Daily Papers

Self-tuning algorithms that adapt the learning process online encourage more effective and robust learning. Among all the methods available, meta-gradients have emerged as a promising approach. They leverage the differentiability of the learning rule with respect to some hyper-parameters to adapt them in an online fashion. Although meta-gradients can be accumulated over multiple learning steps to avoid myopic updates, this is rarely used in practice. In this work, we demonstrate that whilst multi-step meta-gradients do provide a better learning signal in expectation, this comes at the cost of a significant increase in variance, hindering performance. In the light of this analysis, we introduce a novel method mixing multiple inner steps that enjoys a more accurate and robust meta-gradient signal, essentially trading off bias and variance in meta-gradient estimation. When applied to the Snake game, the mixing meta-gradient algorithm can cut the variance by a factor of 3 while achieving similar or higher performance.

Large language models encode impressively broad world knowledge in their parameters. However, the knowledge in static language models falls out of date, limiting the model's effective "shelf life." While online fine-tuning can reduce this degradation, we find that naively fine-tuning on a stream of documents leads to a low level of information uptake. We hypothesize that online fine-tuning does not sufficiently attend to important information. That is, the gradient signal from important tokens representing factual information is drowned out by the gradient from inherently noisy tokens, suggesting that a dynamic, context-aware learning rate may be beneficial. We therefore propose learning which tokens to upweight. We meta-train a small, autoregressive model to reweight the language modeling loss for each token during online fine-tuning, with the objective of maximizing the out-of-date base question-answering model's ability to answer questions about a document after a single weighted gradient step. We call this approach Context-aware Meta-learned Loss Scaling (CaMeLS). Across three different distributions of documents, our experiments find that CaMeLS provides substantially improved information uptake on streams of thousands of documents compared with standard fine-tuning and baseline heuristics for reweighting token losses.

Neural fields, which represent signals as a function parameterized by a neural network, are a promising alternative to traditional discrete vector or grid-based representations. Compared to discrete representations, neural representations both scale well with increasing resolution, are continuous, and can be many-times differentiable. However, given a dataset of signals that we would like to represent, having to optimize a separate neural field for each signal is inefficient, and cannot capitalize on shared information or structures among signals. Existing generalization methods view this as a meta-learning problem and employ gradient-based meta-learning to learn an initialization which is then fine-tuned with test-time optimization, or learn hypernetworks to produce the weights of a neural field. We instead propose a new paradigm that views the large-scale training of neural representations as a part of a partially-observed neural process framework, and leverage neural process algorithms to solve this task. We demonstrate that this approach outperforms both state-of-the-art gradient-based meta-learning approaches and hypernetwork approaches.

Gradient-based meta-learning has proven to be highly effective at learning model initializations, representations, and update rules that allow fast adaptation from a few samples. The core idea behind these approaches is to use fast adaptation and generalization -- two second-order metrics -- as training signals on a meta-training dataset. However, little attention has been given to other possible second-order metrics. In this paper, we investigate a different training signal -- robustness to catastrophic interference -- and demonstrate that representations learned by directing minimizing interference are more conducive to incremental learning than those learned by just maximizing fast adaptation.

Coordinate-based neural representations have shown significant promise as an alternative to discrete, array-based representations for complex low dimensional signals. However, optimizing a coordinate-based network from randomly initialized weights for each new signal is inefficient. We propose applying standard meta-learning algorithms to learn the initial weight parameters for these fully-connected networks based on the underlying class of signals being represented (e.g., images of faces or 3D models of chairs). Despite requiring only a minor change in implementation, using these learned initial weights enables faster convergence during optimization and can serve as a strong prior over the signal class being modeled, resulting in better generalization when only partial observations of a given signal are available. We explore these benefits across a variety of tasks, including representing 2D images, reconstructing CT scans, and recovering 3D shapes and scenes from 2D image observations.

A major challenge in training large-scale machine learning models is configuring the training process to maximize model performance, i.e., finding the best training setup from a vast design space. In this work, we unlock a gradient-based approach to this problem. We first introduce an algorithm for efficiently calculating metagradients -- gradients through model training -- at scale. We then introduce a "smooth model training" framework that enables effective optimization using metagradients. With metagradient descent (MGD), we greatly improve on existing dataset selection methods, outperform accuracy-degrading data poisoning attacks by an order of magnitude, and automatically find competitive learning rate schedules.

Fully automating machine learning pipelines is one of the key challenges of current artificial intelligence research, since practical machine learning often requires costly and time-consuming human-powered processes such as model design, algorithm development, and hyperparameter tuning. In this paper, we verify that automated architecture search synergizes with the effect of gradient-based meta learning. We adopt the progressive neural architecture search liu:pnas_google:DBLP:journals/corr/abs-1712-00559 to find optimal architectures for meta-learners. The gradient based meta-learner whose architecture was automatically found achieved state-of-the-art results on the 5-shot 5-way Mini-ImageNet classification problem with 74.65% accuracy, which is 11.54% improvement over the result obtained by the first gradient-based meta-learner called MAML finn:maml:DBLP:conf/icml/FinnAL17. To our best knowledge, this work is the first successful neural architecture search implementation in the context of meta learning.

Pre-training (PT) followed by fine-tuning (FT) is an effective method for training neural networks, and has led to significant performance improvements in many domains. PT can incorporate various design choices such as task and data reweighting strategies, augmentation policies, and noise models, all of which can significantly impact the quality of representations learned. The hyperparameters introduced by these strategies therefore must be tuned appropriately. However, setting the values of these hyperparameters is challenging. Most existing methods either struggle to scale to high dimensions, are too slow and memory-intensive, or cannot be directly applied to the two-stage PT and FT learning process. In this work, we propose an efficient, gradient-based algorithm to meta-learn PT hyperparameters. We formalize the PT hyperparameter optimization problem and propose a novel method to obtain PT hyperparameter gradients by combining implicit differentiation and backpropagation through unrolled optimization. We demonstrate that our method improves predictive performance on two real-world domains. First, we optimize high-dimensional task weighting hyperparameters for multitask pre-training on protein-protein interaction graphs and improve AUROC by up to 3.9%. Second, we optimize a data augmentation neural network for self-supervised PT with SimCLR on electrocardiography data and improve AUROC by up to 1.9%.

We propose an algorithm for meta-learning that is model-agnostic, in the sense that it is compatible with any model trained with gradient descent and applicable to a variety of different learning problems, including classification, regression, and reinforcement learning. The goal of meta-learning is to train a model on a variety of learning tasks, such that it can solve new learning tasks using only a small number of training samples. In our approach, the parameters of the model are explicitly trained such that a small number of gradient steps with a small amount of training data from a new task will produce good generalization performance on that task. In effect, our method trains the model to be easy to fine-tune. We demonstrate that this approach leads to state-of-the-art performance on two few-shot image classification benchmarks, produces good results on few-shot regression, and accelerates fine-tuning for policy gradient reinforcement learning with neural network policies.

Iterative methods are ubiquitous in large-scale scientific computing applications, and a number of approaches based on meta-learning have been recently proposed to accelerate them. However, a systematic study of these approaches and how they differ from meta-learning is lacking. In this paper, we propose a framework to analyze such learning-based acceleration approaches, where one can immediately identify a departure from classical meta-learning. We show that this departure may lead to arbitrary deterioration of model performance. Based on our analysis, we introduce a novel training method for learning-based acceleration of iterative methods. Furthermore, we theoretically prove that the proposed method improves upon the existing methods, and demonstrate its significant advantage and versatility through various numerical applications.

It is believed that Gradient Descent (GD) induces an implicit bias towards good generalization in training machine learning models. This paper provides a fine-grained analysis of the dynamics of GD for the matrix sensing problem, whose goal is to recover a low-rank ground-truth matrix from near-isotropic linear measurements. It is shown that GD with small initialization behaves similarly to the greedy low-rank learning heuristics (Li et al., 2020) and follows an incremental learning procedure (Gissin et al., 2019): GD sequentially learns solutions with increasing ranks until it recovers the ground truth matrix. Compared to existing works which only analyze the first learning phase for rank-1 solutions, our result provides characterizations for the whole learning process. Moreover, besides the over-parameterized regime that many prior works focused on, our analysis of the incremental learning procedure also applies to the under-parameterized regime. Finally, we conduct numerical experiments to confirm our theoretical findings.

We propose a new dataset distillation algorithm using reparameterization and convexification of implicit gradients (RCIG), that substantially improves the state-of-the-art. To this end, we first formulate dataset distillation as a bi-level optimization problem. Then, we show how implicit gradients can be effectively used to compute meta-gradient updates. We further equip the algorithm with a convexified approximation that corresponds to learning on top of a frozen finite-width neural tangent kernel. Finally, we improve bias in implicit gradients by parameterizing the neural network to enable analytical computation of final-layer parameters given the body parameters. RCIG establishes the new state-of-the-art on a diverse series of dataset distillation tasks. Notably, with one image per class, on resized ImageNet, RCIG sees on average a 108% improvement over the previous state-of-the-art distillation algorithm. Similarly, we observed a 66% gain over SOTA on Tiny-ImageNet and 37% on CIFAR-100.

Metalenses offer significant potential for ultra-compact computational imaging but face challenges from complex optical degradation and computational restoration difficulties. Existing methods typically rely on precise optical calibration or massive paired datasets, which are non-trivial for real-world imaging systems. Furthermore, a lack of control over the inference process often results in undesirable hallucinated artifacts. We introduce Degradation-Modeled Multipath Diffusion for tunable metalens photography, leveraging powerful natural image priors from pretrained models instead of large datasets. Our framework uses positive, neutral, and negative-prompt paths to balance high-frequency detail generation, structural fidelity, and suppression of metalens-specific degradation, alongside pseudo data augmentation. A tunable decoder enables controlled trade-offs between fidelity and perceptual quality. Additionally, a spatially varying degradation-aware attention (SVDA) module adaptively models complex optical and sensor-induced degradation. Finally, we design and build a millimeter-scale MetaCamera for real-world validation. Extensive results show that our approach outperforms state-of-the-art methods, achieving high-fidelity and sharp image reconstruction. More materials: https://dmdiff.github.io/.

This paper introduces WaveGrad, a conditional model for waveform generation which estimates gradients of the data density. The model is built on prior work on score matching and diffusion probabilistic models. It starts from a Gaussian white noise signal and iteratively refines the signal via a gradient-based sampler conditioned on the mel-spectrogram. WaveGrad offers a natural way to trade inference speed for sample quality by adjusting the number of refinement steps, and bridges the gap between non-autoregressive and autoregressive models in terms of audio quality. We find that it can generate high fidelity audio samples using as few as six iterations. Experiments reveal WaveGrad to generate high fidelity audio, outperforming adversarial non-autoregressive baselines and matching a strong likelihood-based autoregressive baseline using fewer sequential operations. Audio samples are available at https://wavegrad.github.io/.

Sparse training is emerging as a promising avenue for reducing the computational cost of training neural networks. Several recent studies have proposed pruning methods using learnable thresholds to efficiently explore the non-uniform distribution of sparsity inherent within the models. In this paper, we propose Gradient Annealing (GA), where gradients of masked weights are scaled down in a non-linear manner. GA provides an elegant trade-off between sparsity and accuracy without the need for additional sparsity-inducing regularization. We integrated GA with the latest learnable pruning methods to create an automated sparse training algorithm called AutoSparse, which achieves better accuracy and/or training/inference FLOPS reduction than existing learnable pruning methods for sparse ResNet50 and MobileNetV1 on ImageNet-1K: AutoSparse achieves (2x, 7x) reduction in (training,inference) FLOPS for ResNet50 on ImageNet at 80% sparsity. Finally, AutoSparse outperforms sparse-to-sparse SotA method MEST (uniform sparsity) for 80% sparse ResNet50 with similar accuracy, where MEST uses 12% more training FLOPS and 50% more inference FLOPS.

Recent research in medical image analysis with deep learning almost exclusively focuses on grid- or voxel-based data representations. We challenge this common choice by introducing MedFuncta, a modality-agnostic continuous data representation based on neural fields. We demonstrate how to scale neural fields from single instances to large datasets by exploiting redundancy in medical signals and by applying an efficient meta-learning approach with a context reduction scheme. We further address the spectral bias in commonly used SIREN activations, by introducing an omega_0-schedule, improving reconstruction quality and convergence speed. We validate our proposed approach on a large variety of medical signals of different dimensions and modalities (1D: ECG; 2D: Chest X-ray, Retinal OCT, Fundus Camera, Dermatoscope, Colon Histopathology, Cell Microscopy; 3D: Brain MRI, Lung CT) and successfully demonstrate that we can solve relevant downstream tasks on these representations. We additionally release a large-scale dataset of > 550k annotated neural fields to promote research in this direction.

Learned optimizers (LOs) can significantly reduce the wall-clock training time of neural networks, substantially reducing training costs. However, they often suffer from poor meta-generalization, especially when training networks larger than those seen during meta-training. To address this, we use the recently proposed Maximal Update Parametrization (muP), which allows zero-shot generalization of optimizer hyperparameters from smaller to larger models. We extend muP theory to learned optimizers, treating the meta-training problem as finding the learned optimizer under muP. Our evaluation shows that LOs meta-trained with muP substantially improve meta-generalization as compared to LOs trained under standard parametrization (SP). Notably, when applied to large-width models, our best muLO, trained for 103 GPU-hours, matches or exceeds the performance of VeLO, the largest publicly available learned optimizer, meta-trained with 4000 TPU-months of compute. Moreover, muLOs demonstrate better generalization than their SP counterparts to deeper networks and to much longer training horizons (25 times longer) than those seen during meta-training.

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.

Can meta-learning discover generic ways of processing time series (TS) from a diverse dataset so as to greatly improve generalization on new TS coming from different datasets? This work provides positive evidence to this using a broad meta-learning framework which we show subsumes many existing meta-learning algorithms. Our theoretical analysis suggests that residual connections act as a meta-learning adaptation mechanism, generating a subset of task-specific parameters based on a given TS input, thus gradually expanding the expressive power of the architecture on-the-fly. The same mechanism is shown via linearization analysis to have the interpretation of a sequential update of the final linear layer. Our empirical results on a wide range of data emphasize the importance of the identified meta-learning mechanisms for successful zero-shot univariate forecasting, suggesting that it is viable to train a neural network on a source TS dataset and deploy it on a different target TS dataset without retraining, resulting in performance that is at least as good as that of state-of-practice univariate forecasting models.

Gradient regularization (GR) is a method that penalizes the gradient norm of the training loss during training. While some studies have reported that GR can improve generalization performance, little attention has been paid to it from the algorithmic perspective, that is, the algorithms of GR that efficiently improve the performance. In this study, we first reveal that a specific finite-difference computation, composed of both gradient ascent and descent steps, reduces the computational cost of GR. Next, we show that the finite-difference computation also works better in the sense of generalization performance. We theoretically analyze a solvable model, a diagonal linear network, and clarify that GR has a desirable implicit bias to so-called rich regime and finite-difference computation strengthens this bias. Furthermore, finite-difference GR is closely related to some other algorithms based on iterative ascent and descent steps for exploring flat minima. In particular, we reveal that the flooding method can perform finite-difference GR in an implicit way. Thus, this work broadens our understanding of GR for both practice and theory.

Popular machine learning approaches forgo second-order information due to the difficulty of computing curvature in high dimensions. We present FOSI, a novel meta-algorithm that improves the performance of any base first-order optimizer by efficiently incorporating second-order information during the optimization process. In each iteration, FOSI implicitly splits the function into two quadratic functions defined on orthogonal subspaces, then uses a second-order method to minimize the first, and the base optimizer to minimize the other. We formally analyze FOSI's convergence and the conditions under which it improves a base optimizer. Our empirical evaluation demonstrates that FOSI improves the convergence rate and optimization time of first-order methods such as Heavy-Ball and Adam, and outperforms second-order methods (K-FAC and L-BFGS).

Machine learning methods can be a valuable aid in the scientific process, but they need to face challenging settings where data come from inhomogeneous experimental conditions. Recent meta-learning methods have made significant progress in multi-task learning, but they rely on black-box neural networks, resulting in high computational costs and limited interpretability. Leveraging the structure of the learning problem, we argue that multi-environment generalization can be achieved using a simpler learning model, with an affine structure with respect to the learning task. Crucially, we prove that this architecture can identify the physical parameters of the system, enabling interpreable learning. We demonstrate the competitive generalization performance and the low computational cost of our method by comparing it to state-of-the-art algorithms on physical systems, ranging from toy models to complex, non-analytical systems. The interpretability of our method is illustrated with original applications to physical-parameter-induced adaptation and to adaptive control.

Model-Agnostic Meta-Learning (MAML) has become increasingly popular for training models that can quickly adapt to new tasks via one or few stochastic gradient descent steps. However, the MAML objective is significantly more difficult to optimize compared to standard non-adaptive learning (NAL), and little is understood about how much MAML improves over NAL in terms of the fast adaptability of their solutions in various scenarios. We analytically address this issue in a linear regression setting consisting of a mixture of easy and hard tasks, where hardness is related to the rate that gradient descent converges on the task. Specifically, we prove that in order for MAML to achieve substantial gain over NAL, (i) there must be some discrepancy in hardness among the tasks, and (ii) the optimal solutions of the hard tasks must be closely packed with the center far from the center of the easy tasks optimal solutions. We also give numerical and analytical results suggesting that these insights apply to two-layer neural networks. Finally, we provide few-shot image classification experiments that support our insights for when MAML should be used and emphasize the importance of training MAML on hard tasks in practice.

Post-hoc gradient-based interpretability methods [Simonyan et al., 2013, Smilkov et al., 2017] that provide instance-specific explanations of model predictions are often based on assumption (A): magnitude of input gradients -- gradients of logits with respect to input -- noisily highlight discriminative task-relevant features. In this work, we test the validity of assumption (A) using a three-pronged approach. First, we develop an evaluation framework, DiffROAR, to test assumption (A) on four image classification benchmarks. Our results suggest that (i) input gradients of standard models (i.e., trained on original data) may grossly violate (A), whereas (ii) input gradients of adversarially robust models satisfy (A). Second, we introduce BlockMNIST, an MNIST-based semi-real dataset, that by design encodes a priori knowledge of discriminative features. Our analysis on BlockMNIST leverages this information to validate as well as characterize differences between input gradient attributions of standard and robust models. Finally, we theoretically prove that our empirical findings hold on a simplified version of the BlockMNIST dataset. Specifically, we prove that input gradients of standard one-hidden-layer MLPs trained on this dataset do not highlight instance-specific signal coordinates, thus grossly violating assumption (A). Our findings motivate the need to formalize and test common assumptions in interpretability in a falsifiable manner [Leavitt and Morcos, 2020]. We believe that the DiffROAR evaluation framework and BlockMNIST-based datasets can serve as sanity checks to audit instance-specific interpretability methods; code and data available at https://github.com/harshays/inputgradients.

Post-Training Quantization (PTQ) has received significant attention because it requires only a small set of calibration data to quantize a full-precision model, which is more practical in real-world applications in which full access to a large training set is not available. However, it often leads to overfitting on the small calibration dataset. Several methods have been proposed to address this issue, yet they still rely on only the calibration set for the quantization and they do not validate the quantized model due to the lack of a validation set. In this work, we propose a novel meta-learning based approach to enhance the performance of post-training quantization. Specifically, to mitigate the overfitting problem, instead of only training the quantized model using the original calibration set without any validation during the learning process as in previous PTQ works, in our approach, we both train and validate the quantized model using two different sets of images. In particular, we propose a meta-learning based approach to jointly optimize a transformation network and a quantized model through bi-level optimization. The transformation network modifies the original calibration data and the modified data will be used as the training set to learn the quantized model with the objective that the quantized model achieves a good performance on the original calibration data. Extensive experiments on the widely used ImageNet dataset with different neural network architectures demonstrate that our approach outperforms the state-of-the-art PTQ methods.

The goal of few-shot learning is to generalize and achieve high performance on new unseen learning tasks, where each task has only a limited number of examples available. Gradient-based meta-learning attempts to address this challenging task by learning how to learn new tasks by embedding inductive biases informed by prior learning experiences into the components of the learning algorithm. In this work, we build upon prior research and propose Neural Procedural Bias Meta-Learning (NPBML), a novel framework designed to meta-learn task-adaptive procedural biases. Our approach aims to consolidate recent advancements in meta-learned initializations, optimizers, and loss functions by learning them simultaneously and making them adapt to each individual task to maximize the strength of the learned inductive biases. This imbues each learning task with a unique set of procedural biases which is specifically designed and selected to attain strong learning performance in only a few gradient steps. The experimental results show that by meta-learning the procedural biases of a neural network, we can induce strong inductive biases towards a distribution of learning tasks, enabling robust learning performance across many well-established few-shot learning benchmarks.

Nesterov's accelerated gradient (AG) is a popular technique to optimize objective functions comprising two components: a convex loss and a penalty function. While AG methods perform well for convex penalties, such as the LASSO, convergence issues may arise when it is applied to nonconvex penalties, such as SCAD. A recent proposal generalizes Nesterov's AG method to the nonconvex setting. The proposed algorithm requires specification of several hyperparameters for its practical application. Aside from some general conditions, there is no explicit rule for selecting the hyperparameters, and how different selection can affect convergence of the algorithm. In this article, we propose a hyperparameter setting based on the complexity upper bound to accelerate convergence, and consider the application of this nonconvex AG algorithm to high-dimensional linear and logistic sparse learning problems. We further establish the rate of convergence and present a simple and useful bound to characterize our proposed optimal damping sequence. Simulation studies show that convergence can be made, on average, considerably faster than that of the conventional proximal gradient algorithm. Our experiments also show that the proposed method generally outperforms the current state-of-the-art methods in terms of signal recovery.

Learning compact discrete representations of data is a key task on its own or for facilitating subsequent processing of data. In this paper we present a model that produces Discrete InfoMax Codes (DIMCO); we learn a probabilistic encoder that yields k-way d-dimensional codes associated with input data. Our model's learning objective is to maximize the mutual information between codes and labels with a regularization, which enforces entries of a codeword to be as independent as possible. We show that the infomax principle also justifies previous loss functions (e.g., cross-entropy) as its special cases. Our analysis also shows that using shorter codes, as DIMCO does, reduces overfitting in the context of few-shot classification. Through experiments in various domains, we observe this implicit meta-regularization effect of DIMCO. Furthermore, we show that the codes learned by DIMCO are efficient in terms of both memory and retrieval time compared to previous methods.

The backpropagation algorithm has long been the canonical training method for neural networks. Modern paradigms are implicitly optimized for it, and numerous guidelines exist to ensure its proper use. Recently, synthetic gradients methods -where the error gradient is only roughly approximated - have garnered interest. These methods not only better portray how biological brains are learning, but also open new computational possibilities, such as updating layers asynchronously. Even so, they have failed to scale past simple tasks like MNIST or CIFAR-10. This is in part due to a lack of standards, leading to ill-suited models and practices forbidding such methods from performing to the best of their abilities. In this work, we focus on direct feedback alignment and present a set of best practices justified by observations of the alignment angles. We characterize a bottleneck effect that prevents alignment in narrow layers, and hypothesize it may explain why feedback alignment methods have yet to scale to large convolutional networks.

A major goal of unsupervised learning is to discover data representations that are useful for subsequent tasks, without access to supervised labels during training. Typically, this involves minimizing a surrogate objective, such as the negative log likelihood of a generative model, with the hope that representations useful for subsequent tasks will arise as a side effect. In this work, we propose instead to directly target later desired tasks by meta-learning an unsupervised learning rule which leads to representations useful for those tasks. Specifically, we target semi-supervised classification performance, and we meta-learn an algorithm -- an unsupervised weight update rule -- that produces representations useful for this task. Additionally, we constrain our unsupervised update rule to a be a biologically-motivated, neuron-local function, which enables it to generalize to different neural network architectures, datasets, and data modalities. We show that the meta-learned update rule produces useful features and sometimes outperforms existing unsupervised learning techniques. We further show that the meta-learned unsupervised update rule generalizes to train networks with different widths, depths, and nonlinearities. It also generalizes to train on data with randomly permuted input dimensions and even generalizes from image datasets to a text task.

Meta-learning algorithms are able to learn a new task using previously learned knowledge, but they often require a large number of meta-training tasks which may not be readily available. To address this issue, we propose a method for few-shot learning with fewer tasks, which we call MetaModulation. The key idea is to use a neural network to increase the density of the meta-training tasks by modulating batch normalization parameters during meta-training. Additionally, we modify parameters at various network levels, rather than just a single layer, to increase task diversity. To account for the uncertainty caused by the limited training tasks, we propose a variational MetaModulation where the modulation parameters are treated as latent variables. We also introduce learning variational feature hierarchies by the variational MetaModulation, which modulates features at all layers and can consider task uncertainty and generate more diverse tasks. The ablation studies illustrate the advantages of utilizing a learnable task modulation at different levels and demonstrate the benefit of incorporating probabilistic variants in few-task meta-learning. Our MetaModulation and its variational variants consistently outperform state-of-the-art alternatives on four few-task meta-learning benchmarks.

Second-order training methods have better convergence properties than gradient descent but are rarely used in practice for large-scale training due to their computational overhead. This can be viewed as a hardware limitation (imposed by digital computers). Here we show that natural gradient descent (NGD), a second-order method, can have a similar computational complexity per iteration to a first-order method, when employing appropriate hardware. We present a new hybrid digital-analog algorithm for training neural networks that is equivalent to NGD in a certain parameter regime but avoids prohibitively costly linear system solves. Our algorithm exploits the thermodynamic properties of an analog system at equilibrium, and hence requires an analog thermodynamic computer. The training occurs in a hybrid digital-analog loop, where the gradient and Fisher information matrix (or any other positive semi-definite curvature matrix) are calculated at given time intervals while the analog dynamics take place. We numerically demonstrate the superiority of this approach over state-of-the-art digital first- and second-order training methods on classification tasks and language model fine-tuning tasks.

Bilevel optimization has been recently revisited for designing and analyzing algorithms in hyperparameter tuning and meta learning tasks. However, due to its nested structure, evaluating exact gradients for high-dimensional problems is computationally challenging. One heuristic to circumvent this difficulty is to use the approximate gradient given by performing truncated back-propagation through the iterative optimization procedure that solves the lower-level problem. Although promising empirical performance has been reported, its theoretical properties are still unclear. In this paper, we analyze the properties of this family of approximate gradients and establish sufficient conditions for convergence. We validate this on several hyperparameter tuning and meta learning tasks. We find that optimization with the approximate gradient computed using few-step back-propagation often performs comparably to optimization with the exact gradient, while requiring far less memory and half the computation time.

A central challenge to many fields of science and engineering involves minimizing non-convex error functions over continuous, high dimensional spaces. Gradient descent or quasi-Newton methods are almost ubiquitously used to perform such minimizations, and it is often thought that a main source of difficulty for the ability of these local methods to find the global minimum is the proliferation of local minima with much higher error than the global minimum. Here we argue, based on results from statistical physics, random matrix theory, and neural network theory, that a deeper and more profound difficulty originates from the proliferation of saddle points, not local minima, especially in high dimensional problems of practical interest. Such saddle points are surrounded by high error plateaus that can dramatically slow down learning, and give the illusory impression of the existence of a local minimum. Motivated by these arguments, we propose a new algorithm, the saddle-free Newton method, that can rapidly escape high dimensional saddle points, unlike gradient descent and quasi-Newton methods. We apply this algorithm to deep neural network training, and provide preliminary numerical evidence for its superior performance.

Meta-learning has emerged as a powerful approach to train neural networks to learn new tasks quickly from limited data. Broad exposure to different tasks leads to versatile representations enabling general problem solving. But, what are the limits of meta-learning? In this work, we explore the potential of amortizing the most powerful universal predictor, namely Solomonoff Induction (SI), into neural networks via leveraging meta-learning to its limits. We use Universal Turing Machines (UTMs) to generate training data used to expose networks to a broad range of patterns. We provide theoretical analysis of the UTM data generation processes and meta-training protocols. We conduct comprehensive experiments with neural architectures (e.g. LSTMs, Transformers) and algorithmic data generators of varying complexity and universality. Our results suggest that UTM data is a valuable resource for meta-learning, and that it can be used to train neural networks capable of learning universal prediction strategies.

Metamaterials, engineered materials with architected structures across multiple length scales, offer unprecedented and tunable mechanical properties that surpass those of conventional materials. However, leveraging advanced machine learning (ML) for metamaterial discovery is hindered by three fundamental challenges: (C1) Data Heterogeneity Challenge arises from heterogeneous data sources, heterogeneous composition scales, and heterogeneous structure categories; (C2) Model Complexity Challenge stems from the intricate geometric constraints of ML models, which complicate their adaptation to metamaterial structures; and (C3) Human-AI Collaboration Challenge comes from the "dual black-box'' nature of sophisticated ML models and the need for intuitive user interfaces. To tackle these challenges, we introduce a unified framework, named MetamatBench, that operates on three levels. (1) At the data level, we integrate and standardize 5 heterogeneous, multi-modal metamaterial datasets. (2) The ML level provides a comprehensive toolkit that adapts 17 state-of-the-art ML methods for metamaterial discovery. It also includes a comprehensive evaluation suite with 12 novel performance metrics with finite element-based assessments to ensure accurate and reliable model validation. (3) The user level features a visual-interactive interface that bridges the gap between complex ML techniques and non-ML researchers, advancing property prediction and inverse design of metamaterials for research and applications. MetamatBench offers a unified platform deployed at http://zhoulab-1.cs.vt.edu:5550 that enables machine learning researchers and practitioners to develop and evaluate new methodologies in metamaterial discovery. For accessibility and reproducibility, we open-source our benchmark and the codebase at https://github.com/cjpcool/Metamaterial-Benchmark.

We introduce a framework based on bilevel programming that unifies gradient-based hyperparameter optimization and meta-learning. We show that an approximate version of the bilevel problem can be solved by taking into explicit account the optimization dynamics for the inner objective. Depending on the specific setting, the outer variables take either the meaning of hyperparameters in a supervised learning problem or parameters of a meta-learner. We provide sufficient conditions under which solutions of the approximate problem converge to those of the exact problem. We instantiate our approach for meta-learning in the case of deep learning where representation layers are treated as hyperparameters shared across a set of training episodes. In experiments, we confirm our theoretical findings, present encouraging results for few-shot learning and contrast the bilevel approach against classical approaches for learning-to-learn.

We study the use of amortized optimization to predict optimal transport (OT) maps from the input measures, which we call Meta OT. This helps repeatedly solve similar OT problems between different measures by leveraging the knowledge and information present from past problems to rapidly predict and solve new problems. Otherwise, standard methods ignore the knowledge of the past solutions and suboptimally re-solve each problem from scratch. We instantiate Meta OT models in discrete and continuous settings between grayscale images, spherical data, classification labels, and color palettes and use them to improve the computational time of standard OT solvers. Our source code is available at http://github.com/facebookresearch/meta-ot

Saliency methods seek to explain the predictions of a model by producing an importance map across each input sample. A popular class of such methods is based on backpropagating a signal and analyzing the resulting gradient. Despite much research on such methods, relatively little work has been done to clarify the differences between such methods as well as the desiderata of these techniques. Thus, there is a need for rigorously understanding the relationships between different methods as well as their failure modes. In this work, we conduct a thorough analysis of backpropagation-based saliency methods and propose a single framework under which several such methods can be unified. As a result of our study, we make three additional contributions. First, we use our framework to propose NormGrad, a novel saliency method based on the spatial contribution of gradients of convolutional weights. Second, we combine saliency maps at different layers to test the ability of saliency methods to extract complementary information at different network levels (e.g.~trading off spatial resolution and distinctiveness) and we explain why some methods fail at specific layers (e.g., Grad-CAM anywhere besides the last convolutional layer). Third, we introduce a class-sensitivity metric and a meta-learning inspired paradigm applicable to any saliency method for improving sensitivity to the output class being explained.

MetaFormer, the abstracted architecture of Transformer, has been found to play a significant role in achieving competitive performance. In this paper, we further explore the capacity of MetaFormer, again, without focusing on token mixer design: we introduce several baseline models under MetaFormer using the most basic or common mixers, and summarize our observations as follows: (1) MetaFormer ensures solid lower bound of performance. By merely adopting identity mapping as the token mixer, the MetaFormer model, termed IdentityFormer, achieves >80% accuracy on ImageNet-1K. (2) MetaFormer works well with arbitrary token mixers. When specifying the token mixer as even a random matrix to mix tokens, the resulting model RandFormer yields an accuracy of >81%, outperforming IdentityFormer. Rest assured of MetaFormer's results when new token mixers are adopted. (3) MetaFormer effortlessly offers state-of-the-art results. With just conventional token mixers dated back five years ago, the models instantiated from MetaFormer already beat state of the art. (a) ConvFormer outperforms ConvNeXt. Taking the common depthwise separable convolutions as the token mixer, the model termed ConvFormer, which can be regarded as pure CNNs, outperforms the strong CNN model ConvNeXt. (b) CAFormer sets new record on ImageNet-1K. By simply applying depthwise separable convolutions as token mixer in the bottom stages and vanilla self-attention in the top stages, the resulting model CAFormer sets a new record on ImageNet-1K: it achieves an accuracy of 85.5% at 224x224 resolution, under normal supervised training without external data or distillation. In our expedition to probe MetaFormer, we also find that a new activation, StarReLU, reduces 71% FLOPs of activation compared with GELU yet achieves better performance. We expect StarReLU to find great potential in MetaFormer-like models alongside other neural networks.

Machine learning systems typically assume that the distributions of training and test sets match closely. However, a critical requirement of such systems in the real world is their ability to generalize to unseen domains. Here, we propose an inter-domain gradient matching objective that targets domain generalization by maximizing the inner product between gradients from different domains. Since direct optimization of the gradient inner product can be computationally prohibitive -- requires computation of second-order derivatives -- we derive a simpler first-order algorithm named Fish that approximates its optimization. We demonstrate the efficacy of Fish on 6 datasets from the Wilds benchmark, which captures distribution shift across a diverse range of modalities. Our method produces competitive results on these datasets and surpasses all baselines on 4 of them. We perform experiments on both the Wilds benchmark, which captures distribution shift in the real world, as well as datasets in DomainBed benchmark that focuses more on synthetic-to-real transfer. Our method produces competitive results on both benchmarks, demonstrating its effectiveness across a wide range of domain generalization tasks.

This paper provides a review and commentary on the past, present, and future of numerical optimization algorithms in the context of machine learning applications. Through case studies on text classification and the training of deep neural networks, we discuss how optimization problems arise in machine learning and what makes them challenging. A major theme of our study is that large-scale machine learning represents a distinctive setting in which the stochastic gradient (SG) method has traditionally played a central role while conventional gradient-based nonlinear optimization techniques typically falter. Based on this viewpoint, we present a comprehensive theory of a straightforward, yet versatile SG algorithm, discuss its practical behavior, and highlight opportunities for designing algorithms with improved performance. This leads to a discussion about the next generation of optimization methods for large-scale machine learning, including an investigation of two main streams of research on techniques that diminish noise in the stochastic directions and methods that make use of second-order derivative approximations.

Explaining the output of a deep network remains a challenge. In the case of an image classifier, one type of explanation is to identify pixels that strongly influence the final decision. A starting point for this strategy is the gradient of the class score function with respect to the input image. This gradient can be interpreted as a sensitivity map, and there are several techniques that elaborate on this basic idea. This paper makes two contributions: it introduces SmoothGrad, a simple method that can help visually sharpen gradient-based sensitivity maps, and it discusses lessons in the visualization of these maps. We publish the code for our experiments and a website with our results.

Recently, interest has grown in exploring the hypothesis that neural activity conveys information through precise spiking motifs. To investigate this phenomenon, various algorithms have been proposed to detect such motifs in Single Unit Activity (SUA) recorded from populations of neurons. In this study, we present a novel detection model based on the inversion of a generative model of raster plot synthesis. Using this generative model, we derive an optimal detection procedure that takes the form of logistic regression combined with temporal convolution. A key advantage of this model is its differentiability, which allows us to formulate a supervised learning approach using a gradient descent on the binary cross-entropy loss. To assess the model's ability to detect spiking motifs in synthetic data, we first perform numerical evaluations. This analysis highlights the advantages of using spiking motifs over traditional firing rate based population codes. We then successfully demonstrate that our learning method can recover synthetically generated spiking motifs, indicating its potential for further applications. In the future, we aim to extend this method to real neurobiological data, where the ground truth is unknown, to explore and detect spiking motifs in a more natural and biologically relevant context.

N:M Structured sparsity has garnered significant interest as a result of relatively modest overhead and improved efficiency. Additionally, this form of sparsity holds considerable appeal for reducing the memory footprint owing to their modest representation overhead. There have been efforts to develop training recipes for N:M structured sparsity, they primarily focus on low-sparsity regions (sim50\%). Nonetheless, performance of models trained using these approaches tends to decline when confronted with high-sparsity regions (>80\%). In this work, we study the effectiveness of existing sparse training recipes at high-sparsity regions and argue that these methods fail to sustain the model quality on par with low-sparsity regions. We demonstrate that the significant factor contributing to this disparity is the presence of elevated levels of induced noise in the gradient magnitudes. To mitigate this undesirable effect, we employ decay mechanisms to progressively restrict the flow of gradients towards pruned elements. Our approach improves the model quality by up to 2% and 5% in vision and language models at high sparsity regime, respectively. We also evaluate the trade-off between model accuracy and training compute cost in terms of FLOPs. At iso-training FLOPs, our method yields better performance compared to conventional sparse training recipes, exhibiting an accuracy improvement of up to 2%. The source code is available at https://github.com/abhibambhaniya/progressive_gradient_flow_nm_sparsity.

One puzzling artifact in machine learning dubbed grokking is where delayed generalization is achieved tenfolds of iterations after near perfect overfitting to the training data. Focusing on the long delay itself on behalf of machine learning practitioners, our goal is to accelerate generalization of a model under grokking phenomenon. By regarding a series of gradients of a parameter over training iterations as a random signal over time, we can spectrally decompose the parameter trajectories under gradient descent into two components: the fast-varying, overfitting-yielding component and the slow-varying, generalization-inducing component. This analysis allows us to accelerate the grokking phenomenon more than times 50 with only a few lines of code that amplifies the slow-varying components of gradients. The experiments show that our algorithm applies to diverse tasks involving images, languages, and graphs, enabling practical availability of this peculiar artifact of sudden generalization. Our code is available at https://github.com/ironjr/grokfast.

Metalens is an emerging optical system with an irreplaceable merit in that it can be manufactured in ultra-thin and compact sizes, which shows great promise of various applications such as medical imaging and augmented/virtual reality (AR/VR). Despite its advantage in miniaturization, its practicality is constrained by severe aberrations and distortions, which significantly degrade the image quality. Several previous arts have attempted to address different types of aberrations, yet most of them are mainly designed for the traditional bulky lens and not convincing enough to remedy harsh aberrations of the metalens. While there have existed aberration correction methods specifically for metalens, they still fall short of restoration quality. In this work, we propose MetaFormer, an aberration correction framework for metalens-captured images, harnessing Vision Transformers (ViT) that has shown remarkable restoration performance in diverse image restoration tasks. Specifically, we devise a Multiple Adaptive Filters Guidance (MAFG), where multiple Wiener filters enrich the degraded input images with various noise-detail balances, enhancing output restoration quality. In addition, we introduce a Spatial and Transposed self-Attention Fusion (STAF) module, which aggregates features from spatial self-attention and transposed self-attention modules to further ameliorate aberration correction. We conduct extensive experiments, including correcting aberrated images and videos, and clean 3D reconstruction from the degraded images. The proposed method outperforms the previous arts by a significant margin. We further fabricate a metalens and verify the practicality of MetaFormer by restoring the images captured with the manufactured metalens in the wild. Code and pre-trained models are available at https://benhenryl.github.io/MetaFormer

While deep learning models have replaced hand-designed features across many domains, these models are still trained with hand-designed optimizers. In this work, we leverage the same scaling approach behind the success of deep learning to learn versatile optimizers. We train an optimizer for deep learning which is itself a small neural network that ingests gradients and outputs parameter updates. Meta-trained with approximately four thousand TPU-months of compute on a wide variety of optimization tasks, our optimizer not only exhibits compelling performance, but optimizes in interesting and unexpected ways. It requires no hyperparameter tuning, instead automatically adapting to the specifics of the problem being optimized. We open source our learned optimizer, meta-training code, the associated train and test data, and an extensive optimizer benchmark suite with baselines at velo-code.github.io.

Traditional saliency map methods, popularized in computer vision, highlight individual points (pixels) of the input that contribute the most to the model's output. However, in time-series they offer limited insights as semantically meaningful features are often found in other domains. We introduce Cross-domain Integrated Gradients, a generalization of Integrated Gradients. Our method enables feature attributions on any domain that can be formulated as an invertible, differentiable transformation of the time domain. Crucially, our derivation extends the original Integrated Gradients into the complex domain, enabling frequency-based attributions. We provide the necessary theoretical guarantees, namely, path independence and completeness. Our approach reveals interpretable, problem-specific attributions that time-domain methods cannot capture, on three real-world tasks: wearable sensor heart rate extraction, electroencephalography-based seizure detection, and zero-shot time-series forecasting. We release an open-source Tensorflow/PyTorch library to enable plug-and-play cross-domain explainability for time-series models. These results demonstrate the ability of cross-domain integrated gradients to provide semantically meaningful insights in time-series models that are impossible with traditional time-domain saliency.

Recent advances in deep learning for physics have focused on discovering shared representations of target systems by incorporating physics priors or inductive biases into neural networks. While effective, these methods are limited to the system domain, where the type of system remains consistent and thus cannot ensure the adaptation to new, or unseen physical systems governed by different laws. For instance, a neural network trained on a mass-spring system cannot guarantee accurate predictions for the behavior of a two-body system or any other system with different physical laws. In this work, we take a significant leap forward by targeting cross domain generalization within the field of Hamiltonian dynamics. We model our system with a graph neural network and employ a meta learning algorithm to enable the model to gain experience over a distribution of tasks and make it adapt to new physics. Our approach aims to learn a unified Hamiltonian representation that is generalizable across multiple system domains, thereby overcoming the limitations of system-specific models. Our results demonstrate that the meta-trained model not only adapts effectively to new systems but also captures a generalized Hamiltonian representation that is consistent across different physical domains. Overall, through the use of meta learning, we offer a framework that achieves cross domain generalization, providing a step towards a unified model for understanding a wide array of dynamical systems via deep learning.

We study the sparse phase retrieval problem, which seeks to recover a sparse signal from a limited set of magnitude-only measurements. In contrast to prevalent sparse phase retrieval algorithms that primarily use first-order methods, we propose an innovative second-order algorithm that employs a Newton-type method with hard thresholding. This algorithm overcomes the linear convergence limitations of first-order methods while preserving their hallmark per-iteration computational efficiency. We provide theoretical guarantees that our algorithm converges to the s-sparse ground truth signal x^{natural} in R^n (up to a global sign) at a quadratic convergence rate after at most O(log (Vertx^{natural} Vert /x_{min}^{natural})) iterations, using Omega(s^2log n) Gaussian random samples. Numerical experiments show that our algorithm achieves a significantly faster convergence rate than state-of-the-art methods.

Multilayer-perceptrons (MLP) are known to struggle with learning functions of high-frequencies, and in particular cases with wide frequency bands. We present a spatially adaptive progressive encoding (SAPE) scheme for input signals of MLP networks, which enables them to better fit a wide range of frequencies without sacrificing training stability or requiring any domain specific preprocessing. SAPE gradually unmasks signal components with increasing frequencies as a function of time and space. The progressive exposure of frequencies is monitored by a feedback loop throughout the neural optimization process, allowing changes to propagate at different rates among local spatial portions of the signal space. We demonstrate the advantage of SAPE on a variety of domains and applications, including regression of low dimensional signals and images, representation learning of occupancy networks, and a geometric task of mesh transfer between 3D shapes.

In spite of their huge success, transformer models remain difficult to scale in depth. In this work, we develop a unified signal propagation theory and provide formulae that govern the moments of the forward and backward signal through the transformer model. Our framework can be used to understand and mitigate vanishing/exploding gradients, rank collapse, and instability associated with high attention scores. We also propose DeepScaleLM, an initialization and scaling scheme that conserves unit output/gradient moments throughout the model, enabling the training of very deep models with 100s of layers. We find that transformer models could be much deeper - our deep models with fewer parameters outperform shallow models in Language Modeling, Speech Translation, and Image Classification, across Encoder-only, Decoder-only and Encoder-Decoder variants, for both Pre-LN and Post-LN transformers, for multiple datasets and model sizes. These improvements also translate into improved performance on downstream Question Answering tasks and improved robustness for image classification.

Hyperspectral pansharpening has received much attention in recent years due to technological and methodological advances that open the door to new application scenarios. However, research on this topic is only now gaining momentum. The most popular methods are still borrowed from the more mature field of multispectral pansharpening and often overlook the unique challenges posed by hyperspectral data fusion, such as i) the very large number of bands, ii) the overwhelming noise in selected spectral ranges, iii) the significant spectral mismatch between panchromatic and hyperspectral components, iv) a typically high resolution ratio. Imprecise data modeling especially affects spectral fidelity. Even state-of-the-art methods perform well in certain spectral ranges and much worse in others, failing to ensure consistent quality across all bands, with the risk of generating unreliable results. Here, we propose a hyperspectral pansharpening method that explicitly addresses this problem and ensures uniform spectral quality. To this end, a single lightweight neural network is used, with weights that adapt on the fly to each band. During fine-tuning, the spatial loss is turned on and off to ensure a fast convergence of the spectral loss to the desired level, according to a hysteresis-like dynamic. Furthermore, the spatial loss itself is appropriately redefined to account for nonlinear dependencies between panchromatic and spectral bands. Overall, the proposed method is fully unsupervised, with no prior training on external data, flexible, and low-complexity. Experiments on a recently published benchmarking toolbox show that it ensures excellent sharpening quality, competitive with the state-of-the-art, consistently across all bands. The software code and the full set of results are shared online on https://github.com/giu-guarino/rho-PNN.

Classifier-free guidance (CFG) is a core technique powering state-of-the-art image generation systems, yet its underlying mechanisms remain poorly understood. In this work, we begin by analyzing CFG in a simplified linear diffusion model, where we show its behavior closely resembles that observed in the nonlinear case. Our analysis reveals that linear CFG improves generation quality via three distinct components: (i) a mean-shift term that approximately steers samples in the direction of class means, (ii) a positive Contrastive Principal Components (CPC) term that amplifies class-specific features, and (iii) a negative CPC term that suppresses generic features prevalent in unconditional data. We then verify that these insights in real-world, nonlinear diffusion models: over a broad range of noise levels, linear CFG resembles the behavior of its nonlinear counterpart. Although the two eventually diverge at low noise levels, we discuss how the insights from the linear analysis still shed light on the CFG's mechanism in the nonlinear regime.

We propose ScaledGD(\lambda), a preconditioned gradient descent method to tackle the low-rank matrix sensing problem when the true rank is unknown, and when the matrix is possibly ill-conditioned. Using overparametrized factor representations, ScaledGD(\lambda) starts from a small random initialization, and proceeds by gradient descent with a specific form of damped preconditioning to combat bad curvatures induced by overparameterization and ill-conditioning. At the expense of light computational overhead incurred by preconditioners, ScaledGD(\lambda) is remarkably robust to ill-conditioning compared to vanilla gradient descent (GD) even with overprameterization. Specifically, we show that, under the Gaussian design, ScaledGD(\lambda) converges to the true low-rank matrix at a constant linear rate after a small number of iterations that scales only logarithmically with respect to the condition number and the problem dimension. This significantly improves over the convergence rate of vanilla GD which suffers from a polynomial dependency on the condition number. Our work provides evidence on the power of preconditioning in accelerating the convergence without hurting generalization in overparameterized learning.

As the physical size of recent CMOS image sensors (CIS) gets smaller, the latest mobile cameras are adopting unique non-Bayer color filter array (CFA) patterns (e.g., Quad, Nona, QxQ), which consist of homogeneous color units with adjacent pixels. These non-Bayer sensors are superior to conventional Bayer CFA thanks to their changeable pixel-bin sizes for different light conditions but may introduce visual artifacts during demosaicing due to their inherent pixel pattern structures and sensor hardware characteristics. Previous demosaicing methods have primarily focused on Bayer CFA, necessitating distinct reconstruction methods for non-Bayer patterned CIS with various CFA modes under different lighting conditions. In this work, we propose an efficient unified demosaicing method that can be applied to both conventional Bayer RAW and various non-Bayer CFAs' RAW data in different operation modes. Our Knowledge Learning-based demosaicing model for Adaptive Patterns, namely KLAP, utilizes CFA-adaptive filters for only 1% key filters in the network for each CFA, but still manages to effectively demosaic all the CFAs, yielding comparable performance to the large-scale models. Furthermore, by employing meta-learning during inference (KLAP-M), our model is able to eliminate unknown sensor-generic artifacts in real RAW data, effectively bridging the gap between synthetic images and real sensor RAW. Our KLAP and KLAP-M methods achieved state-of-the-art demosaicing performance in both synthetic and real RAW data of Bayer and non-Bayer CFAs.

This paper investigates the intriguing question of whether we can create learning algorithms that automatically generate training data, learning environments, and curricula in order to help AI agents rapidly learn. We show that such algorithms are possible via Generative Teaching Networks (GTNs), a general approach that is, in theory, applicable to supervised, unsupervised, and reinforcement learning, although our experiments only focus on the supervised case. GTNs are deep neural networks that generate data and/or training environments that a learner (e.g. a freshly initialized neural network) trains on for a few SGD steps before being tested on a target task. We then differentiate through the entire learning process via meta-gradients to update the GTN parameters to improve performance on the target task. GTNs have the beneficial property that they can theoretically generate any type of data or training environment, making their potential impact large. This paper introduces GTNs, discusses their potential, and showcases that they can substantially accelerate learning. We also demonstrate a practical and exciting application of GTNs: accelerating the evaluation of candidate architectures for neural architecture search (NAS), which is rate-limited by such evaluations, enabling massive speed-ups in NAS. GTN-NAS improves the NAS state of the art, finding higher performing architectures when controlling for the search proposal mechanism. GTN-NAS also is competitive with the overall state of the art approaches, which achieve top performance while using orders of magnitude less computation than typical NAS methods. Speculating forward, GTNs may represent a first step toward the ambitious goal of algorithms that generate their own training data and, in doing so, open a variety of interesting new research questions and directions.

Real-world analog systems intrinsically suffer from noise that can impede model convergence and accuracy on a variety of deep learning models. We demonstrate that differentiable activations like GELU and SiLU enable robust propagation of gradients which help to mitigate analog quantization error that is ubiquitous to all analog systems. We perform analysis and training of convolutional, linear, and transformer networks in the presence of quantized noise. Here, we are able to demonstrate that continuously differentiable activation functions are significantly more noise resilient over conventional rectified activations. As in the case of ReLU, the error in gradients are 100x higher than those in GELU near zero. Our findings provide guidance for selecting appropriate activations to realize performant and reliable hardware implementations across several machine learning domains such as computer vision, signal processing, and beyond.

Graph Neural Networks (GNNs) are limited in their propagation operators. In many cases, these operators often contain non-negative elements only and are shared across channels, limiting the expressiveness of GNNs. Moreover, some GNNs suffer from over-smoothing, limiting their depth. On the other hand, Convolutional Neural Networks (CNNs) can learn diverse propagation filters, and phenomena like over-smoothing are typically not apparent in CNNs. In this paper, we bridge these gaps by incorporating trainable channel-wise weighting factors omega to learn and mix multiple smoothing and sharpening propagation operators at each layer. Our generic method is called omegaGNN, and is easy to implement. We study two variants: omegaGCN and omegaGAT. For omegaGCN, we theoretically analyse its behaviour and the impact of omega on the obtained node features. Our experiments confirm these findings, demonstrating and explaining how both variants do not over-smooth. Additionally, we experiment with 15 real-world datasets on node- and graph-classification tasks, where our omegaGCN and omegaGAT perform on par with state-of-the-art methods.

Can we modify the training data distribution to encourage the underlying optimization method toward finding solutions with superior generalization performance on in-distribution data? In this work, we approach this question for the first time by comparing the inductive bias of gradient descent (GD) with that of sharpness-aware minimization (SAM). By studying a two-layer CNN, we rigorously prove that SAM learns different features more uniformly, particularly in early epochs. That is, SAM is less susceptible to simplicity bias compared to GD. We also show that examples containing features that are learned early are separable from the rest based on the model's output. Based on this observation, we propose a method that (i) clusters examples based on the network output early in training, (ii) identifies a cluster of examples with similar network output, and (iii) upsamples the rest of examples only once to alleviate the simplicity bias. We show empirically that USEFUL effectively improves the generalization performance on the original data distribution when training with various gradient methods, including (S)GD and SAM. Notably, we demonstrate that our method can be combined with SAM variants and existing data augmentation strategies to achieve, to the best of our knowledge, state-of-the-art performance for training ResNet18 on CIFAR10, STL10, CINIC10, Tiny-ImageNet; ResNet34 on CIFAR100; and VGG19 and DenseNet121 on CIFAR10.

Meta-learning usually refers to a learning algorithm that learns from other learning algorithms. The problem of uncertainty in the predictions of neural networks shows that the world is only partially predictable and a learned neural network cannot generalize to its ever-changing surrounding environments. Therefore, the question is how a predictive model can represent multiple predictions simultaneously. We aim to provide a fundamental understanding of learning to learn in the contents of Decentralized Neural Networks (Decentralized NNs) and we believe this is one of the most important questions and prerequisites to building an autonomous intelligence machine. To this end, we shall demonstrate several pieces of evidence for tackling the problems above with Meta Learning in Decentralized NNs. In particular, we will present three different approaches to building such a decentralized learning system: (1) learning from many replica neural networks, (2) building the hierarchy of neural networks for different functions, and (3) leveraging different modality experts to learn cross-modal representations.

In many neural networks, different values of the parameters may result in the same loss value. Parameter space symmetries are loss-invariant transformations that change the model parameters. Teleportation applies such transformations to accelerate optimization. However, the exact mechanism behind this algorithm's success is not well understood. In this paper, we show that teleportation not only speeds up optimization in the short-term, but gives overall faster time to convergence. Additionally, teleporting to minima with different curvatures improves generalization, which suggests a connection between the curvature of the minimum and generalization ability. Finally, we show that integrating teleportation into a wide range of optimization algorithms and optimization-based meta-learning improves convergence. Our results showcase the versatility of teleportation and demonstrate the potential of incorporating symmetry in optimization.

We introduce a new tool for interpreting neural net responses, namely full-gradients, which decomposes the neural net response into input sensitivity and per-neuron sensitivity components. This is the first proposed representation which satisfies two key properties: completeness and weak dependence, which provably cannot be satisfied by any saliency map-based interpretability method. For convolutional nets, we also propose an approximate saliency map representation, called FullGrad, obtained by aggregating the full-gradient components. We experimentally evaluate the usefulness of FullGrad in explaining model behaviour with two quantitative tests: pixel perturbation and remove-and-retrain. Our experiments reveal that our method explains model behaviour correctly, and more comprehensively than other methods in the literature. Visual inspection also reveals that our saliency maps are sharper and more tightly confined to object regions than other methods.

Representing a manifold of very high-dimensional data with generative models has been shown to be computationally efficient in practice. However, this requires that the data manifold admits a global parameterization. In order to represent manifolds of arbitrary topology, we propose to learn a mixture model of variational autoencoders. Here, every encoder-decoder pair represents one chart of a manifold. We propose a loss function for maximum likelihood estimation of the model weights and choose an architecture that provides us the analytical expression of the charts and of their inverses. Once the manifold is learned, we use it for solving inverse problems by minimizing a data fidelity term restricted to the learned manifold. To solve the arising minimization problem we propose a Riemannian gradient descent algorithm on the learned manifold. We demonstrate the performance of our method for low-dimensional toy examples as well as for deblurring and electrical impedance tomography on certain image manifolds.

As models for nature language processing (NLP), computer vision (CV) and recommendation systems (RS) require surging computation, a large number of GPUs/TPUs are paralleled as a large batch (LB) to improve training throughput. However, training such LB tasks often meets large generalization gap and downgrades final precision, which limits enlarging the batch size. In this work, we develop the variance reduced gradient descent technique (VRGD) based on the gradient signal to noise ratio (GSNR) and apply it onto popular optimizers such as SGD/Adam/LARS/LAMB. We carry out a theoretical analysis of convergence rate to explain its fast training dynamics, and a generalization analysis to demonstrate its smaller generalization gap on LB training. Comprehensive experiments demonstrate that VRGD can accelerate training (1sim 2 times), narrow generalization gap and improve final accuracy. We push the batch size limit of BERT pretraining up to 128k/64k and DLRM to 512k without noticeable accuracy loss. We improve ImageNet Top-1 accuracy at 96k by 0.52pp than LARS. The generalization gap of BERT and ImageNet training is significantly reduce by over 65%.

Meta-Bayesian optimisation (meta-BO) aims to improve the sample efficiency of Bayesian optimisation by leveraging data from related tasks. While previous methods successfully meta-learn either a surrogate model or an acquisition function independently, joint training of both components remains an open challenge. This paper proposes the first end-to-end differentiable meta-BO framework that generalises neural processes to learn acquisition functions via transformer architectures. We enable this end-to-end framework with reinforcement learning (RL) to tackle the lack of labelled acquisition data. Early on, we notice that training transformer-based neural processes from scratch with RL is challenging due to insufficient supervision, especially when rewards are sparse. We formalise this claim with a combinatorial analysis showing that the widely used notion of regret as a reward signal exhibits a logarithmic sparsity pattern in trajectory lengths. To tackle this problem, we augment the RL objective with an auxiliary task that guides part of the architecture to learn a valid probabilistic model as an inductive bias. We demonstrate that our method achieves state-of-the-art regret results against various baselines in experiments on standard hyperparameter optimisation tasks and also outperforms others in the real-world problems of mixed-integer programming tuning, antibody design, and logic synthesis for electronic design automation.

We propose a categorical semantics of gradient-based machine learning algorithms in terms of lenses, parametrised maps, and reverse derivative categories. This foundation provides a powerful explanatory and unifying framework: it encompasses a variety of gradient descent algorithms such as ADAM, AdaGrad, and Nesterov momentum, as well as a variety of loss functions such as as MSE and Softmax cross-entropy, shedding new light on their similarities and differences. Our approach to gradient-based learning has examples generalising beyond the familiar continuous domains (modelled in categories of smooth maps) and can be realized in the discrete setting of boolean circuits. Finally, we demonstrate the practical significance of our framework with an implementation in Python.

Spectral bias is an important observation of neural network training, stating that the network will learn a low frequency representation of the target function before converging to higher frequency components. This property is interesting due to its link to good generalization in over-parameterized networks. However, in low dimensional settings, a severe spectral bias occurs that obstructs convergence to high frequency components entirely. In order to overcome this limitation, one can encode the inputs using a high frequency sinusoidal encoding. Previous works attempted to explain this phenomenon using Neural Tangent Kernel (NTK) and Fourier analysis. However, NTK does not capture real network dynamics, and Fourier analysis only offers a global perspective on the network properties that induce this bias. In this paper, we provide a novel approach towards understanding spectral bias by directly studying ReLU MLP training dynamics. Specifically, we focus on the connection between the computations of ReLU networks (activation regions), and the speed of gradient descent convergence. We study these dynamics in relation to the spatial information of the signal to understand how they influence spectral bias. We then use this formulation to study the severity of spectral bias in low dimensional settings, and how positional encoding overcomes this.

This paper investigates the distinctions between gradient methods applied to non-differentiable functions (NGDMs) and classical gradient descents (GDs) designed for differentiable functions. First, we demonstrate significant differences in the convergence properties of NGDMs compared to GDs, challenging the applicability of the extensive neural network convergence literature based on L-smoothness to non-smooth neural networks. Next, we demonstrate the paradoxical nature of NGDM solutions for L_{1}-regularized problems, showing that increasing the regularization penalty leads to an increase in the L_{1} norm of optimal solutions in NGDMs. Consequently, we show that widely adopted L_{1} penalization-based techniques for network pruning do not yield expected results. Finally, we explore the Edge of Stability phenomenon, indicating its inapplicability even to Lipschitz continuous convex differentiable functions, leaving its relevance to non-convex non-differentiable neural networks inconclusive. Our analysis exposes misguided interpretations of NGDMs in widely referenced papers and texts due to an overreliance on strong smoothness assumptions, emphasizing the necessity for a nuanced understanding of foundational assumptions in the analysis of these systems.

We identify a new phenomenon in neural network optimization which arises from the interaction of depth and a particular heavy-tailed structure in natural data. Our result offers intuitive explanations for several previously reported observations about network training dynamics. In particular, it implies a conceptually new cause for progressive sharpening and the edge of stability; we also highlight connections to other concepts in optimization and generalization including grokking, simplicity bias, and Sharpness-Aware Minimization. Experimentally, we demonstrate the significant influence of paired groups of outliers in the training data with strong opposing signals: consistent, large magnitude features which dominate the network output throughout training and provide gradients which point in opposite directions. Due to these outliers, early optimization enters a narrow valley which carefully balances the opposing groups; subsequent sharpening causes their loss to rise rapidly, oscillating between high on one group and then the other, until the overall loss spikes. We describe how to identify these groups, explore what sets them apart, and carefully study their effect on the network's optimization and behavior. We complement these experiments with a mechanistic explanation on a toy example of opposing signals and a theoretical analysis of a two-layer linear network on a simple model. Our finding enables new qualitative predictions of training behavior which we confirm experimentally. It also provides a new lens through which to study and improve modern training practices for stochastic optimization, which we highlight via a case study of Adam versus SGD.

We present an algorithm for minimizing an objective with hard-to-compute gradients by using a related, easier-to-access function as a proxy. Our algorithm is based on approximate proximal point iterations on the proxy combined with relatively few stochastic gradients from the objective. When the difference between the objective and the proxy is delta-smooth, our algorithm guarantees convergence at a rate matching stochastic gradient descent on a delta-smooth objective, which can lead to substantially better sample efficiency. Our algorithm has many potential applications in machine learning, and provides a principled means of leveraging synthetic data, physics simulators, mixed public and private data, and more.

We introduce Reverse Derivative Ascent: a categorical analogue of gradient based methods for machine learning. Our algorithm is defined at the level of so-called reverse differential categories. It can be used to learn the parameters of models which are expressed as morphisms of such categories. Our motivating example is boolean circuits: we show how our algorithm can be applied to such circuits by using the theory of reverse differential categories. Note our methodology allows us to learn the parameters of boolean circuits directly, in contrast to existing binarised neural network approaches. Moreover, we demonstrate its empirical value by giving experimental results on benchmark machine learning datasets.

Computational sensing strategies often suffer from calibration errors in the physical implementation of their ideal sensing models. Such uncertainties are typically addressed by using multiple, accurately chosen training signals to recover the missing information on the sensing model, an approach that can be resource-consuming and cumbersome. Conversely, blind calibration does not employ any training signal, but corresponds to a bilinear inverse problem whose algorithmic solution is an open issue. We here address blind calibration as a non-convex problem for linear random sensing models, in which we aim to recover an unknown signal from its projections on sub-Gaussian random vectors, each subject to an unknown positive multiplicative factor (or gain). To solve this optimisation problem we resort to projected gradient descent starting from a suitable, carefully chosen initialisation point. An analysis of this algorithm allows us to show that it converges to the exact solution provided a sample complexity requirement is met, i.e., relating convergence to the amount of information collected during the sensing process. Interestingly, we show that this requirement grows linearly (up to log factors) in the number of unknowns of the problem. This sample complexity is found both in absence of prior information, as well as when subspace priors are available for both the signal and gains, allowing a further reduction of the number of observations required for our recovery guarantees to hold. Moreover, in the presence of noise we show how our descent algorithm yields a solution whose accuracy degrades gracefully with the amount of noise affecting the measurements. Finally, we present some numerical experiments in an imaging context, where our algorithm allows for a simple solution to blind calibration of the gains in a sensor array.

Neuromorphic computing, which exploits Spiking Neural Networks (SNNs) on neuromorphic chips, is a promising energy-efficient alternative to traditional AI. CNN-based SNNs are the current mainstream of neuromorphic computing. By contrast, no neuromorphic chips are designed especially for Transformer-based SNNs, which have just emerged, and their performance is only on par with CNN-based SNNs, offering no distinct advantage. In this work, we propose a general Transformer-based SNN architecture, termed as ``Meta-SpikeFormer", whose goals are: 1) Lower-power, supports the spike-driven paradigm that there is only sparse addition in the network; 2) Versatility, handles various vision tasks; 3) High-performance, shows overwhelming performance advantages over CNN-based SNNs; 4) Meta-architecture, provides inspiration for future next-generation Transformer-based neuromorphic chip designs. Specifically, we extend the Spike-driven Transformer in yao2023spike into a meta architecture, and explore the impact of structure, spike-driven self-attention, and skip connection on its performance. On ImageNet-1K, Meta-SpikeFormer achieves 80.0\% top-1 accuracy (55M), surpassing the current state-of-the-art (SOTA) SNN baselines (66M) by 3.7\%. This is the first direct training SNN backbone that can simultaneously supports classification, detection, and segmentation, obtaining SOTA results in SNNs. Finally, we discuss the inspiration of the meta SNN architecture for neuromorphic chip design. Source code and models are available at https://github.com/BICLab/Spike-Driven-Transformer-V2.

Forward Gradients - the idea of using directional derivatives in forward differentiation mode - have recently been shown to be utilizable for neural network training while avoiding problems generally associated with backpropagation gradient computation, such as locking and memorization requirements. The cost is the requirement to guess the step direction, which is hard in high dimensions. While current solutions rely on weighted averages over isotropic guess vector distributions, we propose to strongly bias our gradient guesses in directions that are much more promising, such as feedback obtained from small, local auxiliary networks. For a standard computer vision neural network, we conduct a rigorous study systematically covering a variety of combinations of gradient targets and gradient guesses, including those previously presented in the literature. We find that using gradients obtained from a local loss as a candidate direction drastically improves on random noise in Forward Gradient methods.

In this work, we develop new optimization algorithms that use approximate second-order information combined with the gradient regularization technique to achieve fast global convergence rates for both convex and non-convex objectives. The key innovation of our analysis is a novel notion called Gradient-Normalized Smoothness, which characterizes the maximum radius of a ball around the current point that yields a good relative approximation of the gradient field. Our theory establishes a natural intrinsic connection between Hessian approximation and the linearization of the gradient. Importantly, Gradient-Normalized Smoothness does not depend on the specific problem class of the objective functions, while effectively translating local information about the gradient field and Hessian approximation into the global behavior of the method. This new concept equips approximate second-order algorithms with universal global convergence guarantees, recovering state-of-the-art rates for functions with H\"older-continuous Hessians and third derivatives, quasi-self-concordant functions, as well as smooth classes in first-order optimization. These rates are achieved automatically and extend to broader classes, such as generalized self-concordant functions. We demonstrate direct applications of our results for global linear rates in logistic regression and softmax problems with approximate Hessians, as well as in non-convex optimization using Fisher and Gauss-Newton approximations.

Due to their highly structured characteristics, faces are easier to recover than natural scenes for blind image super-resolution. Therefore, we can extract the degradation representation of an image from the low-quality and recovered face pairs. Using the degradation representation, realistic low-quality images can then be synthesized to fine-tune the super-resolution model for the real-world low-quality image. However, such a procedure is time-consuming and laborious, and the gaps between recovered faces and the ground-truths further increase the optimization uncertainty. To facilitate efficient model adaptation towards image-specific degradations, we propose a method dubbed MetaF2N, which leverages the contained Faces to fine-tune model parameters for adapting to the whole Natural image in a Meta-learning framework. The degradation extraction and low-quality image synthesis steps are thus circumvented in our MetaF2N, and it requires only one fine-tuning step to get decent performance. Considering the gaps between the recovered faces and ground-truths, we further deploy a MaskNet for adaptively predicting loss weights at different positions to reduce the impact of low-confidence areas. To evaluate our proposed MetaF2N, we have collected a real-world low-quality dataset with one or multiple faces in each image, and our MetaF2N achieves superior performance on both synthetic and real-world datasets. Source code, pre-trained models, and collected datasets are available at https://github.com/yinzhicun/MetaF2N.

We present a novel adaptive optimization algorithm for large-scale machine learning problems. Equipped with a low-cost estimate of local curvature and Lipschitz smoothness, our method dynamically adapts the search direction and step-size. The search direction contains gradient information preconditioned by a well-scaled diagonal preconditioning matrix that captures the local curvature information. Our methodology does not require the tedious task of learning rate tuning, as the learning rate is updated automatically without adding an extra hyperparameter. We provide convergence guarantees on a comprehensive collection of optimization problems, including convex, strongly convex, and nonconvex problems, in both deterministic and stochastic regimes. We also conduct an extensive empirical evaluation on standard machine learning problems, justifying our algorithm's versatility and demonstrating its strong performance compared to other start-of-the-art first-order and second-order methods.

Using backpropagation to compute gradients of objective functions for optimization has remained a mainstay of machine learning. Backpropagation, or reverse-mode differentiation, is a special case within the general family of automatic differentiation algorithms that also includes the forward mode. We present a method to compute gradients based solely on the directional derivative that one can compute exactly and efficiently via the forward mode. We call this formulation the forward gradient, an unbiased estimate of the gradient that can be evaluated in a single forward run of the function, entirely eliminating the need for backpropagation in gradient descent. We demonstrate forward gradient descent in a range of problems, showing substantial savings in computation and enabling training up to twice as fast in some cases.

Optimization with matrix gradient orthogonalization has recently demonstrated impressive results in the training of deep neural networks (Jordan et al., 2024; Liu et al., 2025). In this paper, we provide a theoretical analysis of this approach. In particular, we show that the orthogonalized gradient method can be seen as a first-order trust-region optimization method, where the trust-region is defined in terms of the matrix spectral norm. Motivated by this observation, we develop the stochastic non-Euclidean trust-region gradient method with momentum, which recovers the Muon optimizer (Jordan et al., 2024) as a special case, along with normalized SGD and signSGD with momentum (Cutkosky and Mehta, 2020; Sun et al., 2023). In addition, we prove state-of-the-art convergence results for the proposed algorithm in a range of scenarios, which involve arbitrary non-Euclidean norms, constrained and composite problems, and non-convex, star-convex, first- and second-order smooth functions. Finally, our theoretical findings provide an explanation for several practical observations, including the practical superiority of Muon compared to the Orthogonal-SGDM algorithm of Tuddenham et al. (2022) and the importance of weight decay in the training of large-scale language models.

Since the introduction of deep learning, a wide scope of representation properties, such as decorrelation, whitening, disentanglement, rank, isotropy, and mutual information, have been studied to improve the quality of representation. However, manipulating such properties can be challenging in terms of implementational effectiveness and general applicability. To address these limitations, we propose to regularize von Neumann entropy~(VNE) of representation. First, we demonstrate that the mathematical formulation of VNE is superior in effectively manipulating the eigenvalues of the representation autocorrelation matrix. Then, we demonstrate that it is widely applicable in improving state-of-the-art algorithms or popular benchmark algorithms by investigating domain-generalization, meta-learning, self-supervised learning, and generative models. In addition, we formally establish theoretical connections with rank, disentanglement, and isotropy of representation. Finally, we provide discussions on the dimension control of VNE and the relationship with Shannon entropy. Code is available at: https://github.com/jaeill/CVPR23-VNE.

JPEG remains one of the most widespread lossy image coding methods. However, the non-differentiable nature of JPEG restricts the application in deep learning pipelines. Several differentiable approximations of JPEG have recently been proposed to address this issue. This paper conducts a comprehensive review of existing diff. JPEG approaches and identifies critical details that have been missed by previous methods. To this end, we propose a novel diff. JPEG approach, overcoming previous limitations. Our approach is differentiable w.r.t. the input image, the JPEG quality, the quantization tables, and the color conversion parameters. We evaluate the forward and backward performance of our diff. JPEG approach against existing methods. Additionally, extensive ablations are performed to evaluate crucial design choices. Our proposed diff. JPEG resembles the (non-diff.) reference implementation best, significantly surpassing the recent-best diff. approach by 3.47dB (PSNR) on average. For strong compression rates, we can even improve PSNR by 9.51dB. Strong adversarial attack results are yielded by our diff. JPEG, demonstrating the effective gradient approximation. Our code is available at https://github.com/necla-ml/Diff-JPEG.

We propose a gradient flow procedure for generative modeling by transporting particles from an initial source distribution to a target distribution, where the gradient field on the particles is given by a noise-adaptive Wasserstein Gradient of the Maximum Mean Discrepancy (MMD). The noise-adaptive MMD is trained on data distributions corrupted by increasing levels of noise, obtained via a forward diffusion process, as commonly used in denoising diffusion probabilistic models. The result is a generalization of MMD Gradient Flow, which we call Diffusion-MMD-Gradient Flow or DMMD. The divergence training procedure is related to discriminator training in Generative Adversarial Networks (GAN), but does not require adversarial training. We obtain competitive empirical performance in unconditional image generation on CIFAR10, MNIST, CELEB-A (64 x64) and LSUN Church (64 x 64). Furthermore, we demonstrate the validity of the approach when MMD is replaced by a lower bound on the KL divergence.

Radio frequency (RF) signal mapping, which is the process of analyzing and predicting the RF signal strength and distribution across specific areas, is crucial for cellular network planning and deployment. Traditional approaches to RF signal mapping rely on statistical models constructed based on measurement data, which offer low complexity but often lack accuracy, or ray tracing tools, which provide enhanced precision for the target area but suffer from increased computational complexity. Recently, machine learning (ML) has emerged as a data-driven method for modeling RF signal propagation, which leverages models trained on synthetic datasets to perform RF signal mapping in "unseen" areas. In this paper, we present Geo2SigMap, an ML-based framework for efficient and high-fidelity RF signal mapping using geographic databases. First, we develop an automated framework that seamlessly integrates three open-source tools: OpenStreetMap (geographic databases), Blender (computer graphics), and Sionna (ray tracing), enabling the efficient generation of large-scale 3D building maps and ray tracing models. Second, we propose a cascaded U-Net model, which is pre-trained on synthetic datasets and employed to generate detailed RF signal maps, leveraging environmental information and sparse measurement data. Finally, we evaluate the performance of Geo2SigMap via a real-world measurement campaign, where three types of user equipment (UE) collect over 45,000 data points related to cellular information from six LTE cells operating in the citizens broadband radio service (CBRS) band. Our results show that Geo2SigMap achieves an average root-mean-square-error (RMSE) of 6.04 dB for predicting the reference signal received power (RSRP) at the UE, representing an average RMSE improvement of 3.59 dB compared to existing methods.

The goal of predictive data attribution is to estimate how adding or removing a given set of training datapoints will affect model predictions. In convex settings, this goal is straightforward (i.e., via the infinitesimal jackknife). In large-scale (non-convex) settings, however, existing methods are far less successful -- current methods' estimates often only weakly correlate with ground truth. In this work, we present a new data attribution method (MAGIC) that combines classical methods and recent advances in metadifferentiation to (nearly) optimally estimate the effect of adding or removing training data on model predictions.

We analyze the convergence of (stochastic) gradient descent algorithm for learning a convolutional filter with Rectified Linear Unit (ReLU) activation function. Our analysis does not rely on any specific form of the input distribution and our proofs only use the definition of ReLU, in contrast with previous works that are restricted to standard Gaussian input. We show that (stochastic) gradient descent with random initialization can learn the convolutional filter in polynomial time and the convergence rate depends on the smoothness of the input distribution and the closeness of patches. To the best of our knowledge, this is the first recovery guarantee of gradient-based algorithms for convolutional filter on non-Gaussian input distributions. Our theory also justifies the two-stage learning rate strategy in deep neural networks. While our focus is theoretical, we also present experiments that illustrate our theoretical findings.

Implicit Neural Representations (INRs) have recently shown impressive results, but their fundamental capacity, implicit biases, and scaling behavior remain poorly understood. We investigate the performance of diverse INRs across a suite of 2D and 3D real and synthetic signals with varying effective bandwidth, as well as both overfitting and generalization tasks including tomography, super-resolution, and denoising. By stratifying performance according to model size as well as signal type and bandwidth, our results shed light on how different INR and grid representations allocate their capacity. We find that, for most tasks and signals, a simple regularized grid with interpolation trains faster and to higher quality than any INR with the same number of parameters. We also find limited settings where INRs outperform grids -- namely fitting signals with underlying lower-dimensional structure such as shape contours -- to guide future use of INRs towards the most advantageous applications. Code and synthetic signals used in our analysis are available at https://github.com/voilalab/INR-benchmark.

Deep Neural Networks lead the state of the art of computer vision tasks. Despite this, Neural Networks are brittle in that small changes in the input can drastically affect their prediction outcome and confidence. Consequently and naturally, research in this area mainly focus on adversarial attacks and defenses. In this paper, we take an alternative stance and introduce the concept of Assistive Signals, which are optimized to improve a model's confidence score regardless if it's under attack or not. We analyse some interesting properties of these assistive perturbations and extend the idea to optimize assistive signals in the 3D space for real-life scenarios simulating different lighting conditions and viewing angles. Experimental evaluations show that the assistive signals generated by our optimization method increase the accuracy and confidence of deep models more than those generated by conventional methods that work in the 2D space. In addition, our Assistive Signals illustrate the intrinsic bias of ML models towards certain patterns in real-life objects. We discuss how we can exploit these insights to re-think, or avoid, some patterns that might contribute to, or degrade, the detectability of objects in the real-world.

Out-of-distribution (OOD) problems in few-shot classification (FSC) occur when novel classes sampled from testing distributions differ from base classes drawn from training distributions, which considerably degrades the performance of deep learning models deployed in real-world applications. Recent studies suggest that the OOD problems in FSC mainly including: (a) cross-domain few-shot classification (CD-FSC) and (b) spurious-correlation few-shot classification (SC-FSC). Specifically, CD-FSC occurs when a classifier learns transferring knowledge from base classes drawn from seen training distributions but recognizes novel classes sampled from unseen testing distributions. In contrast, SC-FSC arises when a classifier relies on non-causal features (or contexts) that happen to be correlated with the labels (or concepts) in base classes but such relationships no longer hold during the model deployment. Despite CD-FSC has been extensively studied, SC-FSC remains understudied due to lack of the corresponding evaluation benchmarks. To this end, we present Meta Concept Context (MetaCoCo), a benchmark with spurious-correlation shifts collected from real-world scenarios. Moreover, to quantify the extent of spurious-correlation shifts of the presented MetaCoCo, we further propose a metric by using CLIP as a pre-trained vision-language model. Extensive experiments on the proposed benchmark are performed to evaluate the state-of-the-art methods in FSC, cross-domain shifts, and self-supervised learning. The experimental results show that the performance of the existing methods degrades significantly in the presence of spurious-correlation shifts. We open-source all codes of our benchmark and hope that the proposed MetaCoCo can facilitate future research on spurious-correlation shifts problems in FSC. The code is available at: https://github.com/remiMZ/MetaCoCo-ICLR24.

In this paper we introduce Feature Gradients, a gradient-based search algorithm for feature selection. Our approach extends a recent result on the estimation of learnability in the sublinear data regime by showing that the calculation can be performed iteratively (i.e., in mini-batches) and in linear time and space with respect to both the number of features D and the sample size N . This, along with a discrete-to-continuous relaxation of the search domain, allows for an efficient, gradient-based search algorithm among feature subsets for very large datasets. Crucially, our algorithm is capable of finding higher-order correlations between features and targets for both the N > D and N < D regimes, as opposed to approaches that do not consider such interactions and/or only consider one regime. We provide experimental demonstration of the algorithm in small and large sample-and feature-size settings.

In this paper, we describe a phenomenon, which we named "super-convergence", where neural networks can be trained an order of magnitude faster than with standard training methods. The existence of super-convergence is relevant to understanding why deep networks generalize well. One of the key elements of super-convergence is training with one learning rate cycle and a large maximum learning rate. A primary insight that allows super-convergence training is that large learning rates regularize the training, hence requiring a reduction of all other forms of regularization in order to preserve an optimal regularization balance. We also derive a simplification of the Hessian Free optimization method to compute an estimate of the optimal learning rate. Experiments demonstrate super-convergence for Cifar-10/100, MNIST and Imagenet datasets, and resnet, wide-resnet, densenet, and inception architectures. In addition, we show that super-convergence provides a greater boost in performance relative to standard training when the amount of labeled training data is limited. The architectures and code to replicate the figures in this paper are available at github.com/lnsmith54/super-convergence. See http://www.fast.ai/2018/04/30/dawnbench-fastai/ for an application of super-convergence to win the DAWNBench challenge (see https://dawn.cs.stanford.edu/benchmark/).

In this work, we propose a concise neural operator architecture for operator learning. Drawing an analogy with a conventional fully connected neural network, we define the neural operator as follows: the output of the i-th neuron in a nonlinear operator layer is defined by mathcal O_i(u) = sigmaleft( sum_j mathcal W_{ij} u + mathcal B_{ij}right). Here, mathcal W_{ij} denotes the bounded linear operator connecting j-th input neuron to i-th output neuron, and the bias mathcal B_{ij} takes the form of a function rather than a scalar. Given its new universal approximation property, the efficient parameterization of the bounded linear operators between two neurons (Banach spaces) plays a critical role. As a result, we introduce MgNO, utilizing multigrid structures to parameterize these linear operators between neurons. This approach offers both mathematical rigor and practical expressivity. Additionally, MgNO obviates the need for conventional lifting and projecting operators typically required in previous neural operators. Moreover, it seamlessly accommodates diverse boundary conditions. Our empirical observations reveal that MgNO exhibits superior ease of training compared to other CNN-based models, while also displaying a reduced susceptibility to overfitting when contrasted with spectral-type neural operators. We demonstrate the efficiency and accuracy of our method with consistently state-of-the-art performance on different types of partial differential equations (PDEs).

We show that in a variety of large-scale deep learning scenarios the gradient dynamically converges to a very small subspace after a short period of training. The subspace is spanned by a few top eigenvectors of the Hessian (equal to the number of classes in the dataset), and is mostly preserved over long periods of training. A simple argument then suggests that gradient descent may happen mostly in this subspace. We give an example of this effect in a solvable model of classification, and we comment on possible implications for optimization and learning.

Recent research has demonstrated that transformers, particularly linear attention models, implicitly execute gradient-descent-like algorithms on data provided in-context during their forward inference step. However, their capability in handling more complex problems remains unexplored. In this paper, we prove that any linear transformer maintains an implicit linear model and can be interpreted as performing a variant of preconditioned gradient descent. We also investigate the use of linear transformers in a challenging scenario where the training data is corrupted with different levels of noise. Remarkably, we demonstrate that for this problem linear transformers discover an intricate and highly effective optimization algorithm, surpassing or matching in performance many reasonable baselines. We reverse-engineer this algorithm and show that it is a novel approach incorporating momentum and adaptive rescaling based on noise levels. Our findings show that even linear transformers possess the surprising ability to discover sophisticated optimization strategies.

We show that diffusion models can achieve image sample quality superior to the current state-of-the-art generative models. We achieve this on unconditional image synthesis by finding a better architecture through a series of ablations. For conditional image synthesis, we further improve sample quality with classifier guidance: a simple, compute-efficient method for trading off diversity for fidelity using gradients from a classifier. We achieve an FID of 2.97 on ImageNet 128times128, 4.59 on ImageNet 256times256, and 7.72 on ImageNet 512times512, and we match BigGAN-deep even with as few as 25 forward passes per sample, all while maintaining better coverage of the distribution. Finally, we find that classifier guidance combines well with upsampling diffusion models, further improving FID to 3.94 on ImageNet 256times256 and 3.85 on ImageNet 512times512. We release our code at https://github.com/openai/guided-diffusion

Non-linear activation functions are crucial in Convolutional Neural Networks. However, until now they have not been well described in the frequency domain. In this work, we study the spectral behavior of ReLU, a popular activation function. We use the ReLU's Taylor expansion to derive its frequency domain behavior. We demonstrate that ReLU introduces higher frequency oscillations in the signal and a constant DC component. Furthermore, we investigate the importance of this DC component, where we demonstrate that it helps the model extract meaningful features related to the input frequency content. We accompany our theoretical derivations with experiments and real-world examples. First, we numerically validate our frequency response model. Then we observe ReLU's spectral behavior on two example models and a real-world one. Finally, we experimentally investigate the role of the DC component introduced by ReLU in the CNN's representations. Our results indicate that the DC helps to converge to a weight configuration that is close to the initial random weights.

It is often advantageous to train models on a subset of the available train examples, because the examples are of variable quality or because one would like to train with fewer examples, without sacrificing performance. We present Gradient Information Optimization (GIO), a scalable, task-agnostic approach to this data selection problem that requires only a small set of (unlabeled) examples representing a target distribution. GIO begins from a natural, information-theoretic objective that is intractable in practice. Our contribution is in showing that it can be made highly scalable through a simple relaxation of the objective and a highly efficient implementation. In experiments with machine translation, spelling correction, and image recognition, we show that GIO delivers outstanding results with very small train sets. These findings are robust to different representation models and hyperparameters for GIO itself. GIO is task- and domain-agnostic and can be applied out-of-the-box to new datasets and domains.

We introduce Gradient Descent with Adaptive Momentum Scaling (Grams), a novel optimization algorithm that decouples the direction and magnitude of parameter updates in deep learning. Unlike traditional optimizers that directly integrate momentum into updates, Grams separates the update direction, derived from current gradients, from momentum, which is used solely for adaptive magnitude scaling. This approach enables Grams to achieve improved loss descent compared to state-of-the-art cautious and momentum-based optimizers. We establish a global convergence guarantee for Grams and validate its effectiveness through extensive empirical evaluations. The results demonstrate Grams' superior performance, including faster convergence and better generalization, compared to widely-used optimizers such as Adam, Lion, and their cautious variants. Our results highlight Grams' potential as a transformative approach for efficient optimization in large-scale machine learning.

Classifier-free guidance (CFG) is crucial for improving both generation quality and alignment between the input condition and final output in diffusion models. While a high guidance scale is generally required to enhance these aspects, it also causes oversaturation and unrealistic artifacts. In this paper, we revisit the CFG update rule and introduce modifications to address this issue. We first decompose the update term in CFG into parallel and orthogonal components with respect to the conditional model prediction and observe that the parallel component primarily causes oversaturation, while the orthogonal component enhances image quality. Accordingly, we propose down-weighting the parallel component to achieve high-quality generations without oversaturation. Additionally, we draw a connection between CFG and gradient ascent and introduce a new rescaling and momentum method for the CFG update rule based on this insight. Our approach, termed adaptive projected guidance (APG), retains the quality-boosting advantages of CFG while enabling the use of higher guidance scales without oversaturation. APG is easy to implement and introduces practically no additional computational overhead to the sampling process. Through extensive experiments, we demonstrate that APG is compatible with various conditional diffusion models and samplers, leading to improved FID, recall, and saturation scores while maintaining precision comparable to CFG, making our method a superior plug-and-play alternative to standard classifier-free guidance.

Restart techniques are common in gradient-free optimization to deal with multimodal functions. Partial warm restarts are also gaining popularity in gradient-based optimization to improve the rate of convergence in accelerated gradient schemes to deal with ill-conditioned functions. In this paper, we propose a simple warm restart technique for stochastic gradient descent to improve its anytime performance when training deep neural networks. We empirically study its performance on the CIFAR-10 and CIFAR-100 datasets, where we demonstrate new state-of-the-art results at 3.14% and 16.21%, respectively. We also demonstrate its advantages on a dataset of EEG recordings and on a downsampled version of the ImageNet dataset. Our source code is available at https://github.com/loshchil/SGDR

Sparse coding, which refers to modeling a signal as sparse linear combinations of the elements of a learned dictionary, has proven to be a successful (and interpretable) approach in applications such as signal processing, computer vision, and medical imaging. While this success has spurred much work on provable guarantees for dictionary recovery when the learned dictionary is the same size as the ground-truth dictionary, work on the setting where the learned dictionary is larger (or over-realized) with respect to the ground truth is comparatively nascent. Existing theoretical results in this setting have been constrained to the case of noise-less data. We show in this work that, in the presence of noise, minimizing the standard dictionary learning objective can fail to recover the elements of the ground-truth dictionary in the over-realized regime, regardless of the magnitude of the signal in the data-generating process. Furthermore, drawing from the growing body of work on self-supervised learning, we propose a novel masking objective for which recovering the ground-truth dictionary is in fact optimal as the signal increases for a large class of data-generating processes. We corroborate our theoretical results with experiments across several parameter regimes showing that our proposed objective also enjoys better empirical performance than the standard reconstruction objective.

Existing image contrast enhancement methods are typically designed for specific tasks such as under-/over-exposure correction, low-light and backlit image enhancement, etc. The learned models, however, exhibit poor generalization performance across different tasks, even across different datasets of a specific task. It is important to explore whether we can learn a universal and generalized model for various contrast enhancement tasks. In this work, we observe that the common key factor of these tasks lies in the need of exposure and contrast adjustment, which can be well-addressed if high-dynamic range (HDR) inputs are available. We hence collect 46,928 HDR raw images from public sources, and render 328,496 sRGB images to build multi-exposure sequences (MES) and the corresponding pseudo sRGB ground-truths via multi-exposure fusion. Consequently, we train a network to generate an MES from a single sRGB image, followed by training another network to fuse the generated MES into an enhanced image. Our proposed method, namely UNiversal Image Contrast Enhancer (UNICE), is free of costly human labeling. However, it demonstrates significantly stronger generalization performance than existing image contrast enhancement methods across and within different tasks, even outperforming manually created ground-truths in multiple no-reference image quality metrics. The dataset, code and model are available at https://github.com/BeyondHeaven/UNICE.

The generalization mystery in deep learning is the following: Why do over-parameterized neural networks trained with gradient descent (GD) generalize well on real datasets even though they are capable of fitting random datasets of comparable size? Furthermore, from among all solutions that fit the training data, how does GD find one that generalizes well (when such a well-generalizing solution exists)? We argue that the answer to both questions lies in the interaction of the gradients of different examples during training. Intuitively, if the per-example gradients are well-aligned, that is, if they are coherent, then one may expect GD to be (algorithmically) stable, and hence generalize well. We formalize this argument with an easy to compute and interpretable metric for coherence, and show that the metric takes on very different values on real and random datasets for several common vision networks. The theory also explains a number of other phenomena in deep learning, such as why some examples are reliably learned earlier than others, why early stopping works, and why it is possible to learn from noisy labels. Moreover, since the theory provides a causal explanation of how GD finds a well-generalizing solution when one exists, it motivates a class of simple modifications to GD that attenuate memorization and improve generalization. Generalization in deep learning is an extremely broad phenomenon, and therefore, it requires an equally general explanation. We conclude with a survey of alternative lines of attack on this problem, and argue that the proposed approach is the most viable one on this basis.

The task of mixture proportion estimation (MPE) is to estimate the weight of a component distribution in a mixture, given observations from both the component and mixture. Previous work on MPE adopts the irreducibility assumption, which ensures identifiablity of the mixture proportion. In this paper, we propose a more general sufficient condition that accommodates several settings of interest where irreducibility does not hold. We further present a resampling-based meta-algorithm that takes any existing MPE algorithm designed to work under irreducibility and adapts it to work under our more general condition. Our approach empirically exhibits improved estimation performance relative to baseline methods and to a recently proposed regrouping-based algorithm.

Optimization in machine learning, both theoretical and applied, is presently dominated by first-order gradient methods such as stochastic gradient descent. Second-order optimization methods, that involve second derivatives and/or second order statistics of the data, are far less prevalent despite strong theoretical properties, due to their prohibitive computation, memory and communication costs. In an attempt to bridge this gap between theoretical and practical optimization, we present a scalable implementation of a second-order preconditioned method (concretely, a variant of full-matrix Adagrad), that along with several critical algorithmic and numerical improvements, provides significant convergence and wall-clock time improvements compared to conventional first-order methods on state-of-the-art deep models. Our novel design effectively utilizes the prevalent heterogeneous hardware architecture for training deep models, consisting of a multicore CPU coupled with multiple accelerator units. We demonstrate superior performance compared to state-of-the-art on very large learning tasks such as machine translation with Transformers, language modeling with BERT, click-through rate prediction on Criteo, and image classification on ImageNet with ResNet-50.

In distributed computing, slower nodes (stragglers) usually become a bottleneck. Gradient Coding (GC), introduced by Tandon et al., is an efficient technique that uses principles of error-correcting codes to distribute gradient computation in the presence of stragglers. In this paper, we consider the distributed computation of a sequence of gradients {g(1),g(2),ldots,g(J)}, where processing of each gradient g(t) starts in round-t and finishes by round-(t+T). Here Tgeq 0 denotes a delay parameter. For the GC scheme, coding is only across computing nodes and this results in a solution where T=0. On the other hand, having T>0 allows for designing schemes which exploit the temporal dimension as well. In this work, we propose two schemes that demonstrate improved performance compared to GC. Our first scheme combines GC with selective repetition of previously unfinished tasks and achieves improved straggler mitigation. In our second scheme, which constitutes our main contribution, we apply GC to a subset of the tasks and repetition for the remainder of the tasks. We then multiplex these two classes of tasks across workers and rounds in an adaptive manner, based on past straggler patterns. Using theoretical analysis, we demonstrate that our second scheme achieves significant reduction in the computational load. In our experiments, we study a practical setting of concurrently training multiple neural networks over an AWS Lambda cluster involving 256 worker nodes, where our framework naturally applies. We demonstrate that the latter scheme can yield a 16\% improvement in runtime over the baseline GC scheme, in the presence of naturally occurring, non-simulated stragglers.

We investigate the training and performance of generative adversarial networks using the Maximum Mean Discrepancy (MMD) as critic, termed MMD GANs. As our main theoretical contribution, we clarify the situation with bias in GAN loss functions raised by recent work: we show that gradient estimators used in the optimization process for both MMD GANs and Wasserstein GANs are unbiased, but learning a discriminator based on samples leads to biased gradients for the generator parameters. We also discuss the issue of kernel choice for the MMD critic, and characterize the kernel corresponding to the energy distance used for the Cramer GAN critic. Being an integral probability metric, the MMD benefits from training strategies recently developed for Wasserstein GANs. In experiments, the MMD GAN is able to employ a smaller critic network than the Wasserstein GAN, resulting in a simpler and faster-training algorithm with matching performance. We also propose an improved measure of GAN convergence, the Kernel Inception Distance, and show how to use it to dynamically adapt learning rates during GAN training.

We consider the training of the first layer of vision models and notice the clear relationship between pixel values and gradient update magnitudes: the gradients arriving at the weights of a first layer are by definition directly proportional to (normalized) input pixel values. Thus, an image with low contrast has a smaller impact on learning than an image with higher contrast, and a very bright or very dark image has a stronger impact on the weights than an image with moderate brightness. In this work, we propose performing gradient descent on the embeddings produced by the first layer of the model. However, switching to discrete inputs with an embedding layer is not a reasonable option for vision models. Thus, we propose the conceptual procedure of (i) a gradient descent step on first layer activations to construct an activation proposal, and (ii) finding the optimal weights of the first layer, i.e., those weights which minimize the squared distance to the activation proposal. We provide a closed form solution of the procedure and adjust it for robust stochastic training while computing everything efficiently. Empirically, we find that TrAct (Training Activations) speeds up training by factors between 1.25x and 4x while requiring only a small computational overhead. We demonstrate the utility of TrAct with different optimizers for a range of different vision models including convolutional and transformer architectures.

Activation patching is a standard method in mechanistic interpretability for localizing the components of a model responsible for specific behaviors, but it is computationally expensive to apply at scale. Attribution patching offers a faster, gradient-based approximation, yet suffers from noise and reduced reliability in deep, highly non-linear networks. In this work, we introduce Relevance Patching (RelP), which replaces the local gradients in attribution patching with propagation coefficients derived from Layer-wise Relevance Propagation (LRP). LRP propagates the network's output backward through the layers, redistributing relevance to lower-level components according to local propagation rules that ensure properties such as relevance conservation or improved signal-to-noise ratio. Like attribution patching, RelP requires only two forward passes and one backward pass, maintaining computational efficiency while improving faithfulness. We validate RelP across a range of models and tasks, showing that it more accurately approximates activation patching than standard attribution patching, particularly when analyzing residual stream and MLP outputs in the Indirect Object Identification (IOI) task. For instance, for MLP outputs in GPT-2 Large, attribution patching achieves a Pearson correlation of 0.006, whereas RelP reaches 0.956, highlighting the improvement offered by RelP. Additionally, we compare the faithfulness of sparse feature circuits identified by RelP and Integrated Gradients (IG), showing that RelP achieves comparable faithfulness without the extra computational cost associated with IG.

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.

Modeling and synthesizing low-light raw noise is a fundamental problem for computational photography and image processing applications. Although most recent works have adopted physics-based models to synthesize noise, the signal-independent noise in low-light conditions is far more complicated and varies dramatically across camera sensors, which is beyond the description of these models. To address this issue, we introduce a new perspective to synthesize the signal-independent noise by a generative model. Specifically, we synthesize the signal-dependent and signal-independent noise in a physics- and learning-based manner, respectively. In this way, our method can be considered as a general model, that is, it can simultaneously learn different noise characteristics for different ISO levels and generalize to various sensors. Subsequently, we present an effective multi-scale discriminator termed Fourier transformer discriminator (FTD) to distinguish the noise distribution accurately. Additionally, we collect a new low-light raw denoising (LRD) dataset for training and benchmarking. Qualitative validation shows that the noise generated by our proposed noise model can be highly similar to the real noise in terms of distribution. Furthermore, extensive denoising experiments demonstrate that our method performs favorably against state-of-the-art methods on different sensors.

Deep networks are increasingly being applied to problems involving image synthesis, e.g., generating images from textual descriptions and reconstructing an input image from a compact representation. Supervised training of image-synthesis networks typically uses a pixel-wise loss (PL) to indicate the mismatch between a generated image and its corresponding target image. We propose instead to use a loss function that is better calibrated to human perceptual judgments of image quality: the multiscale structural-similarity score (MS-SSIM). Because MS-SSIM is differentiable, it is easily incorporated into gradient-descent learning. We compare the consequences of using MS-SSIM versus PL loss on training deterministic and stochastic autoencoders. For three different architectures, we collected human judgments of the quality of image reconstructions. Observers reliably prefer images synthesized by MS-SSIM-optimized models over those synthesized by PL-optimized models, for two distinct PL measures (ell_1 and ell_2 distances). We also explore the effect of training objective on image encoding and analyze conditions under which perceptually-optimized representations yield better performance on image classification. Finally, we demonstrate the superiority of perceptually-optimized networks for super-resolution imaging. Just as computer vision has advanced through the use of convolutional architectures that mimic the structure of the mammalian visual system, we argue that significant additional advances can be made in modeling images through the use of training objectives that are well aligned to characteristics of human perception.

Recently, neural network (NN)-based image compression studies have actively been made and has shown impressive performance in comparison to traditional methods. However, most of the works have focused on non-scalable image compression (single-layer coding) while spatially scalable image compression has drawn less attention although it has many applications. In this paper, we propose a novel NN-based spatially scalable image compression method, called COMPASS, which supports arbitrary-scale spatial scalability. Our proposed COMPASS has a very flexible structure where the number of layers and their respective scale factors can be arbitrarily determined during inference. To reduce the spatial redundancy between adjacent layers for arbitrary scale factors, our COMPASS adopts an inter-layer arbitrary scale prediction method, called LIFF, based on implicit neural representation. We propose a combined RD loss function to effectively train multiple layers. Experimental results show that our COMPASS achieves BD-rate gain of -58.33% and -47.17% at maximum compared to SHVC and the state-of-the-art NN-based spatially scalable image compression method, respectively, for various combinations of scale factors. Our COMPASS also shows comparable or even better coding efficiency than the single-layer coding for various scale factors.

While previous distribution shift detection approaches can identify if a shift has occurred, these approaches cannot localize which specific features have caused a distribution shift -- a critical step in diagnosing or fixing any underlying issue. For example, in military sensor networks, users will want to detect when one or more of the sensors has been compromised, and critically, they will want to know which specific sensors might be compromised. Thus, we first define a formalization of this problem as multiple conditional distribution hypothesis tests and propose both non-parametric and parametric statistical tests. For both efficiency and flexibility, we then propose to use a test statistic based on the density model score function (i.e. gradient with respect to the input) -- which can easily compute test statistics for all dimensions in a single forward and backward pass. Any density model could be used for computing the necessary statistics including deep density models such as normalizing flows or autoregressive models. We additionally develop methods for identifying when and where a shift occurs in multivariate time-series data and show results for multiple scenarios using realistic attack models on both simulated and real world data.

Pan-sharpening involves reconstructing missing high-frequency information in multi-spectral images with low spatial resolution, using a higher-resolution panchromatic image as guidance. Although the inborn connection with frequency domain, existing pan-sharpening research has not almost investigated the potential solution upon frequency domain. To this end, we propose a novel Frequency Adaptive Mixture of Experts (FAME) learning framework for pan-sharpening, which consists of three key components: the Adaptive Frequency Separation Prediction Module, the Sub-Frequency Learning Expert Module, and the Expert Mixture Module. In detail, the first leverages the discrete cosine transform to perform frequency separation by predicting the frequency mask. On the basis of generated mask, the second with low-frequency MOE and high-frequency MOE takes account for enabling the effective low-frequency and high-frequency information reconstruction. Followed by, the final fusion module dynamically weights high-frequency and low-frequency MOE knowledge to adapt to remote sensing images with significant content variations. Quantitative and qualitative experiments over multiple datasets demonstrate that our method performs the best against other state-of-the-art ones and comprises a strong generalization ability for real-world scenes. Code will be made publicly at https://github.com/alexhe101/FAME-Net.

In this paper, we prove representation bottlenecks of a cascaded convolutional decoder network, considering the capacity of representing different frequency components of an input sample. We conduct the discrete Fourier transform on each channel of the feature map in an intermediate layer of the decoder network. Then, we introduce the rule of the forward propagation of such intermediate-layer spectrum maps, which is equivalent to the forward propagation of feature maps through a convolutional layer. Based on this, we find that each frequency component in the spectrum map is forward propagated independently with other frequency components. Furthermore, we prove two bottlenecks in representing feature spectrums. First, we prove that the convolution operation, the zero-padding operation, and a set of other settings all make a convolutional decoder network more likely to weaken high-frequency components. Second, we prove that the upsampling operation generates a feature spectrum, in which strong signals repetitively appears at certain frequencies.

Stochastic Gradient Decent (SGD) is one of the core techniques behind the success of deep neural networks. The gradient provides information on the direction in which a function has the steepest rate of change. The main problem with basic SGD is to change by equal sized steps for all parameters, irrespective of gradient behavior. Hence, an efficient way of deep network optimization is to make adaptive step sizes for each parameter. Recently, several attempts have been made to improve gradient descent methods such as AdaGrad, AdaDelta, RMSProp and Adam. These methods rely on the square roots of exponential moving averages of squared past gradients. Thus, these methods do not take advantage of local change in gradients. In this paper, a novel optimizer is proposed based on the difference between the present and the immediate past gradient (i.e., diffGrad). In the proposed diffGrad optimization technique, the step size is adjusted for each parameter in such a way that it should have a larger step size for faster gradient changing parameters and a lower step size for lower gradient changing parameters. The convergence analysis is done using the regret bound approach of online learning framework. Rigorous analysis is made in this paper over three synthetic complex non-convex functions. The image categorization experiments are also conducted over the CIFAR10 and CIFAR100 datasets to observe the performance of diffGrad with respect to the state-of-the-art optimizers such as SGDM, AdaGrad, AdaDelta, RMSProp, AMSGrad, and Adam. The residual unit (ResNet) based Convolutional Neural Networks (CNN) architecture is used in the experiments. The experiments show that diffGrad outperforms other optimizers. Also, we show that diffGrad performs uniformly well for training CNN using different activation functions. The source code is made publicly available at https://github.com/shivram1987/diffGrad.

Adaptive gradient methods, e.g. Adam, have achieved tremendous success in machine learning. Scaling the learning rate element-wisely by a certain form of second moment estimate of gradients, such methods are able to attain rapid training of modern deep neural networks. Nevertheless, they are observed to suffer from compromised generalization ability compared with stochastic gradient descent (SGD) and tend to be trapped in local minima at an early stage during training. Intriguingly, we discover that substituting the gradient in the second raw moment estimate term with its momentumized version in Adam can resolve the issue. The intuition is that gradient with momentum contains more accurate directional information and therefore its second moment estimation is a more favorable option for learning rate scaling than that of the raw gradient. Thereby we propose AdaMomentum as a new optimizer reaching the goal of training fast while generalizing much better. We further develop a theory to back up the improvement in generalization and provide convergence guarantees under both convex and nonconvex settings. Extensive experiments on a wide range of tasks and models demonstrate that AdaMomentum exhibits state-of-the-art performance and superior training stability consistently.

We propose a new variant of AMSGrad, a popular adaptive gradient based optimization algorithm widely used for training deep neural networks. Our algorithm adds prior knowledge about the sequence of consecutive mini-batch gradients and leverages its underlying structure making the gradients sequentially predictable. By exploiting the predictability and ideas from optimistic online learning, the proposed algorithm can accelerate the convergence and increase sample efficiency. After establishing a tighter upper bound under some convexity conditions on the regret, we offer a complimentary view of our algorithm which generalizes the offline and stochastic version of nonconvex optimization. In the nonconvex case, we establish a non-asymptotic convergence bound independently of the initialization. We illustrate the practical speedup on several deep learning models via numerical experiments.

Autoencoders are a popular model in many branches of machine learning and lossy data compression. However, their fundamental limits, the performance of gradient methods and the features learnt during optimization remain poorly understood, even in the two-layer setting. In fact, earlier work has considered either linear autoencoders or specific training regimes (leading to vanishing or diverging compression rates). Our paper addresses this gap by focusing on non-linear two-layer autoencoders trained in the challenging proportional regime in which the input dimension scales linearly with the size of the representation. Our results characterize the minimizers of the population risk, and show that such minimizers are achieved by gradient methods; their structure is also unveiled, thus leading to a concise description of the features obtained via training. For the special case of a sign activation function, our analysis establishes the fundamental limits for the lossy compression of Gaussian sources via (shallow) autoencoders. Finally, while the results are proved for Gaussian data, numerical simulations on standard datasets display the universality of the theoretical predictions.

We present EGN, a stochastic second-order optimization algorithm that combines the generalized Gauss-Newton (GN) Hessian approximation with low-rank linear algebra to compute the descent direction. Leveraging the Duncan-Guttman matrix identity, the parameter update is obtained by factorizing a matrix which has the size of the mini-batch. This is particularly advantageous for large-scale machine learning problems where the dimension of the neural network parameter vector is several orders of magnitude larger than the batch size. Additionally, we show how improvements such as line search, adaptive regularization, and momentum can be seamlessly added to EGN to further accelerate the algorithm. Moreover, under mild assumptions, we prove that our algorithm converges to an epsilon-stationary point at a linear rate. Finally, our numerical experiments demonstrate that EGN consistently exceeds, or at most matches the generalization performance of well-tuned SGD, Adam, and SGN optimizers across various supervised and reinforcement learning tasks.

Hyperspectral pansharpening is receiving a growing interest since the last few years as testified by a large number of research papers and challenges. It consists in a pixel-level fusion between a lower-resolution hyperspectral datacube and a higher-resolution single-band image, the panchromatic image, with the goal of providing a hyperspectral datacube at panchromatic resolution. Thanks to their powerful representational capabilities, deep learning models have succeeded to provide unprecedented results on many general purpose image processing tasks. However, when moving to domain specific problems, as in this case, the advantages with respect to traditional model-based approaches are much lesser clear-cut due to several contextual reasons. Scarcity of training data, lack of ground-truth, data shape variability, are some such factors that limit the generalization capacity of the state-of-the-art deep learning networks for hyperspectral pansharpening. To cope with these limitations, in this work we propose a new deep learning method which inherits a simple single-band unsupervised pansharpening model nested in a sequential band-wise adaptive scheme, where each band is pansharpened refining the model tuned on the preceding one. By doing so, a simple model is propagated along the wavelength dimension, adaptively and flexibly, with no need to have a fixed number of spectral bands, and, with no need to dispose of large, expensive and labeled training datasets. The proposed method achieves very good results on our datasets, outperforming both traditional and deep learning reference methods. The implementation of the proposed method can be found on https://github.com/giu-guarino/R-PNN

The measure of a machine learning algorithm is the difficulty of the tasks it can perform, and sufficiently difficult tasks are critical drivers of strong machine learning models. However, quantifying the generalization difficulty of machine learning benchmarks has remained challenging. We propose what is to our knowledge the first model-agnostic measure of the inherent generalization difficulty of tasks. Our inductive bias complexity measure quantifies the total information required to generalize well on a task minus the information provided by the data. It does so by measuring the fractional volume occupied by hypotheses that generalize on a task given that they fit the training data. It scales exponentially with the intrinsic dimensionality of the space over which the model must generalize but only polynomially in resolution per dimension, showing that tasks which require generalizing over many dimensions are drastically more difficult than tasks involving more detail in fewer dimensions. Our measure can be applied to compute and compare supervised learning, reinforcement learning and meta-learning generalization difficulties against each other. We show that applied empirically, it formally quantifies intuitively expected trends, e.g. that in terms of required inductive bias, MNIST < CIFAR10 < Imagenet and fully observable Markov decision processes (MDPs) < partially observable MDPs. Further, we show that classification of complex images < few-shot meta-learning with simple images. Our measure provides a quantitative metric to guide the construction of more complex tasks requiring greater inductive bias, and thereby encourages the development of more sophisticated architectures and learning algorithms with more powerful generalization capabilities.

We establish a new theoretical framework for learning under multi-class, instance-dependent label noise. This framework casts learning with label noise as a form of domain adaptation, in particular, domain adaptation under posterior drift. We introduce the concept of relative signal strength (RSS), a pointwise measure that quantifies the transferability from noisy to clean posterior. Using RSS, we establish nearly matching upper and lower bounds on the excess risk. Our theoretical findings support the simple Noise Ignorant Empirical Risk Minimization (NI-ERM) principle, which minimizes empirical risk while ignoring label noise. Finally, we translate this theoretical insight into practice: by using NI-ERM to fit a linear classifier on top of a self-supervised feature extractor, we achieve state-of-the-art performance on the CIFAR-N data challenge.

We introduce a parametric nonlinear transformation that is well-suited for Gaussianizing data from natural images. The data are linearly transformed, and each component is then normalized by a pooled activity measure, computed by exponentiating a weighted sum of rectified and exponentiated components and a constant. We optimize the parameters of the full transformation (linear transform, exponents, weights, constant) over a database of natural images, directly minimizing the negentropy of the responses. The optimized transformation substantially Gaussianizes the data, achieving a significantly smaller mutual information between transformed components than alternative methods including ICA and radial Gaussianization. The transformation is differentiable and can be efficiently inverted, and thus induces a density model on images. We show that samples of this model are visually similar to samples of natural image patches. We demonstrate the use of the model as a prior probability density that can be used to remove additive noise. Finally, we show that the transformation can be cascaded, with each layer optimized using the same Gaussianization objective, thus offering an unsupervised method of optimizing a deep network architecture.

Normalization layers are one of the key building blocks for deep neural networks. Several theoretical studies have shown that batch normalization improves the signal propagation, by avoiding the representations from becoming collinear across the layers. However, results on mean-field theory of batch normalization also conclude that this benefit comes at the expense of exploding gradients in depth. Motivated by these two aspects of batch normalization, in this study we pose the following question: "Can a batch-normalized network keep the optimal signal propagation properties, but avoid exploding gradients?" We answer this question in the affirmative by giving a particular construction of an Multi-Layer Perceptron (MLP) with linear activations and batch-normalization that provably has bounded gradients at any depth. Based on Weingarten calculus, we develop a rigorous and non-asymptotic theory for this constructed MLP that gives a precise characterization of forward signal propagation, while proving that gradients remain bounded for linearly independent input samples, which holds in most practical settings. Inspired by our theory, we also design an activation shaping scheme that empirically achieves the same properties for certain non-linear activations.

Clipping the gradient is a known approach to improving gradient descent, but requires hand selection of a clipping threshold hyperparameter. We present AutoClip, a simple method for automatically and adaptively choosing a gradient clipping threshold, based on the history of gradient norms observed during training. Experimental results show that applying AutoClip results in improved generalization performance for audio source separation networks. Observation of the training dynamics of a separation network trained with and without AutoClip show that AutoClip guides optimization into smoother parts of the loss landscape. AutoClip is very simple to implement and can be integrated readily into a variety of applications across multiple domains.

We introduce MADGRAD, a novel optimization method in the family of AdaGrad adaptive gradient methods. MADGRAD shows excellent performance on deep learning optimization problems from multiple fields, including classification and image-to-image tasks in vision, and recurrent and bidirectionally-masked models in natural language processing. For each of these tasks, MADGRAD matches or outperforms both SGD and ADAM in test set performance, even on problems for which adaptive methods normally perform poorly.

The electrocardiogram (ECG) is an essential non-invasive diagnostic tool for assessing cardiac conditions. Existing automatic interpretation methods suffer from limited generalizability, focusing on a narrow range of cardiac conditions, and typically depend on raw physiological signals, which may not be readily available in resource-limited settings where only printed or digital ECG images are accessible. Recent advancements in multimodal large language models (MLLMs) present promising opportunities for addressing these challenges. However, the application of MLLMs to ECG image interpretation remains challenging due to the lack of instruction tuning datasets and well-established ECG image benchmarks for quantitative evaluation. To address these challenges, we introduce ECGInstruct, a comprehensive ECG image instruction tuning dataset of over one million samples, covering a wide range of ECG-related tasks from diverse data sources. Using ECGInstruct, we develop PULSE, an MLLM tailored for ECG image comprehension. In addition, we curate ECGBench, a new evaluation benchmark covering four key ECG image interpretation tasks across nine different datasets. Our experiments show that PULSE sets a new state-of-the-art, outperforming general MLLMs with an average accuracy improvement of 15% to 30%. This work highlights the potential of PULSE to enhance ECG interpretation in clinical practice.

In this paper, we consider a real-world scenario where a model that is trained on pre-defined classes continually encounters unlabeled data that contains both known and novel classes. The goal is to continually discover novel classes while maintaining the performance in known classes. We name the setting Continual Generalized Category Discovery (C-GCD). Existing methods for novel class discovery cannot directly handle the C-GCD setting due to some unrealistic assumptions, such as the unlabeled data only containing novel classes. Furthermore, they fail to discover novel classes in a continual fashion. In this work, we lift all these assumptions and propose an approach, called MetaGCD, to learn how to incrementally discover with less forgetting. Our proposed method uses a meta-learning framework and leverages the offline labeled data to simulate the testing incremental learning process. A meta-objective is defined to revolve around two conflicting learning objectives to achieve novel class discovery without forgetting. Furthermore, a soft neighborhood-based contrastive network is proposed to discriminate uncorrelated images while attracting correlated images. We build strong baselines and conduct extensive experiments on three widely used benchmarks to demonstrate the superiority of our method.

Diffusion models have emerged as a formidable tool for training-free conditional generation.However, a key hurdle in inference-time guidance techniques is the need for compute-heavy backpropagation through the diffusion network for estimating the guidance direction. Moreover, these techniques often require handcrafted parameter tuning on a case-by-case basis. Although some recent works have introduced minimal compute methods for linear inverse problems, a generic lightweight guidance solution to both linear and non-linear guidance problems is still missing. To this end, we propose Dreamguider, a method that enables inference-time guidance without compute-heavy backpropagation through the diffusion network. The key idea is to regulate the gradient flow through a time-varying factor. Moreover, we propose an empirical guidance scale that works for a wide variety of tasks, hence removing the need for handcrafted parameter tuning. We further introduce an effective lightweight augmentation strategy that significantly boosts the performance during inference-time guidance. We present experiments using Dreamguider on multiple tasks across multiple datasets and models to show the effectiveness of the proposed modules. To facilitate further research, we will make the code public after the review process.

Deep networks often suffer from vanishing or exploding gradients due to inefficient signal propagation, leading to long training times or convergence difficulties. Various architecture designs, sophisticated residual-style networks, and initialization schemes have been shown to improve deep signal propagation. Recently, Pennington et al. used free probability theory to show that dynamical isometry plays an integral role in efficient deep learning. We show that the simplest architecture change of gating each residual connection using a single zero-initialized parameter satisfies initial dynamical isometry and outperforms more complex approaches. Although much simpler than its predecessors, this gate enables training thousands of fully connected layers with fast convergence and better test performance for ResNets trained on CIFAR-10. We apply this technique to language modeling and find that we can easily train 120-layer Transformers. When applied to 12 layer Transformers, it converges 56% faster on enwiki8.

Leveraging second-order information about the loss at the scale of deep networks is one of the main lines of approach for improving the performance of current optimizers for deep learning. Yet, existing approaches for accurate full-matrix preconditioning, such as Full-Matrix Adagrad (GGT) or Matrix-Free Approximate Curvature (M-FAC) suffer from massive storage costs when applied even to small-scale models, as they must store a sliding window of gradients, whose memory requirements are multiplicative in the model dimension. In this paper, we address this issue via a novel and efficient error-feedback technique that can be applied to compress preconditioners by up to two orders of magnitude in practice, without loss of convergence. Specifically, our approach compresses the gradient information via sparsification or low-rank compression before it is fed into the preconditioner, feeding the compression error back into future iterations. Experiments on deep neural networks show that this approach can compress full-matrix preconditioners to up to 99\% sparsity without accuracy loss, effectively removing the memory overhead of full-matrix preconditioners such as GGT and M-FAC. Our code is available at https://github.com/IST-DASLab/EFCP.

Denoising diffusion models have been a mainstream approach for image generation, however, training these models often suffers from slow convergence. In this paper, we discovered that the slow convergence is partly due to conflicting optimization directions between timesteps. To address this issue, we treat the diffusion training as a multi-task learning problem, and introduce a simple yet effective approach referred to as Min-SNR-gamma. This method adapts loss weights of timesteps based on clamped signal-to-noise ratios, which effectively balances the conflicts among timesteps. Our results demonstrate a significant improvement in converging speed, 3.4times faster than previous weighting strategies. It is also more effective, achieving a new record FID score of 2.06 on the ImageNet 256times256 benchmark using smaller architectures than that employed in previous state-of-the-art. The code is available at https://github.com/TiankaiHang/Min-SNR-Diffusion-Training.

In this work, we consider the optimization process of minibatch stochastic gradient descent (SGD) on a 2-layer neural network with data separated by a quadratic ground truth function. We prove that with data drawn from the d-dimensional Boolean hypercube labeled by the quadratic ``XOR'' function y = -x_ix_j, it is possible to train to a population error o(1) with d :polylog(d) samples. Our result considers simultaneously training both layers of the two-layer-neural network with ReLU activations via standard minibatch SGD on the logistic loss. To our knowledge, this work is the first to give a sample complexity of O(d) for efficiently learning the XOR function on isotropic data on a standard neural network with standard training. Our main technique is showing that the network evolves in two phases: a signal-finding phase where the network is small and many of the neurons evolve independently to find features, and a signal-heavy phase, where SGD maintains and balances the features. We leverage the simultaneous training of the layers to show that it is sufficient for only a small fraction of the neurons to learn features, since those neurons will be amplified by the simultaneous growth of their second layer weights.

We perform an average case analysis of the generalization dynamics of large neural networks trained using gradient descent. We study the practically-relevant "high-dimensional" regime where the number of free parameters in the network is on the order of or even larger than the number of examples in the dataset. Using random matrix theory and exact solutions in linear models, we derive the generalization error and training error dynamics of learning and analyze how they depend on the dimensionality of data and signal to noise ratio of the learning problem. We find that the dynamics of gradient descent learning naturally protect against overtraining and overfitting in large networks. Overtraining is worst at intermediate network sizes, when the effective number of free parameters equals the number of samples, and thus can be reduced by making a network smaller or larger. Additionally, in the high-dimensional regime, low generalization error requires starting with small initial weights. We then turn to non-linear neural networks, and show that making networks very large does not harm their generalization performance. On the contrary, it can in fact reduce overtraining, even without early stopping or regularization of any sort. We identify two novel phenomena underlying this behavior in overcomplete models: first, there is a frozen subspace of the weights in which no learning occurs under gradient descent; and second, the statistical properties of the high-dimensional regime yield better-conditioned input correlations which protect against overtraining. We demonstrate that naive application of worst-case theories such as Rademacher complexity are inaccurate in predicting the generalization performance of deep neural networks, and derive an alternative bound which incorporates the frozen subspace and conditioning effects and qualitatively matches the behavior observed in simulation.

Based on the weight-sharing mechanism, one-shot NAS methods train a supernet and then inherit the pre-trained weights to evaluate sub-models, largely reducing the search cost. However, several works have pointed out that the shared weights suffer from different gradient descent directions during training. And we further find that large gradient variance occurs during supernet training, which degrades the supernet ranking consistency. To mitigate this issue, we propose to explicitly minimize the gradient variance of the supernet training by jointly optimizing the sampling distributions of PAth and DAta (PA&DA). We theoretically derive the relationship between the gradient variance and the sampling distributions, and reveal that the optimal sampling probability is proportional to the normalized gradient norm of path and training data. Hence, we use the normalized gradient norm as the importance indicator for path and training data, and adopt an importance sampling strategy for the supernet training. Our method only requires negligible computation cost for optimizing the sampling distributions of path and data, but achieves lower gradient variance during supernet training and better generalization performance for the supernet, resulting in a more consistent NAS. We conduct comprehensive comparisons with other improved approaches in various search spaces. Results show that our method surpasses others with more reliable ranking performance and higher accuracy of searched architectures, showing the effectiveness of our method. Code is available at https://github.com/ShunLu91/PA-DA.

We present CartoonX (Cartoon Explanation), a novel model-agnostic explanation method tailored towards image classifiers and based on the rate-distortion explanation (RDE) framework. Natural images are roughly piece-wise smooth signals -- also called cartoon-like images -- and tend to be sparse in the wavelet domain. CartoonX is the first explanation method to exploit this by requiring its explanations to be sparse in the wavelet domain, thus extracting the relevant piece-wise smooth part of an image instead of relevant pixel-sparse regions. We demonstrate that CartoonX can reveal novel valuable explanatory information, particularly for misclassifications. Moreover, we show that CartoonX achieves a lower distortion with fewer coefficients than other state-of-the-art methods.

Momentum based optimizers are central to a wide range of machine learning applications. These typically rely on an Exponential Moving Average (EMA) of gradients, which decays exponentially the present contribution of older gradients. This accounts for gradients being local linear approximations which lose their relevance as the iterate moves along the loss landscape. This work questions the use of a single EMA to accumulate past gradients and empirically demonstrates how this choice can be sub-optimal: a single EMA cannot simultaneously give a high weight to the immediate past, and a non-negligible weight to older gradients. Building on this observation, we propose AdEMAMix, a simple modification of the Adam optimizer with a mixture of two EMAs to better take advantage of past gradients. Our experiments on language modeling and image classification show -- quite surprisingly -- that gradients can stay relevant for tens of thousands of steps. They help to converge faster, and often to lower minima: e.g., a 1.3B parameter AdEMAMix LLM trained on 101B tokens performs comparably to an AdamW model trained on 197B tokens (+95%). Moreover, our method significantly slows-down model forgetting during training. Our work motivates further exploration of different types of functions to leverage past gradients, beyond EMAs.

Preserving training dynamics across batch sizes is an important tool for practical machine learning as it enables the trade-off between batch size and wall-clock time. This trade-off is typically enabled by a scaling rule, for example, in stochastic gradient descent, one should scale the learning rate linearly with the batch size. Another important tool for practical machine learning is the model Exponential Moving Average (EMA), which is a model copy that does not receive gradient information, but instead follows its target model with some momentum. This model EMA can improve the robustness and generalization properties of supervised learning, stabilize pseudo-labeling, and provide a learning signal for Self-Supervised Learning (SSL). Prior works have treated the model EMA separately from optimization, leading to different training dynamics across batch sizes and lower model performance. In this work, we provide a scaling rule for optimization in the presence of model EMAs and demonstrate its validity across a range of architectures, optimizers, and data modalities. We also show the rule's validity where the model EMA contributes to the optimization of the target model, enabling us to train EMA-based pseudo-labeling and SSL methods at small and large batch sizes. For SSL, we enable training of BYOL up to batch size 24,576 without sacrificing performance, optimally a 6times wall-clock time reduction.

Modern convolutional networks are not shift-invariant, as small input shifts or translations can cause drastic changes in the output. Commonly used downsampling methods, such as max-pooling, strided-convolution, and average-pooling, ignore the sampling theorem. The well-known signal processing fix is anti-aliasing by low-pass filtering before downsampling. However, simply inserting this module into deep networks degrades performance; as a result, it is seldomly used today. We show that when integrated correctly, it is compatible with existing architectural components, such as max-pooling and strided-convolution. We observe increased accuracy in ImageNet classification, across several commonly-used architectures, such as ResNet, DenseNet, and MobileNet, indicating effective regularization. Furthermore, we observe better generalization, in terms of stability and robustness to input corruptions. Our results demonstrate that this classical signal processing technique has been undeservingly overlooked in modern deep networks. Code and anti-aliased versions of popular networks are available at https://richzhang.github.io/antialiased-cnns/ .

Maximum mean discrepancy (MMD) flows suffer from high computational costs in large scale computations. In this paper, we show that MMD flows with Riesz kernels K(x,y) = - |x-y|^r, r in (0,2) have exceptional properties which allow their efficient computation. We prove that the MMD of Riesz kernels, which is also known as energy distance, coincides with the MMD of their sliced version. As a consequence, the computation of gradients of MMDs can be performed in the one-dimensional setting. Here, for r=1, a simple sorting algorithm can be applied to reduce the complexity from O(MN+N^2) to O((M+N)log(M+N)) for two measures with M and N support points. As another interesting follow-up result, the MMD of compactly supported measures can be estimated from above and below by the Wasserstein-1 distance. For the implementations we approximate the gradient of the sliced MMD by using only a finite number P of slices. We show that the resulting error has complexity O(d/P), where d is the data dimension. These results enable us to train generative models by approximating MMD gradient flows by neural networks even for image applications. We demonstrate the efficiency of our model by image generation on MNIST, FashionMNIST and CIFAR10.

Adversarial detection aims to determine whether a given sample is an adversarial one based on the discrepancy between natural and adversarial distributions. Unfortunately, estimating or comparing two data distributions is extremely difficult, especially in high-dimension spaces. Recently, the gradient of log probability density (a.k.a., score) w.r.t. the sample is used as an alternative statistic to compute. However, we find that the score is sensitive in identifying adversarial samples due to insufficient information with one sample only. In this paper, we propose a new statistic called expected perturbation score (EPS), which is essentially the expected score of a sample after various perturbations. Specifically, to obtain adequate information regarding one sample, we perturb it by adding various noises to capture its multi-view observations. We theoretically prove that EPS is a proper statistic to compute the discrepancy between two samples under mild conditions. In practice, we can use a pre-trained diffusion model to estimate EPS for each sample. Last, we propose an EPS-based adversarial detection (EPS-AD) method, in which we develop EPS-based maximum mean discrepancy (MMD) as a metric to measure the discrepancy between the test sample and natural samples. We also prove that the EPS-based MMD between natural and adversarial samples is larger than that among natural samples. Extensive experiments show the superior adversarial detection performance of our EPS-AD.

Shampoo is an online and stochastic optimization algorithm belonging to the AdaGrad family of methods for training neural networks. It constructs a block-diagonal preconditioner where each block consists of a coarse Kronecker product approximation to full-matrix AdaGrad for each parameter of the neural network. In this work, we provide a complete description of the algorithm as well as the performance optimizations that our implementation leverages to train deep networks at-scale in PyTorch. Our implementation enables fast multi-GPU distributed data-parallel training by distributing the memory and computation associated with blocks of each parameter via PyTorch's DTensor data structure and performing an AllGather primitive on the computed search directions at each iteration. This major performance enhancement enables us to achieve at most a 10% performance reduction in per-step wall-clock time compared against standard diagonal-scaling-based adaptive gradient methods. We validate our implementation by performing an ablation study on training ImageNet ResNet50, demonstrating Shampoo's superiority over standard training recipes with minimal hyperparameter tuning.

Recent work shows that path gradient estimators for normalizing flows have lower variance compared to standard estimators for variational inference, resulting in improved training. However, they are often prohibitively more expensive from a computational point of view and cannot be applied to maximum likelihood training in a scalable manner, which severely hinders their widespread adoption. In this work, we overcome these crucial limitations. Specifically, we propose a fast path gradient estimator which improves computational efficiency significantly and works for all normalizing flow architectures of practical relevance. We then show that this estimator can also be applied to maximum likelihood training for which it has a regularizing effect as it can take the form of a given target energy function into account. We empirically establish its superior performance and reduced variance for several natural sciences applications.

Deep neural networks have shown promise for music audio signal processing applications, often surpassing prior approaches, particularly as end-to-end models in the waveform domain. Yet results to date have tended to be constrained by low sample rates, noise, narrow domains of signal types, and/or lack of parameterized controls (i.e. "knobs"), making their suitability for professional audio engineering workflows still lacking. This work expands on prior research published on modeling nonlinear time-dependent signal processing effects associated with music production by means of a deep neural network, one which includes the ability to emulate the parameterized settings you would see on an analog piece of equipment, with the goal of eventually producing commercially viable, high quality audio, i.e. 44.1 kHz sampling rate at 16-bit resolution. The results in this paper highlight progress in modeling these effects through architecture and optimization changes, towards increasing computational efficiency, lowering signal-to-noise ratio, and extending to a larger variety of nonlinear audio effects. Toward these ends, the strategies employed involved a three-pronged approach: model speed, model accuracy, and model generalizability. Most of the presented methods provide marginal or no increase in output accuracy over the original model, with the exception of dataset manipulation. We found that limiting the audio content of the dataset, for example using datasets of just a single instrument, provided a significant improvement in model accuracy over models trained on more general datasets.

Fully quantized training (FQT) accelerates the training of deep neural networks by quantizing the activations, weights, and gradients into lower precision. To explore the ultimate limit of FQT (the lowest achievable precision), we make a first attempt to 1-bit FQT. We provide a theoretical analysis of FQT based on Adam and SGD, revealing that the gradient variance influences the convergence of FQT. Building on these theoretical results, we introduce an Activation Gradient Pruning (AGP) strategy. The strategy leverages the heterogeneity of gradients by pruning less informative gradients and enhancing the numerical precision of remaining gradients to mitigate gradient variance. Additionally, we propose Sample Channel joint Quantization (SCQ), which utilizes different quantization strategies in the computation of weight gradients and activation gradients to ensure that the method is friendly to low-bitwidth hardware. Finally, we present a framework to deploy our algorithm. For fine-tuning VGGNet-16 and ResNet-18 on multiple datasets, our algorithm achieves an average accuracy improvement of approximately 6%, compared to per-sample quantization. Moreover, our training speedup can reach a maximum of 5.13x compared to full precision training.

There are two widely known issues with properly training Recurrent Neural Networks, the vanishing and the exploding gradient problems detailed in Bengio et al. (1994). In this paper we attempt to improve the understanding of the underlying issues by exploring these problems from an analytical, a geometric and a dynamical systems perspective. Our analysis is used to justify a simple yet effective solution. We propose a gradient norm clipping strategy to deal with exploding gradients and a soft constraint for the vanishing gradients problem. We validate empirically our hypothesis and proposed solutions in the experimental section.

Contrastive learning has achieved remarkable success on various high-level tasks, but there are fewer contrastive learning-based methods proposed for low-level tasks. It is challenging to adopt vanilla contrastive learning technologies proposed for high-level visual tasks to low-level image restoration problems straightly. Because the acquired high-level global visual representations are insufficient for low-level tasks requiring rich texture and context information. In this paper, we investigate the contrastive learning-based single image super-resolution from two perspectives: positive and negative sample construction and feature embedding. The existing methods take naive sample construction approaches (e.g., considering the low-quality input as a negative sample and the ground truth as a positive sample) and adopt a prior model (e.g., pre-trained VGG model) to obtain the feature embedding. To this end, we propose a practical contrastive learning framework for SISR, named PCL-SR. We involve the generation of many informative positive and hard negative samples in frequency space. Instead of utilizing an additional pre-trained network, we design a simple but effective embedding network inherited from the discriminator network which is more task-friendly. Compared with existing benchmark methods, we re-train them by our proposed PCL-SR framework and achieve superior performance. Extensive experiments have been conducted to show the effectiveness and technical contributions of our proposed PCL-SR thorough ablation studies. The code and pre-trained models can be found at https://github.com/Aitical/PCL-SISR.

We propose the Signal Dice Similarity Coefficient (SDSC), a structure-aware metric function for time series self-supervised representation learning. Most Self-Supervised Learning (SSL) methods for signals commonly adopt distance-based objectives such as mean squared error (MSE), which are sensitive to amplitude, invariant to waveform polarity, and unbounded in scale. These properties hinder semantic alignment and reduce interpretability. SDSC addresses this by quantifying structural agreement between temporal signals based on the intersection of signed amplitudes, derived from the Dice Similarity Coefficient (DSC).Although SDSC is defined as a structure-aware metric, it can be used as a loss by subtracting from 1 and applying a differentiable approximation of the Heaviside function for gradient-based optimization. A hybrid loss formulation is also proposed to combine SDSC with MSE, improving stability and preserving amplitude where necessary. Experiments on forecasting and classification benchmarks demonstrate that SDSC-based pre-training achieves comparable or improved performance over MSE, particularly in in-domain and low-resource scenarios. The results suggest that structural fidelity in signal representations enhances the semantic representation quality, supporting the consideration of structure-aware metrics as viable alternatives to conventional distance-based methods.

Recent research shows that when Gradient Descent (GD) is applied to neural networks, the loss almost never decreases monotonically. Instead, the loss oscillates as gradient descent converges to its ''Edge of Stability'' (EoS). Here, we find a quantity that does decrease monotonically throughout GD training: the sharpness attained by the gradient flow solution (GFS)-the solution that would be obtained if, from now until convergence, we train with an infinitesimal step size. Theoretically, we analyze scalar neural networks with the squared loss, perhaps the simplest setting where the EoS phenomena still occur. In this model, we prove that the GFS sharpness decreases monotonically. Using this result, we characterize settings where GD provably converges to the EoS in scalar networks. Empirically, we show that GD monotonically decreases the GFS sharpness in a squared regression model as well as practical neural network architectures.

We demonstrate the possibility of what we call sparse learning: accelerated training of deep neural networks that maintain sparse weights throughout training while achieving dense performance levels. We accomplish this by developing sparse momentum, an algorithm which uses exponentially smoothed gradients (momentum) to identify layers and weights which reduce the error efficiently. Sparse momentum redistributes pruned weights across layers according to the mean momentum magnitude of each layer. Within a layer, sparse momentum grows weights according to the momentum magnitude of zero-valued weights. We demonstrate state-of-the-art sparse performance on MNIST, CIFAR-10, and ImageNet, decreasing the mean error by a relative 8%, 15%, and 6% compared to other sparse algorithms. Furthermore, we show that sparse momentum reliably reproduces dense performance levels while providing up to 5.61x faster training. In our analysis, ablations show that the benefits of momentum redistribution and growth increase with the depth and size of the network. Additionally, we find that sparse momentum is insensitive to the choice of its hyperparameters suggesting that sparse momentum is robust and easy to use.

With the rapid deployment of SCADA systems, how to effectively analyze industrial signals and detect abnormal states is an urgent need for the industry. Due to the significant heterogeneity of these signals, which we summarize as the M5 problem, previous works only focus on small sub-problems and employ specialized models, failing to utilize the synergies between modalities and the powerful scaling law. However, we argue that the M5 signals can be modeled in a unified manner due to the intrinsic similarity. As a result, we propose FISHER, a Foundation model for multi-modal Industrial Signal compreHEnsive Representation. To support arbitrary sampling rates, FISHER considers the increment of sampling rate as the concatenation of sub-band information. Specifically, FISHER takes the STFT sub-band as the modeling unit and adopts a teacher student SSL framework for pre-training. We also develop the RMIS benchmark, which evaluates the representations of M5 industrial signals on multiple health management tasks. Compared with top SSL models, FISHER showcases versatile and outstanding capabilities with a general performance gain up to 5.03%, along with much more efficient scaling curves. We also investigate the scaling law on downstream tasks and derive potential avenues for future works. FISHER is now open-sourced on https://github.com/jianganbai/FISHER

Implicitly defined, continuous, differentiable signal representations parameterized by neural networks have emerged as a powerful paradigm, offering many possible benefits over conventional representations. However, current network architectures for such implicit neural representations are incapable of modeling signals with fine detail, and fail to represent a signal's spatial and temporal derivatives, despite the fact that these are essential to many physical signals defined implicitly as the solution to partial differential equations. We propose to leverage periodic activation functions for implicit neural representations and demonstrate that these networks, dubbed sinusoidal representation networks or Sirens, are ideally suited for representing complex natural signals and their derivatives. We analyze Siren activation statistics to propose a principled initialization scheme and demonstrate the representation of images, wavefields, video, sound, and their derivatives. Further, we show how Sirens can be leveraged to solve challenging boundary value problems, such as particular Eikonal equations (yielding signed distance functions), the Poisson equation, and the Helmholtz and wave equations. Lastly, we combine Sirens with hypernetworks to learn priors over the space of Siren functions.

Understanding when the noise in stochastic gradient descent (SGD) affects generalization of deep neural networks remains a challenge, complicated by the fact that networks can operate in distinct training regimes. Here we study how the magnitude of this noise T affects performance as the size of the training set P and the scale of initialization alpha are varied. For gradient descent, alpha is a key parameter that controls if the network is `lazy'(alphagg1) or instead learns features (alphall1). For classification of MNIST and CIFAR10 images, our central results are: (i) obtaining phase diagrams for performance in the (alpha,T) plane. They show that SGD noise can be detrimental or instead useful depending on the training regime. Moreover, although increasing T or decreasing alpha both allow the net to escape the lazy regime, these changes can have opposite effects on performance. (ii) Most importantly, we find that the characteristic temperature T_c where the noise of SGD starts affecting the trained model (and eventually performance) is a power law of P. We relate this finding with the observation that key dynamical quantities, such as the total variation of weights during training, depend on both T and P as power laws. These results indicate that a key effect of SGD noise occurs late in training by affecting the stopping process whereby all data are fitted. Indeed, we argue that due to SGD noise, nets must develop a stronger `signal', i.e. larger informative weights, to fit the data, leading to a longer training time. A stronger signal and a longer training time are also required when the size of the training set P increases. We confirm these views in the perceptron model, where signal and noise can be precisely measured. Interestingly, exponents characterizing the effect of SGD depend on the density of data near the decision boundary, as we explain.

Recent advances in visually-induced audio generation are based on sampling short, low-fidelity, and one-class sounds. Moreover, sampling 1 second of audio from the state-of-the-art model takes minutes on a high-end GPU. In this work, we propose a single model capable of generating visually relevant, high-fidelity sounds prompted with a set of frames from open-domain videos in less time than it takes to play it on a single GPU. We train a transformer to sample a new spectrogram from the pre-trained spectrogram codebook given the set of video features. The codebook is obtained using a variant of VQGAN trained to produce a compact sampling space with a novel spectrogram-based perceptual loss. The generated spectrogram is transformed into a waveform using a window-based GAN that significantly speeds up generation. Considering the lack of metrics for automatic evaluation of generated spectrograms, we also build a family of metrics called FID and MKL. These metrics are based on a novel sound classifier, called Melception, and designed to evaluate the fidelity and relevance of open-domain samples. Both qualitative and quantitative studies are conducted on small- and large-scale datasets to evaluate the fidelity and relevance of generated samples. We also compare our model to the state-of-the-art and observe a substantial improvement in quality, size, and computation time. Code, demo, and samples: v-iashin.github.io/SpecVQGAN

The canonical deep learning approach for learning requires computing a gradient term at each layer by back-propagating the error signal from the output towards each learnable parameter. Given the stacked structure of neural networks, where each layer builds on the representation of the layer below, this approach leads to hierarchical representations. More abstract features live on the top layers of the model, while features on lower layers are expected to be less abstract. In contrast to this, we introduce a new learning method named NoProp, which does not rely on either forward or backwards propagation. Instead, NoProp takes inspiration from diffusion and flow matching methods, where each layer independently learns to denoise a noisy target. We believe this work takes a first step towards introducing a new family of gradient-free learning methods, that does not learn hierarchical representations -- at least not in the usual sense. NoProp needs to fix the representation at each layer beforehand to a noised version of the target, learning a local denoising process that can then be exploited at inference. We demonstrate the effectiveness of our method on MNIST, CIFAR-10, and CIFAR-100 image classification benchmarks. Our results show that NoProp is a viable learning algorithm which achieves superior accuracy, is easier to use and computationally more efficient compared to other existing back-propagation-free methods. By departing from the traditional gradient based learning paradigm, NoProp alters how credit assignment is done within the network, enabling more efficient distributed learning as well as potentially impacting other characteristics of the learning process.

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.

Holographic Metasurface Transceivers (HMTs) are emerging as cost-effective substitutes to large antenna arrays for beamforming in Millimeter and TeraHertz wave communication. However, to achieve desired channel gains through beamforming in HMT, phase-shifts of a large number of elements need to be appropriately set, which is challenging. Also, these optimal phase-shifts depend on the location of the receivers, which could be unknown. In this work, we develop a learning algorithm using a {\it fixed-budget multi-armed bandit framework} to beamform and maximize received signal strength at the receiver for far-field regions. Our algorithm, named \Algo exploits the parametric form of channel gains of the beams, which can be expressed in terms of two {\it phase-shifting parameters}. Even after parameterization, the problem is still challenging as phase-shifting parameters take continuous values. To overcome this, {\it\HB} works with the discrete values of phase-shifting parameters and exploits their unimodal relations with channel gains to learn the optimal values faster. We upper bound the probability of {\it\HB} incorrectly identifying the (discrete) optimal phase-shift parameters in terms of the number of pilots used in learning. We show that this probability decays exponentially with the number of pilot signals. We demonstrate that {\it\HB} outperforms state-of-the-art algorithms through extensive simulations.

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.

We introduce Gravity, another algorithm for gradient-based optimization. In this paper, we explain how our novel idea change parameters to reduce the deep learning model's loss. It has three intuitive hyper-parameters that the best values for them are proposed. Also, we propose an alternative to moving average. To compare the performance of the Gravity optimizer with two common optimizers, Adam and RMSProp, five standard datasets were trained on two VGGNet models with a batch size of 128 for 100 epochs. Gravity hyper-parameters did not need to be tuned for different models. As will be explained more in the paper, to investigate the direct impact of the optimizer itself on loss reduction no overfitting prevention technique was used. The obtained results show that the Gravity optimizer has more stable performance than Adam and RMSProp and gives greater values of validation accuracy for datasets with more output classes like CIFAR-100 (Fine).

Low frequency oscillator (LFO) driven audio effects such as phaser, flanger, and chorus, modify an input signal using time-varying filters and delays, resulting in characteristic sweeping or widening effects. It has been shown that these effects can be modeled using neural networks when conditioned with the ground truth LFO signal. However, in most cases, the LFO signal is not accessible and measurement from the audio signal is nontrivial, hindering the modeling process. To address this, we propose a framework capable of extracting arbitrary LFO signals from processed audio across multiple digital audio effects, parameter settings, and instrument configurations. Since our system imposes no restrictions on the LFO signal shape, we demonstrate its ability to extract quasiperiodic, combined, and distorted modulation signals that are relevant to effect modeling. Furthermore, we show how coupling the extraction model with a simple processing network enables training of end-to-end black-box models of unseen analog or digital LFO-driven audio effects using only dry and wet audio pairs, overcoming the need to access the audio effect or internal LFO signal. We make our code available and provide the trained audio effect models in a real-time VST plugin.

The commitment to single-precision floating-point arithmetic is widespread in the deep learning community. To evaluate whether this commitment is justified, the influence of computing precision (single and double precision) on the optimization performance of the Conjugate Gradient (CG) method (a second-order optimization algorithm) and RMSprop (a first-order algorithm) has been investigated. Tests of neural networks with one to five fully connected hidden layers and moderate or strong nonlinearity with up to 4 million network parameters have been optimized for Mean Square Error (MSE). The training tasks have been set up so that their MSE minimum was known to be zero. Computing experiments have disclosed that single-precision can keep up (with superlinear convergence) with double-precision as long as line search finds an improvement. First-order methods such as RMSprop do not benefit from double precision. However, for moderately nonlinear tasks, CG is clearly superior. For strongly nonlinear tasks, both algorithm classes find only solutions fairly poor in terms of mean square error as related to the output variance. CG with double floating-point precision is superior whenever the solutions have the potential to be useful for the application goal.

Previous works (Donahue et al., 2018a; Engel et al., 2019a) have found that generating coherent raw audio waveforms with GANs is challenging. In this paper, we show that it is possible to train GANs reliably to generate high quality coherent waveforms by introducing a set of architectural changes and simple training techniques. Subjective evaluation metric (Mean Opinion Score, or MOS) shows the effectiveness of the proposed approach for high quality mel-spectrogram inversion. To establish the generality of the proposed techniques, we show qualitative results of our model in speech synthesis, music domain translation and unconditional music synthesis. We evaluate the various components of the model through ablation studies and suggest a set of guidelines to design general purpose discriminators and generators for conditional sequence synthesis tasks. Our model is non-autoregressive, fully convolutional, with significantly fewer parameters than competing models and generalizes to unseen speakers for mel-spectrogram inversion. Our pytorch implementation runs at more than 100x faster than realtime on GTX 1080Ti GPU and more than 2x faster than real-time on CPU, without any hardware specific optimization tricks.

Recently, there has been extensive research interest in training deep networks to denoise images without clean reference. However, the representative approaches such as Noise2Noise, Noise2Void, Stein's unbiased risk estimator (SURE), etc. seem to differ from one another and it is difficult to find the coherent mathematical structure. To address this, here we present a novel approach, called Noise2Score, which reveals a missing link in order to unite these seemingly different approaches. Specifically, we show that image denoising problems without clean images can be addressed by finding the mode of the posterior distribution and that the Tweedie's formula offers an explicit solution through the score function (i.e. the gradient of log likelihood). Our method then uses the recent finding that the score function can be stably estimated from the noisy images using the amortized residual denoising autoencoder, the method of which is closely related to Noise2Noise or Nose2Void. Our Noise2Score approach is so universal that the same network training can be used to remove noises from images that are corrupted by any exponential family distributions and noise parameters. Using extensive experiments with Gaussian, Poisson, and Gamma noises, we show that Noise2Score significantly outperforms the state-of-the-art self-supervised denoising methods in the benchmark data set such as (C)BSD68, Set12, and Kodak, etc.

Most popular optimizers for deep learning can be broadly categorized as adaptive methods (e.g. Adam) and accelerated schemes (e.g. stochastic gradient descent (SGD) with momentum). For many models such as convolutional neural networks (CNNs), adaptive methods typically converge faster but generalize worse compared to SGD; for complex settings such as generative adversarial networks (GANs), adaptive methods are typically the default because of their stability.We propose AdaBelief to simultaneously achieve three goals: fast convergence as in adaptive methods, good generalization as in SGD, and training stability. The intuition for AdaBelief is to adapt the stepsize according to the "belief" in the current gradient direction. Viewing the exponential moving average (EMA) of the noisy gradient as the prediction of the gradient at the next time step, if the observed gradient greatly deviates from the prediction, we distrust the current observation and take a small step; if the observed gradient is close to the prediction, we trust it and take a large step. We validate AdaBelief in extensive experiments, showing that it outperforms other methods with fast convergence and high accuracy on image classification and language modeling. Specifically, on ImageNet, AdaBelief achieves comparable accuracy to SGD. Furthermore, in the training of a GAN on Cifar10, AdaBelief demonstrates high stability and improves the quality of generated samples compared to a well-tuned Adam optimizer. Code is available at https://github.com/juntang-zhuang/Adabelief-Optimizer

We introduce a new algorithm named WGAN, an alternative to traditional GAN training. In this new model, we show that we can improve the stability of learning, get rid of problems like mode collapse, and provide meaningful learning curves useful for debugging and hyperparameter searches. Furthermore, we show that the corresponding optimization problem is sound, and provide extensive theoretical work highlighting the deep connections to other distances between distributions.

Optimization and generalization are two essential aspects of statistical machine learning. In this paper, we propose a framework to connect optimization with generalization by analyzing the generalization error based on the optimization trajectory under the gradient flow algorithm. The key ingredient of this framework is the Uniform-LGI, a property that is generally satisfied when training machine learning models. Leveraging the Uniform-LGI, we first derive convergence rates for gradient flow algorithm, then we give generalization bounds for a large class of machine learning models. We further apply our framework to three distinct machine learning models: linear regression, kernel regression, and two-layer neural networks. Through our approach, we obtain generalization estimates that match or extend previous results.

Electroencephalography (EEG) signals, known for convenient non-invasive acquisition but low signal-to-noise ratio, have recently gained substantial attention due to the potential to decode natural images. This paper presents a self-supervised framework to demonstrate the feasibility of learning image representations from EEG signals, particularly for object recognition. The framework utilizes image and EEG encoders to extract features from paired image stimuli and EEG responses. Contrastive learning aligns these two modalities by constraining their similarity. With the framework, we attain significantly above-chance results on a comprehensive EEG-image dataset, achieving a top-1 accuracy of 15.6% and a top-5 accuracy of 42.8% in challenging 200-way zero-shot tasks. Moreover, we perform extensive experiments to explore the biological plausibility by resolving the temporal, spatial, spectral, and semantic aspects of EEG signals. Besides, we introduce attention modules to capture spatial correlations, providing implicit evidence of the brain activity perceived from EEG data. These findings yield valuable insights for neural decoding and brain-computer interfaces in real-world scenarios. The code will be released on https://github.com/eeyhsong/NICE-EEG.

In this paper, we propose a general deep learning training framework XGrad which introduces weight prediction into the popular gradient-based optimizers to boost their convergence and generalization when training the deep neural network (DNN) models. In particular, ahead of each mini-batch training, the future weights are predicted according to the update rule of the used optimizer and are then applied to both the forward pass and backward propagation. In this way, during the whole training period, the optimizer always utilizes the gradients w.r.t. the future weights to update the DNN parameters, making the gradient-based optimizer achieve better convergence and generalization compared to the original optimizer without weight prediction. XGrad is rather straightforward to implement yet pretty effective in boosting the convergence of gradient-based optimizers and the accuracy of DNN models. Empirical results concerning the most three popular gradient-based optimizers including SGD with momentum, Adam, and AdamW demonstrate the effectiveness of our proposal. The experimental results validate that XGrad can attain higher model accuracy than the original optimizers when training the DNN models. The code of XGrad will be available at: https://github.com/guanleics/XGrad.

Harmonic retrieval techniques are the foundation of radio channel sounding, estimation and modeling. This paper introduces a Deep Learning approach for two-dimensional spectral estimation from frequency and time samples of a radio channel transfer function. Our work can estimate two-dimensional parameters from a signal containing an unknown number of paths. In contrast to existing deep learning-based methods, the signal parameters are not estimated via classification but instead in a quasi-grid-free manner. This alleviates the bias, spectral leakage, and ghost targets that grid-based approaches inherently produce. The proposed architecture also reliably estimates the number of spectral components in the measurement. Hence, the architecture jointly solves the model order selection problem and the parameter estimation task. Additionally, we propose a multi-channel windowing of the data during preprocessing, increasing the resulting estimator's robustness. We verify the performance compared to existing harmonic retrieval methods and also show how it can be integrated into an existing maximum likelihood estimator for efficient initialization of a gradient-based iteration.

We provide a new efficient version of the backpropagation algorithm, specialized to the case where the weights of the neural network being trained are sparse. Our algorithm is general, as it applies to arbitrary (unstructured) sparsity and common layer types (e.g., convolutional or linear). We provide a fast vectorized implementation on commodity CPUs, and show that it can yield speedups in end-to-end runtime experiments, both in transfer learning using already-sparsified networks, and in training sparse networks from scratch. Thus, our results provide the first support for sparse training on commodity hardware.

Stochastic optimizers are central to deep learning, yet widely used methods such as Adam and Adan can degrade in non-stationary or noisy environments, partly due to their reliance on momentum-based magnitude estimates. We introduce Ano, a novel optimizer that decouples direction and magnitude: momentum is used for directional smoothing, while instantaneous gradient magnitudes determine step size. This design improves robustness to gradient noise while retaining the simplicity and efficiency of first-order methods. We further propose Anolog, which removes sensitivity to the momentum coefficient by expanding its window over time via a logarithmic schedule. We establish non-convex convergence guarantees with a convergence rate similar to other sign-based methods, and empirically show that Ano provides substantial gains in noisy and non-stationary regimes such as reinforcement learning, while remaining competitive on low-noise tasks such as standard computer vision benchmarks.

We derive a simple and model-independent formula for the change in the generalization gap due to a gradient descent update. We then compare the change in the test error for stochastic gradient descent to the change in test error from an equivalent number of gradient descent updates and show explicitly that stochastic gradient descent acts to regularize generalization error by decorrelating nearby updates. These calculations depends on the details of the model only through the mean and covariance of the gradient distribution, which may be readily measured for particular models of interest. We discuss further improvements to these calculations and comment on possible implications for stochastic optimization.

While the field of multi-modal learning keeps growing fast, the deficiency of the standard joint training paradigm has become clear through recent studies. They attribute the sub-optimal performance of the jointly trained model to the modality competition phenomenon. Existing works attempt to improve the jointly trained model by modulating the training process. Despite their effectiveness, those methods can only apply to late fusion models. More importantly, the mechanism of the modality competition remains unexplored. In this paper, we first propose an adaptive gradient modulation method that can boost the performance of multi-modal models with various fusion strategies. Extensive experiments show that our method surpasses all existing modulation methods. Furthermore, to have a quantitative understanding of the modality competition and the mechanism behind the effectiveness of our modulation method, we introduce a novel metric to measure the competition strength. This metric is built on the mono-modal concept, a function that is designed to represent the competition-less state of a modality. Through systematic investigation, our results confirm the intuition that the modulation encourages the model to rely on the more informative modality. In addition, we find that the jointly trained model typically has a preferred modality on which the competition is weaker than other modalities. However, this preferred modality need not dominate others. Our code will be available at https://github.com/lihong2303/AGM_ICCV2023.

While conditional diffusion models are known to have good coverage of the data distribution, they still face limitations in output diversity, particularly when sampled with a high classifier-free guidance scale for optimal image quality or when trained on small datasets. We attribute this problem to the role of the conditioning signal in inference and offer an improved sampling strategy for diffusion models that can increase generation diversity, especially at high guidance scales, with minimal loss of sample quality. Our sampling strategy anneals the conditioning signal by adding scheduled, monotonically decreasing Gaussian noise to the conditioning vector during inference to balance diversity and condition alignment. Our Condition-Annealed Diffusion Sampler (CADS) can be used with any pretrained model and sampling algorithm, and we show that it boosts the diversity of diffusion models in various conditional generation tasks. Further, using an existing pretrained diffusion model, CADS achieves a new state-of-the-art FID of 1.70 and 2.31 for class-conditional ImageNet generation at 256times256 and 512times512 respectively.

We present a machine sound dataset to benchmark domain generalization techniques for anomalous sound detection (ASD). Domain shifts are differences in data distributions that can degrade the detection performance, and handling them is a major issue for the application of ASD systems. While currently available datasets for ASD tasks assume that occurrences of domain shifts are known, in practice, they can be difficult to detect. To handle such domain shifts, domain generalization techniques that perform well regardless of the domains should be investigated. In this paper, we present the first ASD dataset for the domain generalization techniques, called MIMII DG. The dataset consists of five machine types and three domain shift scenarios for each machine type. The dataset is dedicated to the domain generalization task with features such as multiple different values for parameters that cause domain shifts and introduction of domain shifts that can be difficult to detect, such as shifts in the background noise. Experimental results using two baseline systems indicate that the dataset reproduces domain shift scenarios and is useful for benchmarking domain generalization techniques.

Training deep generative models like Variational Autoencoders (VAEs) is often hindered by the need to backpropagate gradients through the stochastic sampling of their latent variables, a process that inherently introduces estimation variance, which can slow convergence and degrade performance. In this paper, we propose a new perspective that sidesteps this problem, which we call Silent Gradients. Instead of improving stochastic estimators, we leverage specific decoder architectures to analytically compute the expected ELBO, yielding a gradient with zero variance. We first provide a theoretical foundation for this method and demonstrate its superiority over existing estimators in a controlled setting with a linear decoder. To generalize our approach for practical use with complex, expressive decoders, we introduce a novel training dynamic that uses the exact, zero-variance gradient to guide the early stages of encoder training before annealing to a standard stochastic estimator. Our experiments show that this technique consistently improves the performance of established baselines, including reparameterization, Gumbel-Softmax, and REINFORCE, across multiple datasets. This work opens a new direction for training generative models by combining the stability of analytical computation with the expressiveness of deep, nonlinear architecture.

We investigate the expressive power of depth-2 bandlimited random neural networks. A random net is a neural network where the hidden layer parameters are frozen with random assignment, and only the output layer parameters are trained by loss minimization. Using random weights for a hidden layer is an effective method to avoid non-convex optimization in standard gradient descent learning. It has also been adopted in recent deep learning theories. Despite the well-known fact that a neural network is a universal approximator, in this study, we mathematically show that when hidden parameters are distributed in a bounded domain, the network may not achieve zero approximation error. In particular, we derive a new nontrivial approximation error lower bound. The proof utilizes the technique of ridgelet analysis, a harmonic analysis method designed for neural networks. This method is inspired by fundamental principles in classical signal processing, specifically the idea that signals with limited bandwidth may not always be able to perfectly recreate the original signal. We corroborate our theoretical results with various simulation studies, and generally, two main take-home messages are offered: (i) Not any distribution for selecting random weights is feasible to build a universal approximator; (ii) A suitable assignment of random weights exists but to some degree is associated with the complexity of the target function.

Explaining the predictions of deep neural nets has been a topic of great interest in the computer vision literature. While several gradient-based interpretation schemes have been proposed to reveal the influential variables in a neural net's prediction, standard gradient-based interpretation frameworks have been commonly observed to lack robustness to input perturbations and flexibility for incorporating prior knowledge of sparsity and group-sparsity structures. In this work, we propose MoreauGrad as an interpretation scheme based on the classifier neural net's Moreau envelope. We demonstrate that MoreauGrad results in a smooth and robust interpretation of a multi-layer neural network and can be efficiently computed through first-order optimization methods. Furthermore, we show that MoreauGrad can be naturally combined with L_1-norm regularization techniques to output a sparse or group-sparse explanation which are prior conditions applicable to a wide range of deep learning applications. We empirically evaluate the proposed MoreauGrad scheme on standard computer vision datasets, showing the qualitative and quantitative success of the MoreauGrad approach in comparison to standard gradient-based interpretation methods.

Weight sharing is a fundamental concept in neural architecture search (NAS), enabling gradient-based methods to explore cell-based architecture spaces significantly faster than traditional blackbox approaches. In parallel, weight entanglement has emerged as a technique for intricate parameter sharing among architectures within macro-level search spaces. %However, the macro structure of such spaces poses compatibility challenges for gradient-based NAS methods. %As a result, blackbox optimization methods have been commonly employed, particularly in conjunction with supernet training, to maintain search efficiency. %Due to the inherent differences in the structure of these search spaces, these Since weight-entanglement poses compatibility challenges for gradient-based NAS methods, these two paradigms have largely developed independently in parallel sub-communities. This paper aims to bridge the gap between these sub-communities by proposing a novel scheme to adapt gradient-based methods for weight-entangled spaces. This enables us to conduct an in-depth comparative assessment and analysis of the performance of gradient-based NAS in weight-entangled search spaces. Our findings reveal that this integration of weight-entanglement and gradient-based NAS brings forth the various benefits of gradient-based methods (enhanced performance, improved supernet training properties and superior any-time performance), while preserving the memory efficiency of weight-entangled spaces. The code for our work is openly accessible https://anonymous.4open.science/r/TangleNAS-527C{here}

We consider stochastic unconstrained bilevel optimization problems when only the first-order gradient oracles are available. While numerous optimization methods have been proposed for tackling bilevel problems, existing methods either tend to require possibly expensive calculations regarding Hessians of lower-level objectives, or lack rigorous finite-time performance guarantees. In this work, we propose a Fully First-order Stochastic Approximation (F2SA) method, and study its non-asymptotic convergence properties. Specifically, we show that F2SA converges to an epsilon-stationary solution of the bilevel problem after epsilon^{-7/2}, epsilon^{-5/2}, and epsilon^{-3/2} iterations (each iteration using O(1) samples) when stochastic noises are in both level objectives, only in the upper-level objective, and not present (deterministic settings), respectively. We further show that if we employ momentum-assisted gradient estimators, the iteration complexities can be improved to epsilon^{-5/2}, epsilon^{-4/2}, and epsilon^{-3/2}, respectively. We demonstrate even superior practical performance of the proposed method over existing second-order based approaches on MNIST data-hypercleaning experiments.

Gradient descent is the method of choice for training large artificial intelligence systems. As these systems become larger, a better understanding of the mechanisms behind gradient training would allow us to alleviate compute costs and help steer these systems away from harmful behaviors. To that end, we suggest utilizing the circuit perspective brought forward by mechanistic interpretability. After laying out our intuition, we illustrate how it enables us to design a curriculum for efficient learning in a controlled setting. The code is available at https://github.com/facebookresearch/pal.

While backpropagation (BP) is the mainstream approach for gradient computation in neural network training, its heavy reliance on the chain rule of differentiation constrains the designing flexibility of network architecture and training pipelines. We avoid the recursive computation in BP and develop a unified likelihood ratio (ULR) method for gradient estimation with just one forward propagation. Not only can ULR be extended to train a wide variety of neural network architectures, but the computation flow in BP can also be rearranged by ULR for better device adaptation. Moreover, we propose several variance reduction techniques to further accelerate the training process. Our experiments offer numerical results across diverse aspects, including various neural network training scenarios, computation flow rearrangement, and fine-tuning of pre-trained models. All findings demonstrate that ULR effectively enhances the flexibility of neural network training by permitting localized module training without compromising the global objective and significantly boosts the network robustness.

In an increasing number of domains it has been demonstrated that deep learning models can be trained using relatively large batch sizes without sacrificing data efficiency. However the limits of this massive data parallelism seem to differ from domain to domain, ranging from batches of tens of thousands in ImageNet to batches of millions in RL agents that play the game Dota 2. To our knowledge there is limited conceptual understanding of why these limits to batch size differ or how we might choose the correct batch size in a new domain. In this paper, we demonstrate that a simple and easy-to-measure statistic called the gradient noise scale predicts the largest useful batch size across many domains and applications, including a number of supervised learning datasets (MNIST, SVHN, CIFAR-10, ImageNet, Billion Word), reinforcement learning domains (Atari and Dota), and even generative model training (autoencoders on SVHN). We find that the noise scale increases as the loss decreases over a training run and depends on the model size primarily through improved model performance. Our empirically-motivated theory also describes the tradeoff between compute-efficiency and time-efficiency, and provides a rough model of the benefits of adaptive batch-size training.

Recent work by Baratin et al. (2021) sheds light on an intriguing pattern that occurs during the training of deep neural networks: some layers align much more with data compared to other layers (where the alignment is defined as the euclidean product of the tangent features matrix and the data labels matrix). The curve of the alignment as a function of layer index (generally) exhibits an ascent-descent pattern where the maximum is reached for some hidden layer. In this work, we provide the first explanation for this phenomenon. We introduce the Equilibrium Hypothesis which connects this alignment pattern to signal propagation in deep neural networks. Our experiments demonstrate an excellent match with the theoretical predictions.

In this work, we introduce a single parameter omega, to effectively control granularity in diffusion-based synthesis. This parameter is incorporated during the denoising steps of the diffusion model's reverse process. Our approach does not require model retraining, architectural modifications, or additional computational overhead during inference, yet enables precise control over the level of details in the generated outputs. Moreover, spatial masks or denoising schedules with varying omega values can be applied to achieve region-specific or timestep-specific granularity control. Prior knowledge of image composition from control signals or reference images further facilitates the creation of precise omega masks for granularity control on specific objects. To highlight the parameter's role in controlling subtle detail variations, the technique is named Omegance, combining "omega" and "nuance". Our method demonstrates impressive performance across various image and video synthesis tasks and is adaptable to advanced diffusion models. The code is available at https://github.com/itsmag11/Omegance.

Out-of-distribution (OOD) detection is crucial to modern deep learning applications by identifying and alerting about the OOD samples that should not be tested or used for making predictions. Current OOD detection methods have made significant progress when in-distribution (ID) and OOD samples are drawn from static distributions. However, this can be unrealistic when applied to real-world systems which often undergo continuous variations and shifts in ID and OOD distributions over time. Therefore, for an effective application in real-world systems, the development of OOD detection methods that can adapt to these dynamic and evolving distributions is essential. In this paper, we propose a novel and more realistic setting called continuously adaptive out-of-distribution (CAOOD) detection which targets on developing an OOD detection model that enables dynamic and quick adaptation to a new arriving distribution, with insufficient ID samples during deployment time. To address CAOOD, we develop meta OOD learning (MOL) by designing a learning-to-adapt diagram such that a good initialized OOD detection model is learned during the training process. In the testing process, MOL ensures OOD detection performance over shifting distributions by quickly adapting to new distributions with a few adaptations. Extensive experiments on several OOD benchmarks endorse the effectiveness of our method in preserving both ID classification accuracy and OOD detection performance on continuously shifting distributions.

Although Neural Radiance Fields (NeRFs) have markedly improved novel view synthesis, accurate uncertainty quantification in their image predictions remains an open problem. The prevailing methods for estimating uncertainty, including the state-of-the-art Density-aware NeRF Ensembles (DANE) [29], quantify uncertainty without calibration. This frequently leads to over- or under-confidence in image predictions, which can undermine their real-world applications. In this paper, we propose a method which, for the first time, achieves calibrated uncertainties for NeRFs. To accomplish this, we overcome a significant challenge in adapting existing calibration techniques to NeRFs: a need to hold out ground truth images from the target scene, reducing the number of images left to train the NeRF. This issue is particularly problematic in sparse-view settings, where we can operate with as few as three images. To address this, we introduce the concept of a meta-calibrator that performs uncertainty calibration for NeRFs with a single forward pass without the need for holding out any images from the target scene. Our meta-calibrator is a neural network that takes as input the NeRF images and uncalibrated uncertainty maps and outputs a scene-specific calibration curve that corrects the NeRF's uncalibrated uncertainties. We show that the meta-calibrator can generalize on unseen scenes and achieves well-calibrated and state-of-the-art uncertainty for NeRFs, significantly beating DANE and other approaches. This opens opportunities to improve applications that rely on accurate NeRF uncertainty estimates such as next-best view planning and potentially more trustworthy image reconstruction for medical diagnosis. The code is available at https://niki-amini-naieni.github.io/instantcalibration.github.io/.

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.

Stochastic gradient descent method and its variants constitute the core optimization algorithms that achieve good convergence rates for solving machine learning problems. These rates are obtained especially when these algorithms are fine-tuned for the application at hand. Although this tuning process can require large computational costs, recent work has shown that these costs can be reduced by line search methods that iteratively adjust the stepsize. We propose an alternative approach to stochastic line search by using a new algorithm based on forward step model building. This model building step incorporates second-order information that allows adjusting not only the stepsize but also the search direction. Noting that deep learning model parameters come in groups (layers of tensors), our method builds its model and calculates a new step for each parameter group. This novel diagonalization approach makes the selected step lengths adaptive. We provide convergence rate analysis, and experimentally show that the proposed algorithm achieves faster convergence and better generalization in well-known test problems. More precisely, SMB requires less tuning, and shows comparable performance to other adaptive methods.

Gradient descent optimization algorithms, while increasingly popular, are often used as black-box optimizers, as practical explanations of their strengths and weaknesses are hard to come by. This article aims to provide the reader with intuitions with regard to the behaviour of different algorithms that will allow her to put them to use. In the course of this overview, we look at different variants of gradient descent, summarize challenges, introduce the most common optimization algorithms, review architectures in a parallel and distributed setting, and investigate additional strategies for optimizing gradient descent.

This study presents a deep convolutional autoencoder network for filtering reverberation clutter from transthoracic echocardiographic (TTE) image sequences. Given the spatiotemporal nature of this type of clutter, the filtering network employs 3D convolutional layers to suppress it throughout the cardiac cycle. The design of the network incorporates two key features that contribute to the effectiveness of the filter: 1) an attention mechanism for focusing on cluttered regions and leveraging contextual information, and 2) residual learning for preserving fine image structures. To train the network, a diverse set of artifact patterns was simulated and superimposed onto ultra-realistic synthetic TTE sequences from six ultrasound vendors, generating input for the filtering network. The artifact-free sequences served as ground-truth. Performance of the filtering network was evaluated using unseen synthetic and in vivo artifactual sequences. Results from the in vivo dataset confirmed the network's strong generalization capabilities, despite being trained solely on synthetic data and simulated artifacts. The suitability of the filtered sequences for downstream processing was assessed by computing segmental strain curves. A significant reduction in the discrepancy between strain profiles computed from cluttered and clutter-free segments was observed after filtering the cluttered sequences with the proposed network. The trained network processes a TTE sequence in a fraction of a second, enabling real-time clutter filtering and potentially improving the precision of clinically relevant indices derived from TTE sequences. The source code of the proposed method and example video files of the filtering results are available at: https://github.com/MahdiTabassian/Deep-Clutter-Filtering/tree/main{https://github.com/MahdiTabassian/Deep-Clutter-Filtering/tree/main}.

Deep neural network is difficult to train and this predicament becomes worse as the depth increases. The essence of this problem exists in the magnitude of backpropagated errors that will result in gradient vanishing or exploding phenomenon. We show that a variant of regularizer which utilizes orthonormality among different filter banks can alleviate this problem. Moreover, we design a backward error modulation mechanism based on the quasi-isometry assumption between two consecutive parametric layers. Equipped with these two ingredients, we propose several novel optimization solutions that can be utilized for training a specific-structured (repetitively triple modules of Conv-BNReLU) extremely deep convolutional neural network (CNN) WITHOUT any shortcuts/ identity mappings from scratch. Experiments show that our proposed solutions can achieve distinct improvements for a 44-layer and a 110-layer plain networks on both the CIFAR-10 and ImageNet datasets. Moreover, we can successfully train plain CNNs to match the performance of the residual counterparts. Besides, we propose new principles for designing network structure from the insights evoked by orthonormality. Combined with residual structure, we achieve comparative performance on the ImageNet dataset.

Pre-trained foundation models have demonstrated remarkable success in vision and language, yet their potential for general machine signal modeling-covering acoustic, vibration, and other industrial sensor data-remains under-explored. Existing approach using sub-band-based encoders has achieved competitive results but are limited by fixed input lengths, and the absence of explicit frequency positional encoding. In this work, we propose a novel foundation model that integrates an advanced band-split architecture with relative frequency positional embeddings, enabling precise spectral localization across arbitrary sampling configurations. The model supports inputs of arbitrary length without padding or segmentation, producing a concise embedding that retains both temporal and spectral fidelity. We evaluate our method on SIREN (https://github.com/yucongzh/SIREN), a newly introduced large-scale benchmark for machine signal encoding that unifies multiple datasets, including all DCASE task 2 challenges (2020-2025) and widely-used industrial signal corpora. Experimental results demonstrate consistent state-of-the-art performance in anomaly detection and fault identification, confirming the effectiveness and generalization capability of the proposed model. We open-sourced ECHO on https://github.com/yucongzh/ECHO.

In recent years, there has been a growing interest in deep learning-based pansharpening. Thus far, research has mainly focused on architectures. Nonetheless, model training is an equally important issue. A first problem is the absence of ground truths, unavoidable in pansharpening. This is often addressed by training networks in a reduced resolution domain and using the original data as ground truth, relying on an implicit scale invariance assumption. However, on full resolution images results are often disappointing, suggesting such invariance not to hold. A further problem is the scarcity of training data, which causes a limited generalization ability and a poor performance on off-training test images. In this paper, we propose a full-resolution training framework for deep learning-based pansharpening. The framework is fully general and can be used for any deep learning-based pansharpening model. Training takes place in the high-resolution domain, relying only on the original data, thus avoiding any loss of information. To ensure spectral and spatial fidelity, a suitable two-component loss is defined. The spectral component enforces consistency between the pansharpened output and the low-resolution multispectral input. The spatial component, computed at high-resolution, maximizes the local correlation between each pansharpened band and the panchromatic input. At testing time, the target-adaptive operating modality is adopted, achieving good generalization with a limited computational overhead. Experiments carried out on WorldView-3, WorldView-2, and GeoEye-1 images show that methods trained with the proposed framework guarantee a pretty good performance in terms of both full-resolution numerical indexes and visual quality.

We propose a novel theoretical framework of analysis for Generative Adversarial Networks (GANs). We reveal a fundamental flaw of previous analyses which, by incorrectly modeling GANs' training scheme, are subject to ill-defined discriminator gradients. We overcome this issue which impedes a principled study of GAN training, solving it within our framework by taking into account the discriminator's architecture. To this end, we leverage the theory of infinite-width neural networks for the discriminator via its Neural Tangent Kernel. We characterize the trained discriminator for a wide range of losses and establish general differentiability properties of the network. From this, we derive new insights about the convergence of the generated distribution, advancing our understanding of GANs' training dynamics. We empirically corroborate these results via an analysis toolkit based on our framework, unveiling intuitions that are consistent with GAN practice.

Recent studies have demonstrated that gradient matching-based dataset synthesis, or dataset condensation (DC), methods can achieve state-of-the-art performance when applied to data-efficient learning tasks. However, in this study, we prove that the existing DC methods can perform worse than the random selection method when task-irrelevant information forms a significant part of the training dataset. We attribute this to the lack of participation of the contrastive signals between the classes resulting from the class-wise gradient matching strategy. To address this problem, we propose Dataset Condensation with Contrastive signals (DCC) by modifying the loss function to enable the DC methods to effectively capture the differences between classes. In addition, we analyze the new loss function in terms of training dynamics by tracking the kernel velocity. Furthermore, we introduce a bi-level warm-up strategy to stabilize the optimization. Our experimental results indicate that while the existing methods are ineffective for fine-grained image classification tasks, the proposed method can successfully generate informative synthetic datasets for the same tasks. Moreover, we demonstrate that the proposed method outperforms the baselines even on benchmark datasets such as SVHN, CIFAR-10, and CIFAR-100. Finally, we demonstrate the high applicability of the proposed method by applying it to continual learning tasks.

Data imbalance is a common problem in machine learning that can have a critical effect on the performance of a model. Various solutions exist but their impact on the convergence of the learning dynamics is not understood. Here, we elucidate the significant negative impact of data imbalance on learning, showing that the learning curves for minority and majority classes follow sub-optimal trajectories when training with a gradient-based optimizer. This slowdown is related to the imbalance ratio and can be traced back to a competition between the optimization of different classes. Our main contribution is the analysis of the convergence of full-batch (GD) and stochastic gradient descent (SGD), and of variants that renormalize the contribution of each per-class gradient. We find that GD is not guaranteed to decrease the loss for each class but that this problem can be addressed by performing a per-class normalization of the gradient. With SGD, class imbalance has an additional effect on the direction of the gradients: the minority class suffers from a higher directional noise, which reduces the effectiveness of the per-class gradient normalization. Our findings not only allow us to understand the potential and limitations of strategies involving the per-class gradients, but also the reason for the effectiveness of previously used solutions for class imbalance such as oversampling.

Despite extensive studies, the underlying reason as to why overparameterized neural networks can generalize remains elusive. Existing theory shows that common stochastic optimizers prefer flatter minimizers of the training loss, and thus a natural potential explanation is that flatness implies generalization. This work critically examines this explanation. Through theoretical and empirical investigation, we identify the following three scenarios for two-layer ReLU networks: (1) flatness provably implies generalization; (2) there exist non-generalizing flattest models and sharpness minimization algorithms fail to generalize, and (3) perhaps most surprisingly, there exist non-generalizing flattest models, but sharpness minimization algorithms still generalize. Our results suggest that the relationship between sharpness and generalization subtly depends on the data distributions and the model architectures and sharpness minimization algorithms do not only minimize sharpness to achieve better generalization. This calls for the search for other explanations for the generalization of over-parameterized neural networks.

Gradient clipping is a popular modification to standard (stochastic) gradient descent, at every iteration limiting the gradient norm to a certain value c >0. It is widely used for example for stabilizing the training of deep learning models (Goodfellow et al., 2016), or for enforcing differential privacy (Abadi et al., 2016). Despite popularity and simplicity of the clipping mechanism, its convergence guarantees often require specific values of c and strong noise assumptions. In this paper, we give convergence guarantees that show precise dependence on arbitrary clipping thresholds c and show that our guarantees are tight with both deterministic and stochastic gradients. In particular, we show that (i) for deterministic gradient descent, the clipping threshold only affects the higher-order terms of convergence, (ii) in the stochastic setting convergence to the true optimum cannot be guaranteed under the standard noise assumption, even under arbitrary small step-sizes. We give matching upper and lower bounds for convergence of the gradient norm when running clipped SGD, and illustrate these results with experiments.