020one,sun2022exploring,shen2024towards,singh2024rethinking,mindlin2024beyond,lakkaraju2022rethinking,cheng2019explaining,liu2021understanding and raises needs for future research. Our work contributes to the field by open-sourcing an interactive tool for manipulating model attention, and it lays the groundwork for future research to enable effective human-AI interaction in computer vision. We release code and data on https://anonymous.4open.science/r/CHMCorrPlusPlus/{github}. Our interface are available http://137.184.82.109:7080/{here}.

We reformulate the problem of supervised learning as learning to learn with two nested loops (i.e. learning problems). The inner loop learns on each individual instance with self-supervision before final prediction. The outer loop learns the self-supervised task used by the inner loop, such that its final prediction improves. Our inner loop turns out to be equivalent to linear attention when the inner-loop learner is only a linear model, and to self-attention when it is a kernel estimator. For practical comparison with linear or self-attention layers, we replace each of them in a transformer with an inner loop, so our outer loop is equivalent to training the architecture. When each inner-loop learner is a neural network, our approach vastly outperforms transformers with linear attention on ImageNet from 224 x 224 raw pixels in both accuracy and FLOPs, while (regular) transformers cannot run.

Automated math word problem solvers based on neural networks have successfully managed to obtain 70-80\% accuracy in solving arithmetic word problems. However, it has been shown that these solvers may rely on superficial patterns to obtain their equations. In order to determine what information math word problem solvers use to generate solutions, we remove parts of the input and measure the model's performance on the perturbed dataset. Our results show that the model is not sensitive to the removal of many words from the input and can still manage to find a correct answer when given a nonsense question. This indicates that automatic solvers do not follow the semantic logic of math word problems, and may be overfitting to the presence of specific words.

We present TURJUMAN, a neural toolkit for translating from 20 languages into Modern Standard Arabic (MSA). TURJUMAN exploits the recently-introduced text-to-text Transformer AraT5 model, endowing it with a powerful ability to decode into Arabic. The toolkit offers the possibility of employing a number of diverse decoding methods, making it suited for acquiring paraphrases for the MSA translations as an added value. To train TURJUMAN, we sample from publicly available parallel data employing a simple semantic similarity method to ensure data quality. This allows us to prepare and release AraOPUS-20, a new machine translation benchmark. We publicly release our translation toolkit (TURJUMAN) as well as our benchmark dataset (AraOPUS-20).

Portfolio optimization has been a broad and intense area of interest for quantitative and statistical finance researchers and financial analysts. It is a challenging task to design a portfolio of stocks to arrive at the optimized values of the return and risk. This paper presents an algorithmic approach for designing optimum risk and eigen portfolios for five thematic sectors of the NSE of India. The prices of the stocks are extracted from the web from Jan 1, 2016, to Dec 31, 2020. Optimum risk and eigen portfolios for each sector are designed based on ten critical stocks from the sector. An LSTM model is designed for predicting future stock prices. Seven months after the portfolios were formed, on Aug 3, 2021, the actual returns of the portfolios are compared with the LSTM-predicted returns. The predicted and the actual returns indicate a very high-level accuracy of the LSTM model.

Although Kolmogorov-Arnold based interpretable networks (KAN) have strong theoretical expressiveness, they face significant parameter explosion and high-frequency feature capture challenges in high-dimensional tasks. To address this issue, we propose the Kolmogorov-Arnold-Fourier Network (KAF), which effectively integrates trainable Random Fourier Features (RFF) and a novel hybrid GELU-Fourier activation mechanism to balance parameter efficiency and spectral representation capabilities. Our key technical contributions include: (1) merging KAN's dual-matrix structure through matrix association properties to substantially reduce parameters; (2) introducing learnable RFF initialization strategies to eliminate spectral distortion in high-dimensional approximation tasks; (3) implementing an adaptive hybrid activation function that progressively enhances frequency representation during the training process. Comprehensive experiments demonstrate the superiority of our KAF across various domains including vision, NLP, audio processing, and differential equation-solving tasks, effectively combining theoretical interpretability with practical utility and computational efficiency.

Kolmogorov-Arnold Networks (KAN) are a new class of neural network architecture representing a promising alternative to the Multilayer Perceptron (MLP), demonstrating improved expressiveness and interpretability. However, KANs suffer from slow training and inference speeds relative to MLPs due in part to the recursive nature of the underlying B-spline calculations. This issue is particularly apparent with respect to KANs utilizing high-degree B-splines, as the number of required non-parallelizable recursions is proportional to B-spline degree. We solve this issue by proposing MatrixKAN, a novel optimization that parallelizes B-spline calculations with matrix representation and operations, thus significantly improving effective computation time for models utilizing high-degree B-splines. In this paper, we demonstrate the superior scaling of MatrixKAN's computation time relative to B-spline degree. Further, our experiments demonstrate speedups of approximately 40x relative to KAN, with significant additional speedup potential for larger datasets or higher spline degrees.

We propose a new bound for generalization of neural networks using Koopman operators. Whereas most of existing works focus on low-rank weight matrices, we focus on full-rank weight matrices. Our bound is tighter than existing norm-based bounds when the condition numbers of weight matrices are small. Especially, it is completely independent of the width of the network if the weight matrices are orthogonal. Our bound does not contradict to the existing bounds but is a complement to the existing bounds. As supported by several existing empirical results, low-rankness is not the only reason for generalization. Furthermore, our bound can be combined with the existing bounds to obtain a tighter bound. Our result sheds new light on understanding generalization of neural networks with full-rank weight matrices, and it provides a connection between operator-theoretic analysis and generalization of neural networks.

Learned representations are a central component in modern ML systems, serving a multitude of downstream tasks. When training such representations, it is often the case that computational and statistical constraints for each downstream task are unknown. In this context rigid, fixed capacity representations can be either over or under-accommodating to the task at hand. This leads us to ask: can we design a flexible representation that can adapt to multiple downstream tasks with varying computational resources? Our main contribution is Matryoshka Representation Learning (MRL) which encodes information at different granularities and allows a single embedding to adapt to the computational constraints of downstream tasks. MRL minimally modifies existing representation learning pipelines and imposes no additional cost during inference and deployment. MRL learns coarse-to-fine representations that are at least as accurate and rich as independently trained low-dimensional representations. The flexibility within the learned Matryoshka Representations offer: (a) up to 14x smaller embedding size for ImageNet-1K classification at the same level of accuracy; (b) up to 14x real-world speed-ups for large-scale retrieval on ImageNet-1K and 4K; and (c) up to 2% accuracy improvements for long-tail few-shot classification, all while being as robust as the original representations. Finally, we show that MRL extends seamlessly to web-scale datasets (ImageNet, JFT) across various modalities -- vision (ViT, ResNet), vision + language (ALIGN) and language (BERT). MRL code and pretrained models are open-sourced at https://github.com/RAIVNLab/MRL.

We present a combined scaling method - named BASIC - that achieves 85.7% top-1 accuracy on the ImageNet ILSVRC-2012 validation set without learning from any labeled ImageNet example. This accuracy surpasses best published similar models - CLIP and ALIGN - by 9.3%. Our BASIC model also shows significant improvements in robustness benchmarks. For instance, on 5 test sets with natural distribution shifts such as ImageNet-{A,R,V2,Sketch} and ObjectNet, our model achieves 84.3% top-1 average accuracy, only a small drop from its original ImageNet accuracy. To achieve these results, we scale up the contrastive learning framework of CLIP and ALIGN in three dimensions: data size, model size, and batch size. Our dataset has 6.6B noisy image-text pairs, which is 4x larger than ALIGN, and 16x larger than CLIP. Our largest model has 3B weights, which is 3.75x larger in parameters and 8x larger in FLOPs than ALIGN and CLIP. Finally, our batch size is 65536 which is 2x more than CLIP and 4x more than ALIGN. We encountered two main challenges with the scaling rules of BASIC. First, the main challenge with implementing the combined scaling rules of BASIC is the limited memory of accelerators, such as GPUs and TPUs. To overcome the memory limit, we propose two simple methods which make use of gradient checkpointing and model parallelism. Second, while increasing the dataset size and the model size has been the defacto method to improve the performance of deep learning models like BASIC, the effect of a large contrastive batch size on such contrastive-trained image-text models is not well-understood. To shed light on the benefits of large contrastive batch sizes, we develop a theoretical framework which shows that larger contrastive batch sizes lead to smaller generalization gaps for image-text models such as BASIC.

Transformers are widely used to extract semantic meanings from input tokens, yet they usually operate as black-box models. In this paper, we present a simple yet informative decomposition of hidden states (or embeddings) of trained transformers into interpretable components. For any layer, embedding vectors of input sequence samples are represented by a tensor h in R^{C times T times d}. Given embedding vector h_{c,t} in R^d at sequence position t le T in a sequence (or context) c le C, extracting the mean effects yields the decomposition \[ h_{c,t} = \mu + pos_t + ctx_c + resid_{c,t} \] where mu is the global mean vector, pos_t and ctx_c are the mean vectors across contexts and across positions respectively, and resid_{c,t} is the residual vector. For popular transformer architectures and diverse text datasets, empirically we find pervasive mathematical structure: (1) (pos_t)_{t} forms a low-dimensional, continuous, and often spiral shape across layers, (2) (ctx_c)_c shows clear cluster structure that falls into context topics, and (3) (pos_t)_{t} and (ctx_c)_c are mutually nearly orthogonal. We argue that smoothness is pervasive and beneficial to transformers trained on languages, and our decomposition leads to improved model interpretability.

Attention based models such as Transformers involve pairwise interactions between data points, modeled with a learnable attention matrix. Importantly, this attention matrix is normalized with the SoftMax operator, which makes it row-wise stochastic. In this paper, we propose instead to use Sinkhorn's algorithm to make attention matrices doubly stochastic. We call the resulting model a Sinkformer. We show that the row-wise stochastic attention matrices in classical Transformers get close to doubly stochastic matrices as the number of epochs increases, justifying the use of Sinkhorn normalization as an informative prior. On the theoretical side, we show that, unlike the SoftMax operation, this normalization makes it possible to understand the iterations of self-attention modules as a discretized gradient-flow for the Wasserstein metric. We also show in the infinite number of samples limit that, when rescaling both attention matrices and depth, Sinkformers operate a heat diffusion. On the experimental side, we show that Sinkformers enhance model accuracy in vision and natural language processing tasks. In particular, on 3D shapes classification, Sinkformers lead to a significant improvement.

By interpreting the product of the Principal Component Analysis, that is the covariance matrix, as a sequence of nested subspaces naturally coming with weights according to the level of approximation they provide, we are able to embed all d--dimensional Grassmannians into a stratified space of covariance matrices. We observe that Grassmannians constitute the lowest dimensional skeleton of the stratification while it is possible to define a Riemaniann metric on the highest dimensional and dense stratum, such a metric being compatible with the global stratification. With such a Riemaniann metric at hand, it is possible to look for geodesics between two linear subspaces of different dimensions that do not go through higher dimensional linear subspaces as would euclidean geodesics. Building upon the proposed embedding of Grassmannians into the stratified space of covariance matrices, we generalize the concept of varifolds to what we call flagfolds in order to model multi-dimensional shapes.

We give an overview of recent developments in the modeling of radiowave propagation, based on machine learning algorithms. We identify the input and output specification and the architecture of the model as the main challenges associated with machine learning-driven propagation models. Relevant papers are discussed and categorized based on their approach to each of these challenges. Emphasis is given on presenting the prospects and open problems in this promising and rapidly evolving area.

Handwritten digit or numeral recognition is one of the classical issues in the area of pattern recognition and has seen tremendous advancement because of the recent wide availability of computing resources. Plentiful works have already done on English, Arabic, Chinese, Japanese handwritten script. Some work on Bangla also have been done but there is space for development. From that angle, in this paper, an architecture has been implemented which achieved the validation accuracy of 99.44% on BHAND dataset and outperforms Alexnet and Inception V3 architecture. Beside digit recognition, digit generation is another field which has recently caught the attention of the researchers though not many works have been done in this field especially on Bangla. In this paper, a Semi-Supervised Generative Adversarial Network or SGAN has been applied to generate Bangla handwritten numerals and it successfully generated Bangla digits.

Although it is known that transformer language models (LMs) pass features from early layers to later layers, it is not well understood how this information is represented and routed by the model. By analyzing particular mechanism LMs use to accomplish this, we find that it is also used to recall items from a list, and show that this mechanism can explain an otherwise arbitrary-seeming sensitivity of the model to the order of items in the prompt. Specifically, we find that models write into low-rank subspaces of the residual stream to represent features which are then read out by specific later layers, forming low-rank communication channels between layers. By decomposing attention head weight matrices with the Singular Value Decomposition (SVD), we find that previously described interactions between heads separated by one or more layers can be predicted via analysis of their weight matrices. We show that it is possible to manipulate the internal model representations as well as edit model weights based on the mechanism we discover in order to significantly improve performance on our synthetic Laundry List task, which requires recall from a list, often improving task accuracy by over 20%. Our analysis reveals a surprisingly intricate interpretable structure learned from language model pretraining, and helps us understand why sophisticated LMs sometimes fail in simple domains, facilitating future analysis of more complex behaviors.

We introduce InstaAug, a method for automatically learning input-specific augmentations from data. Previous methods for learning augmentations have typically assumed independence between the original input and the transformation applied to that input. This can be highly restrictive, as the invariances we hope our augmentation will capture are themselves often highly input dependent. InstaAug instead introduces a learnable invariance module that maps from inputs to tailored transformation parameters, allowing local invariances to be captured. This can be simultaneously trained alongside the downstream model in a fully end-to-end manner, or separately learned for a pre-trained model. We empirically demonstrate that InstaAug learns meaningful input-dependent augmentations for a wide range of transformation classes, which in turn provides better performance on both supervised and self-supervised tasks.

What is the computational model behind a Transformer? Where recurrent neural networks have direct parallels in finite state machines, allowing clear discussion and thought around architecture variants or trained models, Transformers have no such familiar parallel. In this paper we aim to change that, proposing a computational model for the transformer-encoder in the form of a programming language. We map the basic components of a transformer-encoder -- attention and feed-forward computation -- into simple primitives, around which we form a programming language: the Restricted Access Sequence Processing Language (RASP). We show how RASP can be used to program solutions to tasks that could conceivably be learned by a Transformer, and how a Transformer can be trained to mimic a RASP solution. In particular, we provide RASP programs for histograms, sorting, and Dyck-languages. We further use our model to relate their difficulty in terms of the number of required layers and attention heads: analyzing a RASP program implies a maximum number of heads and layers necessary to encode a task in a transformer. Finally, we see how insights gained from our abstraction might be used to explain phenomena seen in recent works.

Neural sequence models, especially transformers, exhibit a remarkable capacity for in-context learning. They can construct new predictors from sequences of labeled examples (x, f(x)) presented in the input without further parameter updates. We investigate the hypothesis that transformer-based in-context learners implement standard learning algorithms implicitly, by encoding smaller models in their activations, and updating these implicit models as new examples appear in the context. Using linear regression as a prototypical problem, we offer three sources of evidence for this hypothesis. First, we prove by construction that transformers can implement learning algorithms for linear models based on gradient descent and closed-form ridge regression. Second, we show that trained in-context learners closely match the predictors computed by gradient descent, ridge regression, and exact least-squares regression, transitioning between different predictors as transformer depth and dataset noise vary, and converging to Bayesian estimators for large widths and depths. Third, we present preliminary evidence that in-context learners share algorithmic features with these predictors: learners' late layers non-linearly encode weight vectors and moment matrices. These results suggest that in-context learning is understandable in algorithmic terms, and that (at least in the linear case) learners may rediscover standard estimation algorithms. Code and reference implementations are released at https://github.com/ekinakyurek/google-research/blob/master/incontext.

With the success of pretraining techniques in representation learning, a number of continual learning methods based on pretrained models have been proposed. Some of these methods design continual learning mechanisms on the pre-trained representations and only allow minimum updates or even no updates of the backbone models during the training of continual learning. In this paper, we question whether the complexity of these models is needed to achieve good performance by comparing them to a simple baseline that we designed. We argue that the pretrained feature extractor itself can be strong enough to achieve a competitive or even better continual learning performance on Split-CIFAR100 and CoRe 50 benchmarks. To validate this, we conduct a very simple baseline that 1) use the frozen pretrained model to extract image features for every class encountered during the continual learning stage and compute their corresponding mean features on training data, and 2) predict the class of the input based on the nearest neighbor distance between test samples and mean features of the classes; i.e., Nearest Mean Classifier (NMC). This baseline is single-headed, exemplar-free, and can be task-free (by updating the means continually). This baseline achieved 88.53% on 10-Split-CIFAR-100, surpassing most state-of-the-art continual learning methods that are all initialized using the same pretrained transformer model. We hope our baseline may encourage future progress in designing learning systems that can continually add quality to the learning representations even if they started from some pretrained weights.

Graph Neural Networks (GNNs), especially message-passing neural networks (MPNNs), have emerged as powerful architectures for learning on graphs in diverse applications. However, MPNNs face challenges when modeling non-local interactions in graphs such as large conjugated molecules, and social networks due to oversmoothing and oversquashing. Although Spectral GNNs and traditional neural networks such as recurrent neural networks and transformers mitigate these challenges, they often lack generalizability, or fail to capture detailed structural relationships or symmetries in the data. To address these concerns, we introduce Matrix Function Neural Networks (MFNs), a novel architecture that parameterizes non-local interactions through analytic matrix equivariant functions. Employing resolvent expansions offers a straightforward implementation and the potential for linear scaling with system size. The MFN architecture achieves stateof-the-art performance in standard graph benchmarks, such as the ZINC and TU datasets, and is able to capture intricate non-local interactions in quantum systems, paving the way to new state-of-the-art force fields.

Large parallel corpora that are automatically obtained from the web, documents or elsewhere often exhibit many corrupted parts that are bound to negatively affect the quality of the systems and models that learn from these corpora. This paper describes frequent problems found in data and such data affects neural machine translation systems, as well as how to identify and deal with them. The solutions are summarised in a set of scripts that remove problematic sentences from input corpora.

This paper reports the first brain-inspired large language model (BriLLM). This is a non-Transformer, non-GPT, non-traditional machine learning input-output controlled generative language model. The model is based on the Signal Fully-connected flowing (SiFu) definition on the directed graph in terms of the neural network, and has the interpretability of all nodes on the graph of the whole model, instead of the traditional machine learning model that only has limited interpretability at the input and output ends. In the language model scenario, the token is defined as a node in the graph. A randomly shaped or user-defined signal flow flows between nodes on the principle of "least resistance" along paths. The next token or node to be predicted or generated is the target of the signal flow. As a language model, BriLLM theoretically supports infinitely long n-gram models when the model size is independent of the input and predicted length of the model. The model's working signal flow provides the possibility of recall activation and innate multi-modal support similar to the cognitive patterns of the human brain. At present, we released the first BriLLM version in Chinese, with 4000 tokens, 32-dimensional node width, 16-token long sequence prediction ability, and language model prediction performance comparable to GPT-1. More computing power will help us explore the infinite possibilities depicted above.

Handwritten mathematical expression recognition (HMER) is a challenging task that has many potential applications. Recent methods for HMER have achieved outstanding performance with an encoder-decoder architecture. However, these methods adhere to the paradigm that the prediction is made "from one character to another", which inevitably yields prediction errors due to the complicated structures of mathematical expressions or crabbed handwritings. In this paper, we propose a simple and efficient method for HMER, which is the first to incorporate syntax information into an encoder-decoder network. Specifically, we present a set of grammar rules for converting the LaTeX markup sequence of each expression into a parsing tree; then, we model the markup sequence prediction as a tree traverse process with a deep neural network. In this way, the proposed method can effectively describe the syntax context of expressions, alleviating the structure prediction errors of HMER. Experiments on three benchmark datasets demonstrate that our method achieves better recognition performance than prior arts. To further validate the effectiveness of our method, we create a large-scale dataset consisting of 100k handwritten mathematical expression images acquired from ten thousand writers. The source code, new dataset, and pre-trained models of this work will be publicly available.

Convolutional networks are large linear systems divided into layers and connected by non-linear units. These units are the "articulations" that allow the network to adapt to the input. To understand how a network manages to solve a problem we must look at the articulated decisions in entirety. If we could capture the actions of non-linear units for a particular input, we would be able to replay the whole system back and forth as if it was always linear. It would also reveal the actions of non-linearities because the resulting linear system, a Linear Interpreter, depends on the input image. We introduce a hooking layer, called a LinearScope, which allows us to run the network and the linear interpreter in parallel. Its implementation is simple, flexible and efficient. From here we can make many curious inquiries: how do these linear systems look like? When the rows and columns of the transformation matrix are images, how do they look like? What type of basis do these linear transformations rely on? The answers depend on the problems presented, through which we take a tour to some popular architectures used for classification, super-resolution (SR) and image-to-image translation (I2I). For classification we observe that popular networks use a pixel-wise vote per class strategy and heavily rely on bias parameters. For SR and I2I we find that CNNs use wavelet-type basis similar to the human visual system. For I2I we reveal copy-move and template-creation strategies to generate outputs.

Artificial neural networks are the heart of machine learning algorithms and artificial intelligence protocols. Historically, the simplest implementation of an artificial neuron traces back to the classical Rosenblatt's `perceptron', but its long term practical applications may be hindered by the fast scaling up of computational complexity, especially relevant for the training of multilayered perceptron networks. Here we introduce a quantum information-based algorithm implementing the quantum computer version of a perceptron, which shows exponential advantage in encoding resources over alternative realizations. We experimentally test a few qubits version of this model on an actual small-scale quantum processor, which gives remarkably good answers against the expected results. We show that this quantum model of a perceptron can be used as an elementary nonlinear classifier of simple patterns, as a first step towards practical training of artificial quantum neural networks to be efficiently implemented on near-term quantum processing hardware.

Sequences have become first class citizens in supervised learning thanks to the resurgence of recurrent neural networks. Many complex tasks that require mapping from or to a sequence of observations can now be formulated with the sequence-to-sequence (seq2seq) framework which employs the chain rule to efficiently represent the joint probability of sequences. In many cases, however, variable sized inputs and/or outputs might not be naturally expressed as sequences. For instance, it is not clear how to input a set of numbers into a model where the task is to sort them; similarly, we do not know how to organize outputs when they correspond to random variables and the task is to model their unknown joint probability. In this paper, we first show using various examples that the order in which we organize input and/or output data matters significantly when learning an underlying model. We then discuss an extension of the seq2seq framework that goes beyond sequences and handles input sets in a principled way. In addition, we propose a loss which, by searching over possible orders during training, deals with the lack of structure of output sets. We show empirical evidence of our claims regarding ordering, and on the modifications to the seq2seq framework on benchmark language modeling and parsing tasks, as well as two artificial tasks -- sorting numbers and estimating the joint probability of unknown graphical models.

We present Manify, an open-source Python library for non-Euclidean representation learning. Leveraging manifold learning techniques, Manify provides tools for learning embeddings in (products of) non-Euclidean spaces, performing classification and regression with data that lives in such spaces, and estimating the curvature of a manifold. Manify aims to advance research and applications in machine learning by offering a comprehensive suite of tools for manifold-based data analysis. Our source code, examples, datasets, results, and documentation are available at https://github.com/pchlenski/manify

In this paper we show how tensor networks help in developing explainability of machine learning algorithms. Specifically, we develop an unsupervised clustering algorithm based on Matrix Product States (MPS) and apply it in the context of a real use-case of adversary-generated threat intelligence. Our investigation proves that MPS rival traditional deep learning models such as autoencoders and GANs in terms of performance, while providing much richer model interpretability. Our approach naturally facilitates the extraction of feature-wise probabilities, Von Neumann Entropy, and mutual information, offering a compelling narrative for classification of anomalies and fostering an unprecedented level of transparency and interpretability, something fundamental to understand the rationale behind artificial intelligence decisions.

This paper surveys and organizes research works in a new paradigm in natural language processing, which we dub "prompt-based learning". Unlike traditional supervised learning, which trains a model to take in an input x and predict an output y as P(y|x), prompt-based learning is based on language models that model the probability of text directly. To use these models to perform prediction tasks, the original input x is modified using a template into a textual string prompt x' that has some unfilled slots, and then the language model is used to probabilistically fill the unfilled information to obtain a final string x, from which the final output y can be derived. This framework is powerful and attractive for a number of reasons: it allows the language model to be pre-trained on massive amounts of raw text, and by defining a new prompting function the model is able to perform few-shot or even zero-shot learning, adapting to new scenarios with few or no labeled data. In this paper we introduce the basics of this promising paradigm, describe a unified set of mathematical notations that can cover a wide variety of existing work, and organize existing work along several dimensions, e.g.the choice of pre-trained models, prompts, and tuning strategies. To make the field more accessible to interested beginners, we not only make a systematic review of existing works and a highly structured typology of prompt-based concepts, but also release other resources, e.g., a website http://pretrain.nlpedia.ai/ including constantly-updated survey, and paperlist.

In the past few decades, Japanese comics, commonly referred to as Manga, have transcended both cultural and linguistic boundaries to become a true worldwide sensation. Yet, the inherent reliance on visual cues and illustration within manga renders it largely inaccessible to individuals with visual impairments. In this work, we seek to address this substantial barrier, with the aim of ensuring that manga can be appreciated and actively engaged by everyone. Specifically, we tackle the problem of diarisation i.e. generating a transcription of who said what and when, in a fully automatic way. To this end, we make the following contributions: (1) we present a unified model, Magi, that is able to (a) detect panels, text boxes and character boxes, (b) cluster characters by identity (without knowing the number of clusters apriori), and (c) associate dialogues to their speakers; (2) we propose a novel approach that is able to sort the detected text boxes in their reading order and generate a dialogue transcript; (3) we annotate an evaluation benchmark for this task using publicly available [English] manga pages. The code, evaluation datasets and the pre-trained model can be found at: https://github.com/ragavsachdeva/magi.

This open access book provides a comprehensive overview of the state of the art in research and applications of Foundation Models and is intended for readers familiar with basic Natural Language Processing (NLP) concepts. Over the recent years, a revolutionary new paradigm has been developed for training models for NLP. These models are first pre-trained on large collections of text documents to acquire general syntactic knowledge and semantic information. Then, they are fine-tuned for specific tasks, which they can often solve with superhuman accuracy. When the models are large enough, they can be instructed by prompts to solve new tasks without any fine-tuning. Moreover, they can be applied to a wide range of different media and problem domains, ranging from image and video processing to robot control learning. Because they provide a blueprint for solving many tasks in artificial intelligence, they have been called Foundation Models. After a brief introduction to basic NLP models the main pre-trained language models BERT, GPT and sequence-to-sequence transformer are described, as well as the concepts of self-attention and context-sensitive embedding. Then, different approaches to improving these models are discussed, such as expanding the pre-training criteria, increasing the length of input texts, or including extra knowledge. An overview of the best-performing models for about twenty application areas is then presented, e.g., question answering, translation, story generation, dialog systems, generating images from text, etc. For each application area, the strengths and weaknesses of current models are discussed, and an outlook on further developments is given. In addition, links are provided to freely available program code. A concluding chapter summarizes the economic opportunities, mitigation of risks, and potential developments of AI.

Transformers have widely adopted attention networks for sequence mixing and MLPs for channel mixing, playing a pivotal role in achieving breakthroughs across domains. However, recent literature highlights issues with attention networks, including low inductive bias and quadratic complexity concerning input sequence length. State Space Models (SSMs) like S4 and others (Hippo, Global Convolutions, liquid S4, LRU, Mega, and Mamba), have emerged to address the above issues to help handle longer sequence lengths. Mamba, while being the state-of-the-art SSM, has a stability issue when scaled to large networks for computer vision datasets. We propose SiMBA, a new architecture that introduces Einstein FFT (EinFFT) for channel modeling by specific eigenvalue computations and uses the Mamba block for sequence modeling. Extensive performance studies across image and time-series benchmarks demonstrate that SiMBA outperforms existing SSMs, bridging the performance gap with state-of-the-art transformers. Notably, SiMBA establishes itself as the new state-of-the-art SSM on ImageNet and transfer learning benchmarks such as Stanford Car and Flower as well as task learning benchmarks as well as seven time series benchmark datasets. The project page is available on this website ~https://github.com/badripatro/Simba.

Understanding generalization in deep neural networks is an active area of research. A promising avenue of exploration has been that of margin measurements: the shortest distance to the decision boundary for a given sample or its representation internal to the network. While margins have been shown to be correlated with the generalization ability of a model when measured at its hidden representations (hidden margins), no such link between large margins and generalization has been established for input margins. We show that while input margins are not generally predictive of generalization, they can be if the search space is appropriately constrained. We develop such a measure based on input margins, which we refer to as `constrained margins'. The predictive power of this new measure is demonstrated on the 'Predicting Generalization in Deep Learning' (PGDL) dataset and contrasted with hidden representation margins. We find that constrained margins achieve highly competitive scores and outperform other margin measurements in general. This provides a novel insight on the relationship between generalization and classification margins, and highlights the importance of considering the data manifold for investigations of generalization in DNNs.

Standard infinite-width limits of neural networks sacrifice the ability for intermediate layers to learn representations from data. Recent work (A theory of representation learning gives a deep generalisation of kernel methods, Yang et al. 2023) modified the Neural Network Gaussian Process (NNGP) limit of Bayesian neural networks so that representation learning is retained. Furthermore, they found that applying this modified limit to a deep Gaussian process gives a practical learning algorithm which they dubbed the deep kernel machine (DKM). However, they only considered the simplest possible setting: regression in small, fully connected networks with e.g. 10 input features. Here, we introduce convolutional deep kernel machines. This required us to develop a novel inter-domain inducing point approximation, as well as introducing and experimentally assessing a number of techniques not previously seen in DKMs, including analogues to batch normalisation, different likelihoods, and different types of top-layer. The resulting model trains in roughly 77 GPU hours, achieving around 99% test accuracy on MNIST, 72% on CIFAR-100, and 92.7% on CIFAR-10, which is SOTA for kernel methods.

Generating 2-by-2 unitary matrices in floating-precision arithmetic is a delicate task. One way to reduce the accumulation error is to use less floating-point operations to compute each of the entries in the 2-by-2 unitary matrix. This paper shows an algorithm that reduces the number of operations to compute the entries of a Givens rotation. Overall, the new algorithm has more operations in total when compared to algorithms in different releases of LAPACK, but less operations per entry. Numerical tests show that the new algorithm is more accurate on average.

The MNIST dataset has become a standard benchmark for learning, classification and computer vision systems. Contributing to its widespread adoption are the understandable and intuitive nature of the task, its relatively small size and storage requirements and the accessibility and ease-of-use of the database itself. The MNIST database was derived from a larger dataset known as the NIST Special Database 19 which contains digits, uppercase and lowercase handwritten letters. This paper introduces a variant of the full NIST dataset, which we have called Extended MNIST (EMNIST), which follows the same conversion paradigm used to create the MNIST dataset. The result is a set of datasets that constitute a more challenging classification tasks involving letters and digits, and that shares the same image structure and parameters as the original MNIST task, allowing for direct compatibility with all existing classifiers and systems. Benchmark results are presented along with a validation of the conversion process through the comparison of the classification results on converted NIST digits and the MNIST digits.

This paper presents a computationally efficient machine-learned method for natural language response suggestion. Feed-forward neural networks using n-gram embedding features encode messages into vectors which are optimized to give message-response pairs a high dot-product value. An optimized search finds response suggestions. The method is evaluated in a large-scale commercial e-mail application, Inbox by Gmail. Compared to a sequence-to-sequence approach, the new system achieves the same quality at a small fraction of the computational requirements and latency.

The field of machine learning has taken a dramatic twist in recent times, with the rise of the Artificial Neural Network (ANN). These biologically inspired computational models are able to far exceed the performance of previous forms of artificial intelligence in common machine learning tasks. One of the most impressive forms of ANN architecture is that of the Convolutional Neural Network (CNN). CNNs are primarily used to solve difficult image-driven pattern recognition tasks and with their precise yet simple architecture, offers a simplified method of getting started with ANNs. This document provides a brief introduction to CNNs, discussing recently published papers and newly formed techniques in developing these brilliantly fantastic image recognition models. This introduction assumes you are familiar with the fundamentals of ANNs and machine learning.

Selective state-space models (SSMs) are an emerging alternative to the Transformer, offering the unique advantage of parallel training and sequential inference. Although these models have shown promising performance on a variety of tasks, their formal expressiveness and length generalization properties remain underexplored. In this work, we provide insight into the workings of selective SSMs by analyzing their expressiveness and length generalization performance on regular language tasks, i.e., finite-state automaton (FSA) emulation. We address certain limitations of modern SSM-based architectures by introducing the Selective Dense State-Space Model (SD-SSM), the first selective SSM that exhibits perfect length generalization on a set of various regular language tasks using a single layer. It utilizes a dictionary of dense transition matrices, a softmax selection mechanism that creates a convex combination of dictionary matrices at each time step, and a readout consisting of layer normalization followed by a linear map. We then proceed to evaluate variants of diagonal selective SSMs by considering their empirical performance on commutative and non-commutative automata. We explain the experimental results with theoretical considerations. Our code is available at https://github.com/IBM/selective-dense-state-space-model.

We tackle the challenge of open-vocabulary segmentation, where we need to identify objects from a wide range of categories in different environments, using text prompts as our input. To overcome this challenge, existing methods often use multi-modal models like CLIP, which combine image and text features in a shared embedding space to bridge the gap between limited and extensive vocabulary recognition, resulting in a two-stage approach: In the first stage, a mask generator takes an input image to generate mask proposals, and the in the second stage the target mask is picked based on the query. However, the expected target mask may not exist in the generated mask proposals, which leads to an unexpected output mask. In our work, we propose a novel approach named Prompt-guided Mask Proposal (PMP) where the mask generator takes the input text prompts and generates masks guided by these prompts. Compared with mask proposals generated without input prompts, masks generated by PMP are better aligned with the input prompts. To realize PMP, we designed a cross-attention mechanism between text tokens and query tokens which is capable of generating prompt-guided mask proposals after each decoding. We combined our PMP with several existing works employing a query-based segmentation backbone and the experiments on five benchmark datasets demonstrate the effectiveness of this approach, showcasing significant improvements over the current two-stage models (1% ~ 3% absolute performance gain in terms of mIOU). The steady improvement in performance across these benchmarks indicates the effective generalization of our proposed lightweight prompt-aware method.

Continuous word representations, trained on large unlabeled corpora are useful for many natural language processing tasks. Popular models that learn such representations ignore the morphology of words, by assigning a distinct vector to each word. This is a limitation, especially for languages with large vocabularies and many rare words. In this paper, we propose a new approach based on the skipgram model, where each word is represented as a bag of character n-grams. A vector representation is associated to each character n-gram; words being represented as the sum of these representations. Our method is fast, allowing to train models on large corpora quickly and allows us to compute word representations for words that did not appear in the training data. We evaluate our word representations on nine different languages, both on word similarity and analogy tasks. By comparing to recently proposed morphological word representations, we show that our vectors achieve state-of-the-art performance on these tasks.

We introduce ODEFormer, the first transformer able to infer multidimensional ordinary differential equation (ODE) systems in symbolic form from the observation of a single solution trajectory. We perform extensive evaluations on two datasets: (i) the existing "Strogatz" dataset featuring two-dimensional systems; (ii) ODEBench, a collection of one- to four-dimensional systems that we carefully curated from the literature to provide a more holistic benchmark. ODEFormer consistently outperforms existing methods while displaying substantially improved robustness to noisy and irregularly sampled observations, as well as faster inference. We release our code, model and benchmark dataset publicly.

Natural language is composed of words, but modern large language models (LLMs) process sub-words as input. A natural question raised by this discrepancy is whether LLMs encode words internally, and if so how. We present evidence that LLMs engage in an intrinsic detokenization process, where sub-word sequences are combined into coherent whole-word representations at their last token. Our experiments show that this process primarily takes place within the early and middle layers of the model. We further demonstrate its robustness to arbitrary splits (e.g., "cats" to "ca" and "ts"), typos, and importantly-to out-of-vocabulary words: when feeding the last token internal representations of such words to the model as input, it can "understand" them as the complete word despite never seeing such representations as input during training. Our findings suggest that LLMs maintain a latent vocabulary beyond the tokenizer's scope. These insights provide a practical, finetuning-free application for expanding the vocabulary of pre-trained models. By enabling the addition of new vocabulary words, we reduce input length and inference iterations, which reduces both space and model latency, with little to no loss in model accuracy.

Large pre-trained models (LPMs) have demonstrated exceptional performance in diverse natural language processing and computer vision tasks. However, fully fine-tuning these models poses substantial memory challenges, particularly in resource-constrained environments. Parameter-efficient fine-tuning (PEFT) methods, such as LoRA, mitigate this issue by adjusting only a small subset of parameters. Nevertheless, these methods typically employ random initialization for low-rank matrices, which can lead to inefficiencies in gradient descent and diminished generalizability due to suboptimal starting points. To address these limitations, we propose SVFit, a novel PEFT approach that leverages singular value decomposition (SVD) to initialize low-rank matrices using critical singular values as trainable parameters. Specifically, SVFit performs SVD on the pre-trained weight matrix to obtain the best rank-r approximation matrix, emphasizing the most critical singular values that capture over 99% of the matrix's information. These top-r singular values are then used as trainable parameters to scale the fundamental subspaces of the matrix, facilitating rapid domain adaptation. Extensive experiments across various pre-trained models in natural language understanding, text-to-image generation, and image classification tasks reveal that SVFit outperforms LoRA while requiring 16 times fewer trainable parameters.

This dataset represents almost all the harmful diseases for rice in Bangladesh. This dataset consists of 1106 image of five harmful diseases called Brown Spot, Leaf Scaled, Rice Blast, Rice Turngo, Steath Blight in two different background variation named field background picture and white background picture. Two different background variation helps the dataset to perform more accurately so that the user can use this data for field use as well as white background for decision making. The data is collected from rice field of Dhaka Division. This dataset can use for rice leaf diseases classification, diseases detection using Computer Vision and Pattern Recognition for different rice leaf disease.

Riemannian submanifold optimization with momentum is computationally challenging because, to ensure that the iterates remain on the submanifold, we often need to solve difficult differential equations. Here, we simplify such difficulties for a class of structured symmetric positive-definite matrices with the affine-invariant metric. We do so by proposing a generalized version of the Riemannian normal coordinates that dynamically orthonormalizes the metric and locally converts the problem into an unconstrained problem in the Euclidean space. We use our approach to simplify existing approaches for structured covariances and develop matrix-inverse-free 2^nd-order optimizers for deep learning in low precision settings. Code: https://github.com/yorkerlin/StructuredNGD-DL

The task of inserting text into a specified position in a passage, known as fill in the blank (FitB), is useful for a variety of applications where writers interact with a natural language generation (NLG) system to craft text. While previous work has tackled this problem with models trained specifically to do the fill-in-the-blank task, a more useful model is one that can effectively perform _both_ FitB and continuation. In this work, we evaluate the feasibility of using a single model to do both tasks. We show that models pre-trained with a FitB-style objective are capable of both tasks, while models pre-trained for continuation are not. Finally, we show how FitB models can be easily finetuned to allow for fine-grained control over the length and word choice of the generation.

The use of CLIP embeddings to assess the alignment of samples produced by text-to-image generative models has been extensively explored in the literature. While the widely adopted CLIPScore, derived from the cosine similarity of text and image embeddings, effectively measures the relevance of a generated image, it does not quantify the diversity of images generated by a text-to-image model. In this work, we extend the application of CLIP embeddings to quantify and interpret the intrinsic diversity of text-to-image models, which is responsible for generating diverse images from similar text prompts. To achieve this, we propose a decomposition of the CLIP-based kernel covariance matrix of image data into text-based and non-text-based components. Using the Schur complement of the joint image-text kernel covariance matrix, we perform this decomposition and define the matrix-based entropy of the decomposed component as the Schur Complement Entropy (SCE) score, a measure of the intrinsic diversity of a text-to-image model based on data collected with varying text prompts. Additionally, we demonstrate the use of the Schur complement-based decomposition to nullify the influence of a given prompt in the CLIP embedding of an image, enabling focus or defocus of embeddings on specific objects or properties for downstream tasks. We present several numerical results that apply our Schur complement-based approach to evaluate text-to-image models and modify CLIP image embeddings. The codebase is available at https://github.com/aziksh-ospanov/CLIP-DISSECTION

Theano is a Python library that allows to define, optimize, and evaluate mathematical expressions involving multi-dimensional arrays efficiently. Since its introduction, it has been one of the most used CPU and GPU mathematical compilers - especially in the machine learning community - and has shown steady performance improvements. Theano is being actively and continuously developed since 2008, multiple frameworks have been built on top of it and it has been used to produce many state-of-the-art machine learning models. The present article is structured as follows. Section I provides an overview of the Theano software and its community. Section II presents the principal features of Theano and how to use them, and compares them with other similar projects. Section III focuses on recently-introduced functionalities and improvements. Section IV compares the performance of Theano against Torch7 and TensorFlow on several machine learning models. Section V discusses current limitations of Theano and potential ways of improving it.

Inspired by the ability of StyleGAN to generate highly realistic images in a variety of domains, much recent work has focused on understanding how to use the latent spaces of StyleGAN to manipulate generated and real images. However, discovering semantically meaningful latent manipulations typically involves painstaking human examination of the many degrees of freedom, or an annotated collection of images for each desired manipulation. In this work, we explore leveraging the power of recently introduced Contrastive Language-Image Pre-training (CLIP) models in order to develop a text-based interface for StyleGAN image manipulation that does not require such manual effort. We first introduce an optimization scheme that utilizes a CLIP-based loss to modify an input latent vector in response to a user-provided text prompt. Next, we describe a latent mapper that infers a text-guided latent manipulation step for a given input image, allowing faster and more stable text-based manipulation. Finally, we present a method for mapping a text prompts to input-agnostic directions in StyleGAN's style space, enabling interactive text-driven image manipulation. Extensive results and comparisons demonstrate the effectiveness of our approaches.

In the artificial neuron, I replace the dot product with the weighted Lehmer mean, which may emulate different cases of a generalized mean. The single neuron instance is replaced by a multiplet of neurons which have the same averaging weights. A group of outputs feed forward, in lieu of the single scalar. The generalization parameter is typically set to a different value for each neuron in the multiplet. I further extend the concept to a multiplet taken from the Gini mean. Derivatives with respect to the weight parameters and with respect to the two generalization parameters are given. Some properties of the network are investigated, showing the capacity to emulate the classical exclusive-or problem organically in two layers and perform some multiplication and division. The network can instantiate truncated power series and variants, which can be used to approximate different functions, provided that parameters are constrained. Moreover, a mean case slope score is derived that can facilitate a learning-rate novelty based on homogeneity of the selected elements. The multiplet neuron equation provides a way to segment regularization timeframes and approaches.

Humans have the ability to adapt the type of information they use, the procedure they employ, and the amount of time they spend when solving problems. However, most standard neural networks have a fixed function type and computation budget regardless of the sample's nature or difficulty. Adaptivity is a powerful paradigm as it not only imbues practitioners with flexibility pertaining to the downstream usage of these models but can also serve as a powerful inductive bias for solving certain challenging classes of problems. In this work, we introduce a new approach called AdaTape, which allows for dynamic computation in neural networks through adaptive tape tokens. AdaTape utilizes an elastic input sequence by equipping an architecture with a dynamic read-and-write tape. Specifically, we adaptively generate input sequences using tape tokens obtained from a tape bank which can be either trainable or derived from input data. We examine the challenges and requirements to obtain dynamic sequence content and length, and propose the Adaptive Tape Reading (ATR) algorithm to achieve both goals. Through extensive experiments on image recognition tasks, we show that AdaTape can achieve better performance while maintaining the computational cost. To facilitate further research, we have released code at https://github.com/google-research/scenic.

We propose a new learning paradigm called Deep Memory. It has the potential to completely revolutionize the Machine Learning field. Surprisingly, this paradigm has not been reinvented yet, unlike Deep Learning. At the core of this approach is the Learning By Heart principle, well studied in primary schools all over the world. Inspired by poem recitation, or by pi decimal memorization, we propose a concrete algorithm that mimics human behavior. We implement this paradigm on the task of generative modeling, and apply to images, natural language and even the pi decimals as long as one can print them as text. The proposed algorithm even generated this paper, in a one-shot learning setting. In carefully designed experiments, we show that the generated samples are indistinguishable from the training examples, as measured by any statistical tests or metrics.

We propose a novel neural network architecture, the normalized Transformer (nGPT) with representation learning on the hypersphere. In nGPT, all vectors forming the embeddings, MLP, attention matrices and hidden states are unit norm normalized. The input stream of tokens travels on the surface of a hypersphere, with each layer contributing a displacement towards the target output predictions. These displacements are defined by the MLP and attention blocks, whose vector components also reside on the same hypersphere. Experiments show that nGPT learns much faster, reducing the number of training steps required to achieve the same accuracy by a factor of 4 to 20, depending on the sequence length.

The utility of a learned neural representation depends on how well its geometry supports performance in downstream tasks. This geometry depends on the structure of the inputs, the structure of the target outputs, and the architecture of the network. By studying the learning dynamics of networks with one hidden layer, we discovered that the network's activation function has an unexpectedly strong impact on the representational geometry: Tanh networks tend to learn representations that reflect the structure of the target outputs, while ReLU networks retain more information about the structure of the raw inputs. This difference is consistently observed across a broad class of parameterized tasks in which we modulated the degree of alignment between the geometry of the task inputs and that of the task labels. We analyzed the learning dynamics in weight space and show how the differences between the networks with Tanh and ReLU nonlinearities arise from the asymmetric asymptotic behavior of ReLU, which leads feature neurons to specialize for different regions of input space. By contrast, feature neurons in Tanh networks tend to inherit the task label structure. Consequently, when the target outputs are low dimensional, Tanh networks generate neural representations that are more disentangled than those obtained with a ReLU nonlinearity. Our findings shed light on the interplay between input-output geometry, nonlinearity, and learned representations in neural networks.

Machine learning models, such as neural networks, decision trees, random forests, and gradient boosting machines, accept a feature vector, and provide a prediction. These models learn in a supervised fashion where we provide feature vectors mapped to the expected output. It is common practice to engineer new features from the provided feature set. Such engineered features will either augment or replace portions of the existing feature vector. These engineered features are essentially calculated fields based on the values of the other features. Engineering such features is primarily a manual, time-consuming task. Additionally, each type of model will respond differently to different kinds of engineered features. This paper reports empirical research to demonstrate what kinds of engineered features are best suited to various machine learning model types. We provide this recommendation by generating several datasets that we designed to benefit from a particular type of engineered feature. The experiment demonstrates to what degree the machine learning model can synthesize the needed feature on its own. If a model can synthesize a planned feature, it is not necessary to provide that feature. The research demonstrated that the studied models do indeed perform differently with various types of engineered features.

Doctors typically write in incomprehensible handwriting, making it difficult for both the general public and some pharmacists to understand the medications they have prescribed. It is not ideal for them to write the prescription quietly and methodically because they will be dealing with dozens of patients every day and will be swamped with work.As a result, their handwriting is illegible. This may result in reports or prescriptions consisting of short forms and cursive writing that a typical person or pharmacist won't be able to read properly, which will cause prescribed medications to be misspelled. However, some individuals are accustomed to writing prescriptions in regional languages because we all live in an area with a diversity of regional languages. It makes analyzing the content much more challenging. So, in this project, we'll use a recognition system to build a tool that can translate the handwriting of physicians in any language. This system will be made into an application which is fully autonomous in functioning. As the user uploads the prescription image the program will pre-process the image by performing image pre-processing, and word segmentations initially before processing the image for training. And it will be done for every language we require the model to detect. And as of the deduction model will be made using deep learning techniques including CNN, RNN, and LSTM, which are utilized to train the model. To match words from various languages that will be written in the system, Unicode will be used. Furthermore, fuzzy search and market basket analysis are employed to offer an end result that will be optimized from the pharmaceutical database and displayed to the user as a structured output.

We present DictaLM, a large-scale language model tailored for Modern Hebrew. Boasting 7B parameters, this model is predominantly trained on Hebrew-centric data. As a commitment to promoting research and development in the Hebrew language, we release both the foundation model and the instruct-tuned model under a Creative Commons license. Concurrently, we introduce DictaLM-Rab, another foundation model geared towards Rabbinic/Historical Hebrew. These foundation models serve as ideal starting points for fine-tuning various Hebrew-specific tasks, such as instruction, Q&A, sentiment analysis, and more. This release represents a preliminary step, offering an initial Hebrew LLM model for the Hebrew NLP community to experiment with.

Supervised machine learning approaches have been increasingly used in accelerating electronic structure prediction as surrogates of first-principle computational methods, such as density functional theory (DFT). While numerous quantum chemistry datasets focus on chemical properties and atomic forces, the ability to achieve accurate and efficient prediction of the Hamiltonian matrix is highly desired, as it is the most important and fundamental physical quantity that determines the quantum states of physical systems and chemical properties. In this work, we generate a new Quantum Hamiltonian dataset, named as QH9, to provide precise Hamiltonian matrices for 999 or 2998 molecular dynamics trajectories and 130,831 stable molecular geometries, based on the QM9 dataset. By designing benchmark tasks with various molecules, we show that current machine learning models have the capacity to predict Hamiltonian matrices for arbitrary molecules. Both the QH9 dataset and the baseline models are provided to the community through an open-source benchmark, which can be highly valuable for developing machine learning methods and accelerating molecular and materials design for scientific and technological applications. Our benchmark is publicly available at https://github.com/divelab/AIRS/tree/main/OpenDFT/QHBench.

We introduce a large-scale dataset of math word problems and an interpretable neural math problem solver that learns to map problems to operation programs. Due to annotation challenges, current datasets in this domain have been either relatively small in scale or did not offer precise operational annotations over diverse problem types. We introduce a new representation language to model precise operation programs corresponding to each math problem that aim to improve both the performance and the interpretability of the learned models. Using this representation language, our new dataset, MathQA, significantly enhances the AQuA dataset with fully-specified operational programs. We additionally introduce a neural sequence-to-program model enhanced with automatic problem categorization. Our experiments show improvements over competitive baselines in our MathQA as well as the AQuA dataset. The results are still significantly lower than human performance indicating that the dataset poses new challenges for future research. Our dataset is available at: https://math-qa.github.io/math-QA/

Generative Adversarial Networks (GANs), especially the recent style-based generators (StyleGANs), have versatile semantics in the structured latent space. Latent semantics discovery methods emerge to move around the latent code such that only one factor varies during the traversal. Recently, an unsupervised method proposed a promising direction to directly use the eigenvectors of the projection matrix that maps latent codes to features as the interpretable directions. However, one overlooked fact is that the projection matrix is non-orthogonal and the number of eigenvectors is too large. The non-orthogonality would entangle semantic attributes in the top few eigenvectors, and the large dimensionality might result in meaningless variations among the directions even if the matrix is orthogonal. To avoid these issues, we propose Householder Projector, a flexible and general low-rank orthogonal matrix representation based on Householder transformations, to parameterize the projection matrix. The orthogonality guarantees that the eigenvectors correspond to disentangled interpretable semantics, while the low-rank property encourages that each identified direction has meaningful variations. We integrate our projector into pre-trained StyleGAN2/StyleGAN3 and evaluate the models on several benchmarks. Within only 1% of the original training steps for fine-tuning, our projector helps StyleGANs to discover more disentangled and precise semantic attributes without sacrificing image fidelity.

A key aspect of text-to-image personalization methods is the manner in which the target concept is represented within the generative process. This choice greatly affects the visual fidelity, downstream editability, and disk space needed to store the learned concept. In this paper, we explore a new text-conditioning space that is dependent on both the denoising process timestep (time) and the denoising U-Net layers (space) and showcase its compelling properties. A single concept in the space-time representation is composed of hundreds of vectors, one for each combination of time and space, making this space challenging to optimize directly. Instead, we propose to implicitly represent a concept in this space by optimizing a small neural mapper that receives the current time and space parameters and outputs the matching token embedding. In doing so, the entire personalized concept is represented by the parameters of the learned mapper, resulting in a compact, yet expressive, representation. Similarly to other personalization methods, the output of our neural mapper resides in the input space of the text encoder. We observe that one can significantly improve the convergence and visual fidelity of the concept by introducing a textual bypass, where our neural mapper additionally outputs a residual that is added to the output of the text encoder. Finally, we show how one can impose an importance-based ordering over our implicit representation, providing users control over the reconstruction and editability of the learned concept using a single trained model. We demonstrate the effectiveness of our approach over a range of concepts and prompts, showing our method's ability to generate high-quality and controllable compositions without fine-tuning any parameters of the generative model itself.

In this paper, we focus on how artificial intelligence (AI) can be used to assist users in the creation of anime portraits, that is, converting rough sketches into anime portraits during their sketching process. The input is a sequence of incomplete freehand sketches that are gradually refined stroke by stroke, while the output is a sequence of high-quality anime portraits that correspond to the input sketches as guidance. Although recent GANs can generate high quality images, it is a challenging problem to maintain the high quality of generated images from sketches with a low degree of completion due to ill-posed problems in conditional image generation. Even with the latest sketch-to-image (S2I) technology, it is still difficult to create high-quality images from incomplete rough sketches for anime portraits since anime style tend to be more abstract than in realistic style. To address this issue, we adopt a latent space exploration of StyleGAN with a two-stage training strategy. We consider the input strokes of a freehand sketch to correspond to edge information-related attributes in the latent structural code of StyleGAN, and term the matching between strokes and these attributes stroke-level disentanglement. In the first stage, we trained an image encoder with the pre-trained StyleGAN model as a teacher encoder. In the second stage, we simulated the drawing process of the generated images without any additional data (labels) and trained the sketch encoder for incomplete progressive sketches to generate high-quality portrait images with feature alignment to the disentangled representations in the teacher encoder. We verified the proposed progressive S2I system with both qualitative and quantitative evaluations and achieved high-quality anime portraits from incomplete progressive sketches. Our user study proved its effectiveness in art creation assistance for the anime style.

Large deep learning models have achieved remarkable success but are resource-intensive, posing challenges such as memory usage. We introduce CURing, a novel model compression method based on CUR matrix decomposition, which approximates weight matrices as the product of selected columns (C) and rows (R), and a small linking matrix (U). We apply this decomposition to weights chosen based on the combined influence of their magnitudes and activations. By identifying and retaining informative rows and columns, CURing significantly reduces model size with minimal performance loss. For example, it reduces Llama3.1-8B's parameters to 7.32B (-9%) in just 129 seconds, over 20 times faster than prior compression methods.

Transformer models typically calculate attention matrices using dot products, which have limitations when capturing nonlinear relationships between embedding vectors. We propose Neural Attention, a technique that replaces dot products with feed-forward networks, enabling a more expressive representation of relationships between tokens. This approach modifies only the attention matrix calculation while preserving the matrix dimensions, making it easily adaptable to existing transformer-based architectures. We provide a detailed mathematical justification for why Neural Attention increases representational capacity and conduct controlled experiments to validate this claim. When comparing Neural Attention and Dot-Product Attention, NLP experiments on WikiText-103 show a reduction in perplexity of over 5 percent. Similarly, experiments on CIFAR-10 and CIFAR-100 show comparable improvements for image classification tasks. While Neural Attention introduces higher computational demands, we develop techniques to mitigate these challenges, ensuring practical usability without sacrificing the increased expressivity it provides. This work establishes Neural Attention as an effective means of enhancing the predictive capabilities of transformer models across a variety of applications.

We present FOMO60K, a large-scale, heterogeneous dataset of 60,529 brain Magnetic Resonance Imaging (MRI) scans from 13,900 sessions and 11,187 subjects, aggregated from 16 publicly available sources. The dataset includes both clinical- and research-grade images, multiple MRI sequences, and a wide range of anatomical and pathological variability, including scans with large brain anomalies. Minimal preprocessing was applied to preserve the original image characteristics while reducing barriers to entry for new users. Accompanying code for self-supervised pretraining and finetuning is provided. FOMO60K is intended to support the development and benchmarking of self-supervised learning methods in medical imaging at scale.

Countless learning tasks require dealing with sequential data. Image captioning, speech synthesis, and music generation all require that a model produce outputs that are sequences. In other domains, such as time series prediction, video analysis, and musical information retrieval, a model must learn from inputs that are sequences. Interactive tasks, such as translating natural language, engaging in dialogue, and controlling a robot, often demand both capabilities. Recurrent neural networks (RNNs) are connectionist models that capture the dynamics of sequences via cycles in the network of nodes. Unlike standard feedforward neural networks, recurrent networks retain a state that can represent information from an arbitrarily long context window. Although recurrent neural networks have traditionally been difficult to train, and often contain millions of parameters, recent advances in network architectures, optimization techniques, and parallel computation have enabled successful large-scale learning with them. In recent years, systems based on long short-term memory (LSTM) and bidirectional (BRNN) architectures have demonstrated ground-breaking performance on tasks as varied as image captioning, language translation, and handwriting recognition. In this survey, we review and synthesize the research that over the past three decades first yielded and then made practical these powerful learning models. When appropriate, we reconcile conflicting notation and nomenclature. Our goal is to provide a self-contained explication of the state of the art together with a historical perspective and references to primary research.

This tutorial note summarizes the presentation on ``Large Multimodal Models: Towards Building and Surpassing Multimodal GPT-4'', a part of CVPR 2023 tutorial on ``Recent Advances in Vision Foundation Models''. The tutorial consists of three parts. We first introduce the background on recent GPT-like large models for vision-and-language modeling to motivate the research in instruction-tuned large multimodal models (LMMs). As a pre-requisite, we describe the basics of instruction-tuning in large language models, which is further extended to the multimodal space. Lastly, we illustrate how to build the minimum prototype of multimodal GPT-4 like models with the open-source resource, and review the recently emerged topics.

Training algorithms, broadly construed, are an essential part of every deep learning pipeline. Training algorithm improvements that speed up training across a wide variety of workloads (e.g., better update rules, tuning protocols, learning rate schedules, or data selection schemes) could save time, save computational resources, and lead to better, more accurate, models. Unfortunately, as a community, we are currently unable to reliably identify training algorithm improvements, or even determine the state-of-the-art training algorithm. In this work, using concrete experiments, we argue that real progress in speeding up training requires new benchmarks that resolve three basic challenges faced by empirical comparisons of training algorithms: (1) how to decide when training is complete and precisely measure training time, (2) how to handle the sensitivity of measurements to exact workload details, and (3) how to fairly compare algorithms that require hyperparameter tuning. In order to address these challenges, we introduce a new, competitive, time-to-result benchmark using multiple workloads running on fixed hardware, the AlgoPerf: Training Algorithms benchmark. Our benchmark includes a set of workload variants that make it possible to detect benchmark submissions that are more robust to workload changes than current widely-used methods. Finally, we evaluate baseline submissions constructed using various optimizers that represent current practice, as well as other optimizers that have recently received attention in the literature. These baseline results collectively demonstrate the feasibility of our benchmark, show that non-trivial gaps between methods exist, and set a provisional state-of-the-art for future benchmark submissions to try and surpass.

Recently, recurrent models based on linear state space models (SSMs) have shown promising performance in language modeling (LM), competititve with transformers. However, there is little understanding of the in-principle abilities of such models, which could provide useful guidance to the search for better LM architectures. We present a comprehensive theoretical study of the capacity of such SSMs as it compares to that of transformers and traditional RNNs. We find that SSMs and transformers have overlapping but distinct strengths. In star-free state tracking, SSMs implement straightforward and exact solutions to problems that transformers struggle to represent exactly. They can also model bounded hierarchical structure with optimal memory even without simulating a stack. On the other hand, we identify a design choice in current SSMs that limits their expressive power. We discuss implications for SSM and LM research, and verify results empirically on a recent SSM, Mamba.

Pixel-based language models process text rendered as images, which allows them to handle any script, making them a promising approach to open vocabulary language modelling. However, recent approaches use text renderers that produce a large set of almost-equivalent input patches, which may prove sub-optimal for downstream tasks, due to redundancy in the input representations. In this paper, we investigate four approaches to rendering text in the PIXEL model (Rust et al., 2023), and find that simple character bigram rendering brings improved performance on sentence-level tasks without compromising performance on token-level or multilingual tasks. This new rendering strategy also makes it possible to train a more compact model with only 22M parameters that performs on par with the original 86M parameter model. Our analyses show that character bigram rendering leads to a consistently better model but with an anisotropic patch embedding space, driven by a patch frequency bias, highlighting the connections between image patch- and tokenization-based language models.

We conjecture that hidden state vectors corresponding to individual input tokens encode information sufficient to accurately predict several tokens ahead. More concretely, in this paper we ask: Given a hidden (internal) representation of a single token at position t in an input, can we reliably anticipate the tokens that will appear at positions geq t + 2? To test this, we measure linear approximation and causal intervention methods in GPT-J-6B to evaluate the degree to which individual hidden states in the network contain signal rich enough to predict future hidden states and, ultimately, token outputs. We find that, at some layers, we can approximate a model's output with more than 48% accuracy with respect to its prediction of subsequent tokens through a single hidden state. Finally we present a "Future Lens" visualization that uses these methods to create a new view of transformer states.

The neural semi-Markov Conditional Random Field (semi-CRF) framework has demonstrated promise for event-based piano transcription. In this framework, all events (notes or pedals) are represented as closed time intervals tied to specific event types. The neural semi-CRF approach requires an interval scoring matrix that assigns a score for every candidate interval. However, designing an efficient and expressive architecture for scoring intervals is not trivial. This paper introduces a simple method for scoring intervals using scaled inner product operations that resemble how attention scoring is done in transformers. We show theoretically that, due to the special structure from encoding the non-overlapping intervals, under a mild condition, the inner product operations are expressive enough to represent an ideal scoring matrix that can yield the correct transcription result. We then demonstrate that an encoder-only structured non-hierarchical transformer backbone, operating only on a low-time-resolution feature map, is capable of transcribing piano notes and pedals with high accuracy and time precision. The experiment shows that our approach achieves the new state-of-the-art performance across all subtasks in terms of the F1 measure on the Maestro dataset.

Designing machine learning architectures for processing neural networks in their raw weight matrix form is a newly introduced research direction. Unfortunately, the unique symmetry structure of deep weight spaces makes this design very challenging. If successful, such architectures would be capable of performing a wide range of intriguing tasks, from adapting a pre-trained network to a new domain to editing objects represented as functions (INRs or NeRFs). As a first step towards this goal, we present here a novel network architecture for learning in deep weight spaces. It takes as input a concatenation of weights and biases of a pre-trained MLP and processes it using a composition of layers that are equivariant to the natural permutation symmetry of the MLP's weights: Changing the order of neurons in intermediate layers of the MLP does not affect the function it represents. We provide a full characterization of all affine equivariant and invariant layers for these symmetries and show how these layers can be implemented using three basic operations: pooling, broadcasting, and fully connected layers applied to the input in an appropriate manner. We demonstrate the effectiveness of our architecture and its advantages over natural baselines in a variety of learning tasks.

We consider a family of linear systems A_mu alpha=C with system matrix A_mu depending on a parameter mu and for simplicity parameter-independent right-hand side C. These linear systems typically result from the finite-dimensional approximation of a parameter-dependent boundary-value problem. We derive a procedure based on the Empirical Interpolation Method to obtain a separated representation of the system matrix in the form A_muapproxsum_{m}beta_m(mu)A_{mu_m} for some selected values of the parameter. Such a separated representation is in particular useful in the Reduced Basis Method. The procedure is called nonintrusive since it only requires to access the matrices A_{mu_m}. As such, it offers a crucial advantage over existing approaches that instead derive separated representations requiring to enter the code at the level of assembly. Numerical examples illustrate the performance of our new procedure on a simple one-dimensional boundary-value problem and on three-dimensional acoustic scattering problems solved by a boundary element method.

Research on prompting has shown excellent performance with little or even no supervised training across many tasks. However, prompting for machine translation is still under-explored in the literature. We fill this gap by offering a systematic study on prompting strategies for translation, examining various factors for prompt template and demonstration example selection. We further explore the use of monolingual data and the feasibility of cross-lingual, cross-domain, and sentence-to-document transfer learning in prompting. Extensive experiments with GLM-130B (Zeng et al., 2022) as the testbed show that 1) the number and the quality of prompt examples matter, where using suboptimal examples degenerates translation; 2) several features of prompt examples, such as semantic similarity, show significant Spearman correlation with their prompting performance; yet, none of the correlations are strong enough; 3) using pseudo parallel prompt examples constructed from monolingual data via zero-shot prompting could improve translation; and 4) improved performance is achievable by transferring knowledge from prompt examples selected in other settings. We finally provide an analysis on the model outputs and discuss several problems that prompting still suffers from.

In this paper, we have studied the performance and role of local optimizers in quantum variational circuits. We studied the performance of the two most popular optimizers and compared their results with some popular classical machine learning algorithms. The classical algorithms we used in our study are support vector machine (SVM), gradient boosting (GB), and random forest (RF). These were compared with a variational quantum classifier (VQC) using two sets of local optimizers viz AQGD and COBYLA. For experimenting with VQC, IBM Quantum Experience and IBM Qiskit was used while for classical machine learning models, sci-kit learn was used. The results show that machine learning on noisy immediate scale quantum machines can produce comparable results as on classical machines. For our experiments, we have used a popular restaurant sentiment analysis dataset. The extracted features from this dataset and then after applying PCA reduced the feature set into 5 features. Quantum ML models were trained using 100 epochs and 150 epochs on using EfficientSU2 variational circuit. Overall, four Quantum ML models were trained and three Classical ML models were trained. The performance of the trained models was evaluated using standard evaluation measures viz, Accuracy, Precision, Recall, F-Score. In all the cases AQGD optimizer-based model with 100 Epochs performed better than all other models. It produced an accuracy of 77% and an F-Score of 0.785 which were highest across all the trained models.

State-Space Models (SSMs) have recently emerged as a powerful and efficient alternative to the long-standing transformer architecture. However, existing SSM conceptualizations retain deeply rooted biases from their roots in natural language processing. This constrains their ability to appropriately model the spatially-dependent characteristics of visual inputs. In this paper, we address these limitations by re-deriving modern selective state-space techniques, starting from a natively multidimensional formulation. Currently, prior works attempt to apply natively 1D SSMs to 2D data (i.e. images) by relying on arbitrary combinations of 1D scan directions to capture spatial dependencies. In contrast, Mamba2D improves upon this with a single 2D scan direction that factors in both dimensions of the input natively, effectively modelling spatial dependencies when constructing hidden states. Mamba2D shows comparable performance to prior adaptations of SSMs for vision tasks, on standard image classification evaluations with the ImageNet-1K dataset. Source code is available at https://github.com/cocoalex00/Mamba2D.

In this paper, we propose a speed-up approach for subclass discriminant analysis and formulate a novel efficient multi-view solution to it. The speed-up approach is developed based on graph embedding and spectral regression approaches that involve eigendecomposition of the corresponding Laplacian matrix and regression to its eigenvectors. We show that by exploiting the structure of the between-class Laplacian matrix, the eigendecomposition step can be substituted with a much faster process. Furthermore, we formulate a novel criterion for multi-view subclass discriminant analysis and show that an efficient solution for it can be obtained in a similar to the single-view manner. We evaluate the proposed methods on nine single-view and nine multi-view datasets and compare them with related existing approaches. Experimental results show that the proposed solutions achieve competitive performance, often outperforming the existing methods. At the same time, they significantly decrease the training time.

Covariance matrices have proven highly effective across many scientific fields. Since these matrices lie within the Symmetric Positive Definite (SPD) manifold - a Riemannian space with intrinsic non-Euclidean geometry, the primary challenge in representation learning is to respect this underlying geometric structure. Drawing inspiration from the success of Euclidean deep learning, researchers have developed neural networks on the SPD manifolds for more faithful covariance embedding learning. A notable advancement in this area is the implementation of Riemannian batch normalization (RBN), which has been shown to improve the performance of SPD network models. Nonetheless, the Riemannian metric beneath the existing RBN might fail to effectively deal with the ill-conditioned SPD matrices (ICSM), undermining the effectiveness of RBN. In contrast, the Bures-Wasserstein metric (BWM) demonstrates superior performance for ill-conditioning. In addition, the recently introduced Generalized BWM (GBWM) parameterizes the vanilla BWM via an SPD matrix, allowing for a more nuanced representation of vibrant geometries of the SPD manifold. Therefore, we propose a novel RBN algorithm based on the GBW geometry, incorporating a learnable metric parameter. Moreover, the deformation of GBWM by matrix power is also introduced to further enhance the representational capacity of GBWM-based RBN. Experimental results on different datasets validate the effectiveness of our proposed method.

This paper makes a formal connection between two families of widely used matrix factorization algorithms in numerical linear algebra. One family consists of the Jacobi eigenvalue algorithm and its variants for computing the Hermitian eigendecomposition and singular value decomposition. The other consists of Gaussian elimination and the Gram-Schmidt procedure with various pivoting rules for computing the Cholesky decomposition and QR decomposition respectively. Both families are cast as special cases of a more general class of factorization algorithms. We provide a randomized pivoting rule that applies to this general class (which differs substantially from the usual pivoting rules for Gaussian elimination / Gram-Schmidt) which results in the same linear rate of convergence for each algorithm, irrespective of which factorization it computes. A second important consequence of this randomized pivoting rule is a provable, effective bound on the numerical stability of the Jacobi eigenvalue algorithm, which addresses a longstanding open problem of Demmel and Veseli\'c `92.

In this paper, we address the challenge of Optical Music Recognition (OMR) for handwritten jazz lead sheets, a widely used musical score type that encodes melody and chords. The task is challenging due to the presence of chords, a score component not handled by existing OMR systems, and the high variability and quality issues associated with handwritten images. Our contribution is two-fold. We present a novel dataset consisting of 293 handwritten jazz lead sheets of 163 unique pieces, amounting to 2021 total staves aligned with Humdrum **kern and MusicXML ground truth scores. We also supply synthetic score images generated from the ground truth. The second contribution is the development of an OMR model for jazz lead sheets. We discuss specific tokenisation choices related to our kind of data, and the advantages of using synthetic scores and pretrained models. We publicly release all code, data, and models.

This paper proposes a method for the automatic creation of variables (in the case of regression) that complement the information contained in the initial input vector. The method works as a pre-processing step in which the continuous values of the variable to be regressed are discretized into a set of intervals which are then used to define value thresholds. Then classifiers are trained to predict whether the value to be regressed is less than or equal to each of these thresholds. The different outputs of the classifiers are then concatenated in the form of an additional vector of variables that enriches the initial vector of the regression problem. The implemented system can thus be considered as a generic pre-processing tool. We tested the proposed enrichment method with 5 types of regressors and evaluated it in 33 regression datasets. Our experimental results confirm the interest of the approach.

We develop a fast, tractable technique called Net-Trim for simplifying a trained neural network. The method is a convex post-processing module, which prunes (sparsifies) a trained network layer by layer, while preserving the internal responses. We present a comprehensive analysis of Net-Trim from both the algorithmic and sample complexity standpoints, centered on a fast, scalable convex optimization program. Our analysis includes consistency results between the initial and retrained models before and after Net-Trim application and guarantees on the number of training samples needed to discover a network that can be expressed using a certain number of nonzero terms. Specifically, if there is a set of weights that uses at most s terms that can re-create the layer outputs from the layer inputs, we can find these weights from O(slog N/s) samples, where N is the input size. These theoretical results are similar to those for sparse regression using the Lasso, and our analysis uses some of the same recently-developed tools (namely recent results on the concentration of measure and convex analysis). Finally, we propose an algorithmic framework based on the alternating direction method of multipliers (ADMM), which allows a fast and simple implementation of Net-Trim for network pruning and compression.

As robots are increasingly deployed in real-world scenarios, a key question is how to best transfer knowledge learned in one environment to another, where shifting constraints and human preferences render adaptation challenging. A central challenge remains that often, it is difficult (perhaps even impossible) to capture the full complexity of the deployment environment, and therefore the desired tasks, at training time. Consequently, the representation, or abstraction, of the tasks the human hopes for the robot to perform in one environment may be misaligned with the representation of the tasks that the robot has learned in another. We postulate that because humans will be the ultimate evaluator of system success in the world, they are best suited to communicating the aspects of the tasks that matter to the robot. Our key insight is that effective learning from human input requires first explicitly learning good intermediate representations and then using those representations for solving downstream tasks. We highlight three areas where we can use this approach to build interactive systems and offer future directions of work to better create advanced collaborative robots.

The paper discusses an approach to decipher large collections of handwritten index cards of historical dictionaries. Our study provides a working solution that reads the cards, and links their lemmas to a searchable list of dictionary entries, for a large historical dictionary entitled the Dictionary of the 17th- and 18th-century Polish, which comprizes 2.8 million index cards. We apply a tailored handwritten text recognition (HTR) solution that involves (1) an optimized detection model; (2) a recognition model to decipher the handwritten content, designed as a spatial transformer network (STN) followed by convolutional neural network (RCNN) with a connectionist temporal classification layer (CTC), trained using a synthetic set of 500,000 generated Polish words of different length; (3) a post-processing step using constrained Word Beam Search (WBC): the predictions were matched against a list of dictionary entries known in advance. Our model achieved the accuracy of 0.881 on the word level, which outperforms the base RCNN model. Within this study we produced a set of 20,000 manually annotated index cards that can be used for future benchmarks and transfer learning HTR applications.

Despite their widespread success, the application of deep neural networks to functional data remains scarce today. The infinite dimensionality of functional data means standard learning algorithms can be applied only after appropriate dimension reduction, typically achieved via basis expansions. Currently, these bases are chosen a priori without the information for the task at hand and thus may not be effective for the designated task. We instead propose to adaptively learn these bases in an end-to-end fashion. We introduce neural networks that employ a new Basis Layer whose hidden units are each basis functions themselves implemented as a micro neural network. Our architecture learns to apply parsimonious dimension reduction to functional inputs that focuses only on information relevant to the target rather than irrelevant variation in the input function. Across numerous classification/regression tasks with functional data, our method empirically outperforms other types of neural networks, and we prove that our approach is statistically consistent with low generalization error. Code is available at: https://github.com/jwyyy/AdaFNN.

The use of the structural similarity index (SSIM) is widespread. For almost two decades, it has played a major role in image quality assessment in many different research disciplines. Clearly, its merits are indisputable in the research community. However, little deep scrutiny of this index has been performed. Contrary to popular belief, there are some interesting properties of SSIM that merit such scrutiny. In this paper, we analyze the mathematical factors of SSIM and show that it can generate results, in both synthetic and realistic use cases, that are unexpected, sometimes undefined, and nonintuitive. As a consequence, assessing image quality based on SSIM can lead to incorrect conclusions and using SSIM as a loss function for deep learning can guide neural network training in the wrong direction.

For learning with noisy labels, the transition matrix, which explicitly models the relation between noisy label distribution and clean label distribution, has been utilized to achieve the statistical consistency of either the classifier or the risk. Previous researches have focused more on how to estimate this transition matrix well, rather than how to utilize it. We propose good utilization of the transition matrix is crucial and suggest a new utilization method based on resampling, coined RENT. Specifically, we first demonstrate current utilizations can have potential limitations for implementation. As an extension to Reweighting, we suggest the Dirichlet distribution-based per-sample Weight Sampling (DWS) framework, and compare reweighting and resampling under DWS framework. With the analyses from DWS, we propose RENT, a REsampling method with Noise Transition matrix. Empirically, RENT consistently outperforms existing transition matrix utilization methods, which includes reweighting, on various benchmark datasets. Our code is available at https://github.com/BaeHeeSun/RENT.

As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.

We propose PROSE-FD, a zero-shot multimodal PDE foundational model for simultaneous prediction of heterogeneous two-dimensional physical systems related to distinct fluid dynamics settings. These systems include shallow water equations and the Navier-Stokes equations with incompressible and compressible flow, regular and complex geometries, and different buoyancy settings. This work presents a new transformer-based multi-operator learning approach that fuses symbolic information to perform operator-based data prediction, i.e. non-autoregressive. By incorporating multiple modalities in the inputs, the PDE foundation model builds in a pathway for including mathematical descriptions of the physical behavior. We pre-train our foundation model on 6 parametric families of equations collected from 13 datasets, including over 60K trajectories. Our model outperforms popular operator learning, computer vision, and multi-physics models, in benchmark forward prediction tasks. We test our architecture choices with ablation studies.

We present the Manuscripts of Handwritten Arabic~(Muharaf) dataset, which is a machine learning dataset consisting of more than 1,600 historic handwritten page images transcribed by experts in archival Arabic. Each document image is accompanied by spatial polygonal coordinates of its text lines as well as basic page elements. This dataset was compiled to advance the state of the art in handwritten text recognition (HTR), not only for Arabic manuscripts but also for cursive text in general. The Muharaf dataset includes diverse handwriting styles and a wide range of document types, including personal letters, diaries, notes, poems, church records, and legal correspondences. In this paper, we describe the data acquisition pipeline, notable dataset features, and statistics. We also provide a preliminary baseline result achieved by training convolutional neural networks using this data.

Despite the remarkable capabilities of deep neural networks in image recognition, the dependence on activation functions remains a largely unexplored area and has yet to be eliminated. On the other hand, Polynomial Networks is a class of models that does not require activation functions, but have yet to perform on par with modern architectures. In this work, we aim close this gap and propose MONet, which relies solely on multilinear operators. The core layer of MONet, called Mu-Layer, captures multiplicative interactions of the elements of the input token. MONet captures high-degree interactions of the input elements and we demonstrate the efficacy of our approach on a series of image recognition and scientific computing benchmarks. The proposed model outperforms prior polynomial networks and performs on par with modern architectures. We believe that MONet can inspire further research on models that use entirely multilinear operations.

Attention operators have been applied on both 1-D data like texts and higher-order data such as images and videos. Use of attention operators on high-order data requires flattening of the spatial or spatial-temporal dimensions into a vector, which is assumed to follow a multivariate normal distribution. This not only incurs excessive requirements on computational resources, but also fails to preserve structures in data. In this work, we propose to avoid flattening by assuming the data follow matrix-variate normal distributions. Based on this new view, we develop Kronecker attention operators (KAOs) that operate on high-order tensor data directly. More importantly, the proposed KAOs lead to dramatic reductions in computational resources. Experimental results show that our methods reduce the amount of required computational resources by a factor of hundreds, with larger factors for higher-dimensional and higher-order data. Results also show that networks with KAOs outperform models without attention, while achieving competitive performance as those with original attention operators.

We introduce Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments. The method is straightforward to implement, is computationally efficient, has little memory requirements, is invariant to diagonal rescaling of the gradients, and is well suited for problems that are large in terms of data and/or parameters. The method is also appropriate for non-stationary objectives and problems with very noisy and/or sparse gradients. The hyper-parameters have intuitive interpretations and typically require little tuning. Some connections to related algorithms, on which Adam was inspired, are discussed. We also analyze the theoretical convergence properties of the algorithm and provide a regret bound on the convergence rate that is comparable to the best known results under the online convex optimization framework. Empirical results demonstrate that Adam works well in practice and compares favorably to other stochastic optimization methods. Finally, we discuss AdaMax, a variant of Adam based on the infinity norm.

With the goal of understanding the visual concepts that CLIP associates with text prompts, we show that the latent space of CLIP can be visualized solely in terms of linear transformations on simple geometric primitives like circles and straight lines. Although existing approaches achieve this by sketch-synthesis-through-optimization, they do so on the space of B\'ezier curves, which exhibit a wastefully large set of structures that they can evolve into, as most of them are non-essential for generating meaningful sketches. We present CLIPDrawX, an algorithm that provides significantly better visualizations for CLIP text embeddings, using only simple primitive shapes like straight lines and circles. This constrains the set of possible outputs to linear transformations on these primitives, thereby exhibiting an inherently simpler mathematical form. The synthesis process of CLIPDrawX can be tracked end-to-end, with each visual concept being explained exclusively in terms of primitives. Implementation will be released upon acceptance. Project Page: https://clipdrawx.github.io/{https://clipdrawx.github.io/}.

We present Gyan AI Paramanu ("atom"), a family of novel language models for Indian languages. It is a collection of auto-regressive monolingual, bilingual, and multilingual Indic language models pretrained from scratch on a single GPU for 10 Indian languages (Assamese, Bangla, Hindi, Konkani, Maithili, Marathi, Odia, Sanskrit, Tamil, Telugu) across 5 scripts (Bangla, Devanagari, Odia, Tamil, Telugu) of varying sizes ranging from 13.29M to 367.5M.The models are pretrained with a context size of 1024 on a single GPU. The models are very efficient, small, fast, and powerful. We have also developed an efficient most advanced Indic tokenizer that can even tokenize unseen languages. In order to avoid the "curse of multi-linguality" in our multilingual mParamanu model, we pretrained on comparable corpora by typological grouping using the same script. We performed human evaluation of our pretrained models for open end text generation on grammar, coherence, creativity, and factuality metrics for Bangla, Hindi, and Sanskrit. Our Bangla, Hindi, and Sanskrit models outperformed GPT-3.5-Turbo (ChatGPT), Bloom 7B, LLaMa-2 7B, OPT 6.7B, GPT-J 6B, GPTNeo 1.3B, GPT2-XL large language models (LLMs) by a large margin despite being smaller in size by 66 to 20 times compared to standard 7B LLMs. To run inference on our pretrained models, CPU is enough, and GPU is not needed. We also instruction-tuned our pretrained Bangla, Hindi, Marathi, Tamil, and Telugu models on 23k instructions in respective languages. Our pretrained and instruction-tuned models which are first of its kind, most powerful efficient small generative language models ever developed for Indic languages, and the various results lead to the conclusion that high quality generative language models are possible without high amount of compute power and humongous number of parameters. We plan to release our models at https://www.bharatgpts.com.

RNA plays a pivotal role in translating genetic instructions into functional outcomes, underscoring its importance in biological processes and disease mechanisms. Despite the emergence of numerous deep learning approaches for RNA, particularly universal RNA language models, there remains a significant lack of standardized benchmarks to assess the effectiveness of these methods. In this study, we introduce the first comprehensive RNA benchmark BEACON (BEnchmArk for COmprehensive RNA Task and Language Models). First, BEACON comprises 13 distinct tasks derived from extensive previous work covering structural analysis, functional studies, and engineering applications, enabling a comprehensive assessment of the performance of methods on various RNA understanding tasks. Second, we examine a range of models, including traditional approaches like CNNs, as well as advanced RNA foundation models based on language models, offering valuable insights into the task-specific performances of these models. Third, we investigate the vital RNA language model components from the tokenizer and positional encoding aspects. Notably, our findings emphasize the superiority of single nucleotide tokenization and the effectiveness of Attention with Linear Biases (ALiBi) over traditional positional encoding methods. Based on these insights, a simple yet strong baseline called BEACON-B is proposed, which can achieve outstanding performance with limited data and computational resources. The datasets and source code of our benchmark are available at https://github.com/terry-r123/RNABenchmark.

Large language models have been widely adopted but require significant GPU memory for inference. We develop a procedure for Int8 matrix multiplication for feed-forward and attention projection layers in transformers, which cut the memory needed for inference by half while retaining full precision performance. With our method, a 175B parameter 16/32-bit checkpoint can be loaded, converted to Int8, and used immediately without performance degradation. This is made possible by understanding and working around properties of highly systematic emergent features in transformer language models that dominate attention and transformer predictive performance. To cope with these features, we develop a two-part quantization procedure, LLM.int8(). We first use vector-wise quantization with separate normalization constants for each inner product in the matrix multiplication, to quantize most of the features. However, for the emergent outliers, we also include a new mixed-precision decomposition scheme, which isolates the outlier feature dimensions into a 16-bit matrix multiplication while still more than 99.9% of values are multiplied in 8-bit. Using LLM.int8(), we show empirically it is possible to perform inference in LLMs with up to 175B parameters without any performance degradation. This result makes such models much more accessible, for example making it possible to use OPT-175B/BLOOM on a single server with consumer GPUs. We open-source our software.

The Schr\"odinger Bridge (SB) is a powerful framework for solving generative modeling tasks such as unpaired domain translation. Most SB-related research focuses on continuous data space R^{D} and leaves open theoretical and algorithmic questions about applying SB methods to discrete data, e.g, on finite spaces S^{D}. Notable examples of such sets S are codebooks of vector-quantized (VQ) representations of modern autoencoders, tokens in texts, categories of atoms in molecules, etc. In this paper, we provide a theoretical and algorithmic foundation for solving SB in discrete spaces using the recently introduced Iterative Markovian Fitting (IMF) procedure. Specifically, we theoretically justify the convergence of discrete-time IMF (D-IMF) to SB in discrete spaces. This enables us to develop a practical computational algorithm for SB which we call Categorical Schr\"odinger Bridge Matching (CSBM). We show the performance of CSBM via a series of experiments with synthetic data and VQ representations of images.

Large language models (LLMs) have complicated internal dynamics, but induce representations of words and phrases whose geometry we can study. Human language processing is also opaque, but neural response measurements can provide (noisy) recordings of activation during listening or reading, from which we can extract similar representations of words and phrases. Here we study the extent to which the geometries induced by these representations, share similarities in the context of brain decoding. We find that the larger neural language models get, the more their representations are structurally similar to neural response measurements from brain imaging. Code is available at https://github.com/coastalcph/brainlm.

Transformer models are deployed in a wide range of settings, from multi-accelerator clusters to standalone mobile phones. The diverse inference constraints in these scenarios necessitate practitioners to train foundation models such as PaLM 2, Llama, & ViTs as a series of models of varying sizes. Due to significant training costs, only a select few model sizes are trained and supported, limiting more fine-grained control over relevant tradeoffs, including latency, cost, and accuracy. This work introduces MatFormer, a nested Transformer architecture designed to offer elasticity in a variety of deployment constraints. Each Feed Forward Network (FFN) block of a MatFormer model is jointly optimized with a few nested smaller FFN blocks. This training procedure allows for the Mix'n'Match of model granularities across layers -- i.e., a trained universal MatFormer model enables extraction of hundreds of accurate smaller models, which were never explicitly optimized. We empirically demonstrate MatFormer's effectiveness across different model classes (decoders & encoders), modalities (language & vision), and scales (up to 2.6B parameters). We find that a 2.6B decoder-only MatFormer language model (MatLM) allows us to extract smaller models spanning from 1.5B to 2.6B, each exhibiting comparable validation loss and one-shot downstream evaluations to their independently trained counterparts. Furthermore, we observe that smaller encoders extracted from a universal MatFormer-based ViT (MatViT) encoder preserve the metric-space structure for adaptive large-scale retrieval. Finally, we showcase that speculative decoding with the accurate and consistent submodels extracted from MatFormer can further reduce inference latency.

Computer-aided design (CAD) tools are utilized in the manufacturing industry for modeling everything from cups to spacecraft. These programs are complex to use and typically require years of training and experience to master. Structured and well-constrained 2D sketches and 3D constructions are crucial components of CAD modeling. A well-executed CAD model can be seamlessly integrated into the manufacturing process, thereby enhancing production efficiency. Deep generative models of 3D shapes and 3D object reconstruction models have garnered significant research interest. However, most of these models produce discrete forms of 3D objects that are not editable. Moreover, the few models based on CAD operations often have substantial input restrictions. In this work, we fine-tuned pre-trained models to create OpenECAD models (0.55B, 0.89B, 2.4B and 3.1B), leveraging the visual, logical, coding, and general capabilities of visual language models. OpenECAD models can process images of 3D designs as input and generate highly structured 2D sketches and 3D construction commands, ensuring that the designs are editable. These outputs can be directly used with existing CAD tools' APIs to generate project files. To train our network, we created a series of OpenECAD datasets. These datasets are derived from existing public CAD datasets, adjusted and augmented to meet the specific requirements of vision language model (VLM) training. Additionally, we have introduced an approach that utilizes dependency relationships to define and generate sketches, further enriching the content and functionality of the datasets.

Deep neural networks are widely used for classification. These deep models often suffer from a lack of interpretability -- they are particularly difficult to understand because of their non-linear nature. As a result, neural networks are often treated as "black box" models, and in the past, have been trained purely to optimize the accuracy of predictions. In this work, we create a novel network architecture for deep learning that naturally explains its own reasoning for each prediction. This architecture contains an autoencoder and a special prototype layer, where each unit of that layer stores a weight vector that resembles an encoded training input. The encoder of the autoencoder allows us to do comparisons within the latent space, while the decoder allows us to visualize the learned prototypes. The training objective has four terms: an accuracy term, a term that encourages every prototype to be similar to at least one encoded input, a term that encourages every encoded input to be close to at least one prototype, and a term that encourages faithful reconstruction by the autoencoder. The distances computed in the prototype layer are used as part of the classification process. Since the prototypes are learned during training, the learned network naturally comes with explanations for each prediction, and the explanations are loyal to what the network actually computes.

We study the capabilities of generative autoregressive transformer models trained on large amounts of symbolic solo-piano transcriptions. After first pretraining on approximately 60,000 hours of music, we use a comparatively smaller, high-quality subset, to finetune models to produce musical continuations, perform symbolic classification tasks, and produce general-purpose contrastive MIDI embeddings by adapting the SimCLR framework to symbolic music. When evaluating piano continuation coherence, our generative model outperforms leading symbolic generation techniques and remains competitive with proprietary audio generation models. On MIR classification benchmarks, frozen representations from our contrastive model achieve state-of-the-art results in linear probe experiments, while direct finetuning demonstrates the generalizability of pretrained representations, often requiring only a few hundred labeled examples to specialize to downstream tasks.

We begin the study of list-decodable linear regression using batches. In this setting only an alpha in (0,1] fraction of the batches are genuine. Each genuine batch contains ge n i.i.d. samples from a common unknown distribution and the remaining batches may contain arbitrary or even adversarial samples. We derive a polynomial time algorithm that for any nge tilde Omega(1/alpha) returns a list of size mathcal O(1/alpha^2) such that one of the items in the list is close to the true regression parameter. The algorithm requires only mathcal{O}(d/alpha^2) genuine batches and works under fairly general assumptions on the distribution. The results demonstrate the utility of batch structure, which allows for the first polynomial time algorithm for list-decodable regression, which may be impossible for the non-batch setting, as suggested by a recent SQ lower bound diakonikolas2021statistical for the non-batch setting.

Transformers have emerged as a powerful tool for a broad range of natural language processing tasks. A key component that drives the impressive performance of Transformers is the self-attention mechanism that encodes the influence or dependence of other tokens on each specific token. While beneficial, the quadratic complexity of self-attention on the input sequence length has limited its application to longer sequences -- a topic being actively studied in the community. To address this limitation, we propose Nystr\"{o}mformer -- a model that exhibits favorable scalability as a function of sequence length. Our idea is based on adapting the Nystr\"{o}m method to approximate standard self-attention with O(n) complexity. The scalability of Nystr\"{o}mformer enables application to longer sequences with thousands of tokens. We perform evaluations on multiple downstream tasks on the GLUE benchmark and IMDB reviews with standard sequence length, and find that our Nystr\"{o}mformer performs comparably, or in a few cases, even slightly better, than standard self-attention. On longer sequence tasks in the Long Range Arena (LRA) benchmark, Nystr\"{o}mformer performs favorably relative to other efficient self-attention methods. Our code is available at https://github.com/mlpen/Nystromformer.

The attention mechanism is a core primitive in modern large language models (LLMs) and AI more broadly. Since attention by itself is permutation-invariant, position encoding is essential for modeling structured domains such as language. Rotary position encoding (RoPE) has emerged as the de facto standard approach for position encoding and is part of many modern LLMs. However, in RoPE the key/query transformation between two elements in a sequence is only a function of their relative position and otherwise independent of the actual input. This limits the expressivity of RoPE-based transformers. This paper describes PaTH, a flexible data-dependent position encoding scheme based on accumulated products of Householder(like) transformations, where each transformation is data-dependent, i.e., a function of the input. We derive an efficient parallel algorithm for training through exploiting a compact representation of products of Householder matrices, and implement a FlashAttention-style blockwise algorithm that minimizes I/O cost. Across both targeted synthetic benchmarks and moderate-scale real-world language modeling experiments, we find that PaTH demonstrates superior performance compared to RoPE and other recent baselines.

We present Knesset-DictaBERT, a large Hebrew language model fine-tuned on the Knesset Corpus, which comprises Israeli parliamentary proceedings. The model is based on the DictaBERT architecture and demonstrates significant improvements in understanding parliamentary language according to the MLM task. We provide a detailed evaluation of the model's performance, showing improvements in perplexity and accuracy over the baseline DictaBERT model.

Self-supervised learning methods are gaining increasing traction in computer vision due to their recent success in reducing the gap with supervised learning. In natural language processing (NLP) self-supervised learning and transformers are already the methods of choice. The recent literature suggests that the transformers are becoming increasingly popular also in computer vision. So far, the vision transformers have been shown to work well when pretrained either using a large scale supervised data or with some kind of co-supervision, e.g. in terms of teacher network. These supervised pretrained vision transformers achieve very good results in downstream tasks with minimal changes. In this work we investigate the merits of self-supervised learning for pretraining image/vision transformers and then using them for downstream classification tasks. We propose Self-supervised vIsion Transformers (SiT) and discuss several self-supervised training mechanisms to obtain a pretext model. The architectural flexibility of SiT allows us to use it as an autoencoder and work with multiple self-supervised tasks seamlessly. We show that a pretrained SiT can be finetuned for a downstream classification task on small scale datasets, consisting of a few thousand images rather than several millions. The proposed approach is evaluated on standard datasets using common protocols. The results demonstrate the strength of the transformers and their suitability for self-supervised learning. We outperformed existing self-supervised learning methods by large margin. We also observed that SiT is good for few shot learning and also showed that it is learning useful representation by simply training a linear classifier on top of the learned features from SiT. Pretraining, finetuning, and evaluation codes will be available under: https://github.com/Sara-Ahmed/SiT.

We examine the geometry of neural network training using the Jacobian of trained network parameters with respect to their initial values. Our analysis reveals low-dimensional structure in the training process which is dependent on the input data but largely independent of the labels. We find that the singular value spectrum of the Jacobian matrix consists of three distinctive regions: a "chaotic" region of values orders of magnitude greater than one, a large "bulk" region of values extremely close to one, and a "stable" region of values less than one. Along each bulk direction, the left and right singular vectors are nearly identical, indicating that perturbations to the initialization are carried through training almost unchanged. These perturbations have virtually no effect on the network's output in-distribution, yet do have an effect far out-of-distribution. While the Jacobian applies only locally around a single initialization, we find substantial overlap in bulk subspaces for different random seeds. Our code is available at https://github.com/EleutherAI/training-jacobian

This paper explores the task of translating natural language queries into regular expressions which embody their meaning. In contrast to prior work, the proposed neural model does not utilize domain-specific crafting, learning to translate directly from a parallel corpus. To fully explore the potential of neural models, we propose a methodology for collecting a large corpus of regular expression, natural language pairs. Our resulting model achieves a performance gain of 19.6% over previous state-of-the-art models.

Neural Module Networks, originally proposed for the task of visual question answering, are a class of neural network architectures that involve human-specified neural modules, each designed for a specific form of reasoning. In current formulations of such networks only the parameters of the neural modules and/or the order of their execution is learned. In this work, we further expand this approach and also learn the underlying internal structure of modules in terms of the ordering and combination of simple and elementary arithmetic operators. Our results show that one is indeed able to simultaneously learn both internal module structure and module sequencing without extra supervisory signals for module execution sequencing. With this approach, we report performance comparable to models using hand-designed modules.

We propose a method to recommend music for an input video while allowing a user to guide music selection with free-form natural language. A key challenge of this problem setting is that existing music video datasets provide the needed (video, music) training pairs, but lack text descriptions of the music. This work addresses this challenge with the following three contributions. First, we propose a text-synthesis approach that relies on an analogy-based prompting procedure to generate natural language music descriptions from a large-scale language model (BLOOM-176B) given pre-trained music tagger outputs and a small number of human text descriptions. Second, we use these synthesized music descriptions to train a new trimodal model, which fuses text and video input representations to query music samples. For training, we introduce a text dropout regularization mechanism which we show is critical to model performance. Our model design allows for the retrieved music audio to agree with the two input modalities by matching visual style depicted in the video and musical genre, mood, or instrumentation described in the natural language query. Third, to evaluate our approach, we collect a testing dataset for our problem by annotating a subset of 4k clips from the YT8M-MusicVideo dataset with natural language music descriptions which we make publicly available. We show that our approach can match or exceed the performance of prior methods on video-to-music retrieval while significantly improving retrieval accuracy when using text guidance.

We review some recent applications of machine learning to algebraic geometry and physics. Since problems in algebraic geometry can typically be reformulated as mappings between tensors, this makes them particularly amenable to supervised learning. Additionally, unsupervised methods can provide insight into the structure of such geometrical data. At the heart of this programme is the question of how geometry can be machine learned, and indeed how AI helps one to do mathematics. This is a chapter contribution to the book Machine learning and Algebraic Geometry, edited by A. Kasprzyk et al.

Objective: Electroencephalography signals are recorded as a multidimensional dataset. We propose a new framework based on the augmented covariance extracted from an autoregressive model to improve motor imagery classification. Methods: From the autoregressive model can be derived the Yule-Walker equations, which show the emergence of a symmetric positive definite matrix: the augmented covariance matrix. The state-of the art for classifying covariance matrices is based on Riemannian Geometry. A fairly natural idea is therefore to extend the standard approach using these augmented covariance matrices. The methodology for creating the augmented covariance matrix shows a natural connection with the delay embedding theorem proposed by Takens for dynamical systems. Such an embedding method is based on the knowledge of two parameters: the delay and the embedding dimension, respectively related to the lag and the order of the autoregressive model. This approach provides new methods to compute the hyper-parameters in addition to standard grid search. Results: The augmented covariance matrix performed noticeably better than any state-of-the-art methods. We will test our approach on several datasets and several subjects using the MOABB framework, using both within-session and cross-session evaluation. Conclusion: The improvement in results is due to the fact that the augmented covariance matrix incorporates not only spatial but also temporal information, incorporating nonlinear components of the signal through an embedding procedure, which allows the leveraging of dynamical systems algorithms. Significance: These results extend the concepts and the results of the Riemannian distance based classification algorithm.

Despite its widespread use in neural networks, error backpropagation has faced criticism for its lack of biological plausibility, suffering from issues such as the backward locking problem and the weight transport problem. These limitations have motivated researchers to explore more biologically plausible learning algorithms that could potentially shed light on how biological neural systems adapt and learn. Inspired by the counter-current exchange mechanisms observed in biological systems, we propose counter-current learning (CCL), a biologically plausible framework for credit assignment in neural networks. This framework employs a feedforward network to process input data and a feedback network to process targets, with each network enhancing the other through anti-parallel signal propagation. By leveraging the more informative signals from the bottom layer of the feedback network to guide the updates of the top layer of the feedforward network and vice versa, CCL enables the simultaneous transformation of source inputs to target outputs and the dynamic mutual influence of these transformations. Experimental results on MNIST, FashionMNIST, CIFAR10, and CIFAR100 datasets using multi-layer perceptrons and convolutional neural networks demonstrate that CCL achieves comparable performance to other biologically plausible algorithms while offering a more biologically realistic learning mechanism. Furthermore, we showcase the applicability of our approach to an autoencoder task, underscoring its potential for unsupervised representation learning. Our work presents a direction for biologically inspired and plausible learning algorithms, offering an alternative mechanism of learning and adaptation in neural networks.

On-line handwritten character segmentation is often associated with handwriting recognition and even though recognition models include mechanisms to locate relevant positions during the recognition process, it is typically insufficient to produce a precise segmentation. Decoupling the segmentation from the recognition unlocks the potential to further utilize the result of the recognition. We specifically focus on the scenario where the transcription is known beforehand, in which case the character segmentation becomes an assignment problem between sampling points of the stylus trajectory and characters in the text. Inspired by the k-means clustering algorithm, we view it from the perspective of cluster assignment and present a Transformer-based architecture where each cluster is formed based on a learned character query in the Transformer decoder block. In order to assess the quality of our approach, we create character segmentation ground truths for two popular on-line handwriting datasets, IAM-OnDB and HANDS-VNOnDB, and evaluate multiple methods on them, demonstrating that our approach achieves the overall best results.

Understanding the internal representations learned by neural networks is a cornerstone challenge in the science of machine learning. While there have been significant recent strides in some cases towards understanding how neural networks implement specific target functions, this paper explores a complementary question -- why do networks arrive at particular computational strategies? Our inquiry focuses on the algebraic learning tasks of modular addition, sparse parities, and finite group operations. Our primary theoretical findings analytically characterize the features learned by stylized neural networks for these algebraic tasks. Notably, our main technique demonstrates how the principle of margin maximization alone can be used to fully specify the features learned by the network. Specifically, we prove that the trained networks utilize Fourier features to perform modular addition and employ features corresponding to irreducible group-theoretic representations to perform compositions in general groups, aligning closely with the empirical observations of Nanda et al. and Chughtai et al. More generally, we hope our techniques can help to foster a deeper understanding of why neural networks adopt specific computational strategies.

We develop machine translation and speech synthesis systems to complement the efforts of revitalizing Judeo-Spanish, the exiled language of Sephardic Jews, which survived for centuries, but now faces the threat of extinction in the digital age. Building on resources created by the Sephardic community of Turkey and elsewhere, we create corpora and tools that would help preserve this language for future generations. For machine translation, we first develop a Spanish to Judeo-Spanish rule-based machine translation system, in order to generate large volumes of synthetic parallel data in the relevant language pairs: Turkish, English and Spanish. Then, we train baseline neural machine translation engines using this synthetic data and authentic parallel data created from translations by the Sephardic community. For text-to-speech synthesis, we present a 3.5 hour single speaker speech corpus for building a neural speech synthesis engine. Resources, model weights and online inference engines are shared publicly.

Reading text in real-world scenarios often requires understanding the context surrounding it, especially when dealing with poor-quality text. However, current scene text recognizers are unaware of the bigger picture as they operate on cropped text images. In this study, we harness the representative capabilities of modern vision-language models, such as CLIP, to provide scene-level information to the crop-based recognizer. We achieve this by fusing a rich representation of the entire image, obtained from the vision-language model, with the recognizer word-level features via a gated cross-attention mechanism. This component gradually shifts to the context-enhanced representation, allowing for stable fine-tuning of a pretrained recognizer. We demonstrate the effectiveness of our model-agnostic framework, CLIPTER (CLIP TExt Recognition), on leading text recognition architectures and achieve state-of-the-art results across multiple benchmarks. Furthermore, our analysis highlights improved robustness to out-of-vocabulary words and enhanced generalization in low-data regimes.