Daily Papers

The stable periodic patterns present in time series data serve as the foundation for conducting long-horizon forecasts. In this paper, we pioneer the exploration of explicitly modeling this periodicity to enhance the performance of models in long-term time series forecasting (LTSF) tasks. Specifically, we introduce the Residual Cycle Forecasting (RCF) technique, which utilizes learnable recurrent cycles to model the inherent periodic patterns within sequences, and then performs predictions on the residual components of the modeled cycles. Combining RCF with a Linear layer or a shallow MLP forms the simple yet powerful method proposed in this paper, called CycleNet. CycleNet achieves state-of-the-art prediction accuracy in multiple domains including electricity, weather, and energy, while offering significant efficiency advantages by reducing over 90% of the required parameter quantity. Furthermore, as a novel plug-and-play technique, the RCF can also significantly improve the prediction accuracy of existing models, including PatchTST and iTransformer. The source code is available at: https://github.com/ACAT-SCUT/CycleNet.

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

Recurrent neural network is a powerful model that learns temporal patterns in sequential data. For a long time, it was believed that recurrent networks are difficult to train using simple optimizers, such as stochastic gradient descent, due to the so-called vanishing gradient problem. In this paper, we show that learning longer term patterns in real data, such as in natural language, is perfectly possible using gradient descent. This is achieved by using a slight structural modification of the simple recurrent neural network architecture. We encourage some of the hidden units to change their state slowly by making part of the recurrent weight matrix close to identity, thus forming kind of a longer term memory. We evaluate our model in language modeling experiments, where we obtain similar performance to the much more complex Long Short Term Memory (LSTM) networks (Hochreiter & Schmidhuber, 1997).

Recurrent neural networks (RNNs) have fast inference and scale efficiently on long sequences, but they are difficult to train and hard to scale. We propose Hawk, an RNN with gated linear recurrences, and Griffin, a hybrid model that mixes gated linear recurrences with local attention. Hawk exceeds the reported performance of Mamba on downstream tasks, while Griffin matches the performance of Llama-2 despite being trained on over 6 times fewer tokens. We also show that Griffin can extrapolate on sequences significantly longer than those seen during training. Our models match the hardware efficiency of Transformers during training, and during inference they have lower latency and significantly higher throughput. We scale Griffin up to 14B parameters, and explain how to shard our models for efficient distributed training.

Real-time recurrent learning (RTRL) for sequence-processing recurrent neural networks (RNNs) offers certain conceptual advantages over backpropagation through time (BPTT). RTRL requires neither caching past activations nor truncating context, and enables online learning. However, RTRL's time and space complexity make it impractical. To overcome this problem, most recent work on RTRL focuses on approximation theories, while experiments are often limited to diagnostic settings. Here we explore the practical promise of RTRL in more realistic settings. We study actor-critic methods that combine RTRL and policy gradients, and test them in several subsets of DMLab-30, ProcGen, and Atari-2600 environments. On DMLab memory tasks, our system trained on fewer than 1.2 B environmental frames is competitive with or outperforms well-known IMPALA and R2D2 baselines trained on 10 B frames. To scale to such challenging tasks, we focus on certain well-known neural architectures with element-wise recurrence, allowing for tractable RTRL without approximation. Importantly, we also discuss rarely addressed limitations of RTRL in real-world applications, such as its complexity in the multi-layer case.

This study introduces PV-RNN, a novel variational RNN inspired by the predictive-coding ideas. The model learns to extract the probabilistic structures hidden in fluctuating temporal patterns by dynamically changing the stochasticity of its latent states. Its architecture attempts to address two major concerns of variational Bayes RNNs: how can latent variables learn meaningful representations and how can the inference model transfer future observations to the latent variables. PV-RNN does both by introducing adaptive vectors mirroring the training data, whose values can then be adapted differently during evaluation. Moreover, prediction errors during backpropagation, rather than external inputs during the forward computation, are used to convey information to the network about the external data. For testing, we introduce error regression for predicting unseen sequences as inspired by predictive coding that leverages those mechanisms. The model introduces a weighting parameter, the meta-prior, to balance the optimization pressure placed on two terms of a lower bound on the marginal likelihood of the sequential data. We test the model on two datasets with probabilistic structures and show that with high values of the meta-prior the network develops deterministic chaos through which the data's randomness is imitated. For low values, the model behaves as a random process. The network performs best on intermediate values, and is able to capture the latent probabilistic structure with good generalization. Analyzing the meta-prior's impact on the network allows to precisely study the theoretical value and practical benefits of incorporating stochastic dynamics in our model. We demonstrate better prediction performance on a robot imitation task with our model using error regression compared to a standard variational Bayes model lacking such a procedure.

It is known that the learning rate is the most important hyper-parameter to tune for training deep neural networks. This paper describes a new method for setting the learning rate, named cyclical learning rates, which practically eliminates the need to experimentally find the best values and schedule for the global learning rates. Instead of monotonically decreasing the learning rate, this method lets the learning rate cyclically vary between reasonable boundary values. Training with cyclical learning rates instead of fixed values achieves improved classification accuracy without a need to tune and often in fewer iterations. This paper also describes a simple way to estimate "reasonable bounds" -- linearly increasing the learning rate of the network for a few epochs. In addition, cyclical learning rates are demonstrated on the CIFAR-10 and CIFAR-100 datasets with ResNets, Stochastic Depth networks, and DenseNets, and the ImageNet dataset with the AlexNet and GoogLeNet architectures. These are practical tools for everyone who trains neural networks.

The fixed-size context of Transformer makes GPT models incapable of generating arbitrarily long text. In this paper, we introduce RecurrentGPT, a language-based simulacrum of the recurrence mechanism in RNNs. RecurrentGPT is built upon a large language model (LLM) such as ChatGPT and uses natural language to simulate the Long Short-Term Memory mechanism in an LSTM. At each timestep, RecurrentGPT generates a paragraph of text and updates its language-based long-short term memory stored on the hard drive and the prompt, respectively. This recurrence mechanism enables RecurrentGPT to generate texts of arbitrary length without forgetting. Since human users can easily observe and edit the natural language memories, RecurrentGPT is interpretable and enables interactive generation of long text. RecurrentGPT is an initial step towards next-generation computer-assisted writing systems beyond local editing suggestions. In addition to producing AI-generated content (AIGC), we also demonstrate the possibility of using RecurrentGPT as an interactive fiction that directly interacts with consumers. We call this usage of generative models by ``AI As Contents'' (AIAC), which we believe is the next form of conventional AIGC. We further demonstrate the possibility of using RecurrentGPT to create personalized interactive fiction that directly interacts with readers instead of interacting with writers. More broadly, RecurrentGPT demonstrates the utility of borrowing ideas from popular model designs in cognitive science and deep learning for prompting LLMs. Our code is available at https://github.com/aiwaves-cn/RecurrentGPT and an online demo is available at https://www.aiwaves.org/recurrentgpt.

A major problem with Active Learning (AL) is high training costs since models are typically retrained from scratch after every query round. We start by demonstrating that standard AL on neural networks with warm starting fails, both to accelerate training and to avoid catastrophic forgetting when using fine-tuning over AL query rounds. We then develop a new class of techniques, circumventing this problem, by biasing further training towards previously labeled sets. We accomplish this by employing existing, and developing novel, replay-based Continual Learning (CL) algorithms that are effective at quickly learning the new without forgetting the old, especially when data comes from an evolving distribution. We call this paradigm Continual Active Learning (CAL). We show CAL achieves significant speedups using a plethora of replay schemes that use model distillation and that select diverse, uncertain points from the history. We conduct experiments across many data domains, including natural language, vision, medical imaging, and computational biology, each with different neural architectures and dataset sizes. CAL consistently provides a 3x reduction in training time, while retaining performance.

Conventional neural architectures for sequential data present important limitations. Recurrent networks suffer from exploding and vanishing gradients, small effective memory horizons, and must be trained sequentially. Convolutional networks are unable to handle sequences of unknown size and their memory horizon must be defined a priori. In this work, we show that all these problems can be solved by formulating convolutional kernels in CNNs as continuous functions. The resulting Continuous Kernel Convolution (CKConv) allows us to model arbitrarily long sequences in a parallel manner, within a single operation, and without relying on any form of recurrence. We show that Continuous Kernel Convolutional Networks (CKCNNs) obtain state-of-the-art results in multiple datasets, e.g., permuted MNIST, and, thanks to their continuous nature, are able to handle non-uniformly sampled datasets and irregularly-sampled data natively. CKCNNs match or perform better than neural ODEs designed for these purposes in a faster and simpler manner.

Recurrent Neural Networks (RNNs) laid the foundation for sequence modeling, but their intrinsic sequential nature restricts parallel computation, creating a fundamental barrier to scaling. This has led to the dominance of parallelizable architectures like Transformers and, more recently, State Space Models (SSMs). While SSMs achieve efficient parallelization through structured linear recurrences, this linearity constraint limits their expressive power and precludes modeling complex, nonlinear sequence-wise dependencies. To address this, we present ParaRNN, a framework that breaks the sequence-parallelization barrier for nonlinear RNNs. Building on prior work, we cast the sequence of nonlinear recurrence relationships as a single system of equations, which we solve in parallel using Newton's iterations combined with custom parallel reductions. Our implementation achieves speedups of up to 665x over naive sequential application, allowing training nonlinear RNNs at unprecedented scales. To showcase this, we apply ParaRNN to adaptations of LSTM and GRU architectures, successfully training models of 7B parameters that attain perplexity comparable to similarly-sized Transformers and Mamba2 architectures. To accelerate research in efficient sequence modeling, we release the ParaRNN codebase as an open-source framework for automatic training-parallelization of nonlinear RNNs, enabling researchers and practitioners to explore new nonlinear RNN models at scale.

Recurrent Neural Networks (RNNs), and specifically a variant with Long Short-Term Memory (LSTM), are enjoying renewed interest as a result of successful applications in a wide range of machine learning problems that involve sequential data. However, while LSTMs provide exceptional results in practice, the source of their performance and their limitations remain rather poorly understood. Using character-level language models as an interpretable testbed, we aim to bridge this gap by providing an analysis of their representations, predictions and error types. In particular, our experiments reveal the existence of interpretable cells that keep track of long-range dependencies such as line lengths, quotes and brackets. Moreover, our comparative analysis with finite horizon n-gram models traces the source of the LSTM improvements to long-range structural dependencies. Finally, we provide analysis of the remaining errors and suggests areas for further study.

We introduce a new class of time-continuous recurrent neural network models. Instead of declaring a learning system's dynamics by implicit nonlinearities, we construct networks of linear first-order dynamical systems modulated via nonlinear interlinked gates. The resulting models represent dynamical systems with varying (i.e., liquid) time-constants coupled to their hidden state, with outputs being computed by numerical differential equation solvers. These neural networks exhibit stable and bounded behavior, yield superior expressivity within the family of neural ordinary differential equations, and give rise to improved performance on time-series prediction tasks. To demonstrate these properties, we first take a theoretical approach to find bounds over their dynamics and compute their expressive power by the trajectory length measure in latent trajectory space. We then conduct a series of time-series prediction experiments to manifest the approximation capability of Liquid Time-Constant Networks (LTCs) compared to classical and modern RNNs. Code and data are available at https://github.com/raminmh/liquid_time_constant_networks

In this note (work in progress towards a full-length paper) we show that a family of sequence models based on recurrent linear layers~(including S4, S5, and the LRU) interleaved with position-wise multi-layer perceptrons~(MLPs) can approximate arbitrarily well any sufficiently regular non-linear sequence-to-sequence map. The main idea behind our result is to see recurrent layers as compression algorithms that can faithfully store information about the input sequence into an inner state, before it is processed by the highly expressive MLP.

We introduce a neural network with a recurrent attention model over a possibly large external memory. The architecture is a form of Memory Network (Weston et al., 2015) but unlike the model in that work, it is trained end-to-end, and hence requires significantly less supervision during training, making it more generally applicable in realistic settings. It can also be seen as an extension of RNNsearch to the case where multiple computational steps (hops) are performed per output symbol. The flexibility of the model allows us to apply it to tasks as diverse as (synthetic) question answering and to language modeling. For the former our approach is competitive with Memory Networks, but with less supervision. For the latter, on the Penn TreeBank and Text8 datasets our approach demonstrates comparable performance to RNNs and LSTMs. In both cases we show that the key concept of multiple computational hops yields improved results.

Catastrophic forgetting in neural networks is a significant problem for continual learning. A majority of the current methods replay previous data during training, which violates the constraints of an ideal continual learning system. Additionally, current approaches that deal with forgetting ignore the problem of catastrophic remembering, i.e. the worsening ability to discriminate between data from different tasks. In our work, we introduce Relevance Mapping Networks (RMNs) which are inspired by the Optimal Overlap Hypothesis. The mappings reflects the relevance of the weights for the task at hand by assigning large weights to essential parameters. We show that RMNs learn an optimized representational overlap that overcomes the twin problem of catastrophic forgetting and remembering. Our approach achieves state-of-the-art performance across all common continual learning datasets, even significantly outperforming data replay methods while not violating the constraints for an ideal continual learning system. Moreover, RMNs retain the ability to detect data from new tasks in an unsupervised manner, thus proving their resilience against catastrophic remembering.

Neural networks have become an increasingly popular tool for solving many real-world problems. They are a general framework for differentiable optimization which includes many other machine learning approaches as special cases. In this thesis we build a category-theoretic formalism around a class of neural networks exemplified by CycleGAN. CycleGAN is a collection of neural networks, closed under composition, whose inductive bias is increased by enforcing composition invariants, i.e. cycle-consistencies. Inspired by Functorial Data Migration, we specify the interconnection of these networks using a categorical schema, and network instances as set-valued functors on this schema. We also frame neural network architectures, datasets, models, and a number of other concepts in a categorical setting and thus show a special class of functors, rather than functions, can be learned using gradient descent. We use the category-theoretic framework to conceive a novel neural network architecture whose goal is to learn the task of object insertion and object deletion in images with unpaired data. We test the architecture on three different datasets and obtain promising results.

We introduce RecurrentGemma, an open language model which uses Google's novel Griffin architecture. Griffin combines linear recurrences with local attention to achieve excellent performance on language. It has a fixed-sized state, which reduces memory use and enables efficient inference on long sequences. We provide a pre-trained model with 2B non-embedding parameters, and an instruction tuned variant. Both models achieve comparable performance to Gemma-2B despite being trained on fewer tokens.

In this work, we propose Retentive Network (RetNet) as a foundation architecture for large language models, simultaneously achieving training parallelism, low-cost inference, and good performance. We theoretically derive the connection between recurrence and attention. Then we propose the retention mechanism for sequence modeling, which supports three computation paradigms, i.e., parallel, recurrent, and chunkwise recurrent. Specifically, the parallel representation allows for training parallelism. The recurrent representation enables low-cost O(1) inference, which improves decoding throughput, latency, and GPU memory without sacrificing performance. The chunkwise recurrent representation facilitates efficient long-sequence modeling with linear complexity, where each chunk is encoded parallelly while recurrently summarizing the chunks. Experimental results on language modeling show that RetNet achieves favorable scaling results, parallel training, low-cost deployment, and efficient inference. The intriguing properties make RetNet a strong successor to Transformer for large language models. Code will be available at https://aka.ms/retnet.

Models based on deep convolutional networks have dominated recent image interpretation tasks; we investigate whether models which are also recurrent, or "temporally deep", are effective for tasks involving sequences, visual and otherwise. We develop a novel recurrent convolutional architecture suitable for large-scale visual learning which is end-to-end trainable, and demonstrate the value of these models on benchmark video recognition tasks, image description and retrieval problems, and video narration challenges. In contrast to current models which assume a fixed spatio-temporal receptive field or simple temporal averaging for sequential processing, recurrent convolutional models are "doubly deep"' in that they can be compositional in spatial and temporal "layers". Such models may have advantages when target concepts are complex and/or training data are limited. Learning long-term dependencies is possible when nonlinearities are incorporated into the network state updates. Long-term RNN models are appealing in that they directly can map variable-length inputs (e.g., video frames) to variable length outputs (e.g., natural language text) and can model complex temporal dynamics; yet they can be optimized with backpropagation. Our recurrent long-term models are directly connected to modern visual convnet models and can be jointly trained to simultaneously learn temporal dynamics and convolutional perceptual representations. Our results show such models have distinct advantages over state-of-the-art models for recognition or generation which are separately defined and/or optimized.

Transformers have surpassed RNNs in popularity due to their superior abilities in parallel training and long-term dependency modeling. Recently, there has been a renewed interest in using linear RNNs for efficient sequence modeling. These linear RNNs often employ gating mechanisms in the output of the linear recurrence layer while ignoring the significance of using forget gates within the recurrence. In this paper, we propose a gated linear RNN model dubbed Hierarchically Gated Recurrent Neural Network (HGRN), which includes forget gates that are lower bounded by a learnable value. The lower bound increases monotonically when moving up layers. This allows the upper layers to model long-term dependencies and the lower layers to model more local, short-term dependencies. Experiments on language modeling, image classification, and long-range arena benchmarks showcase the efficiency and effectiveness of our proposed model. The source code is available at https://github.com/OpenNLPLab/HGRN.

Linear Recurrence has proven to be a powerful tool for modeling long sequences efficiently. In this work, we show that existing models fail to take full advantage of its potential. Motivated by this finding, we develop GateLoop, a foundational sequence model that generalizes linear recurrent models such as S4, S5, LRU and RetNet, by employing data-controlled state transitions. Utilizing this theoretical advance, GateLoop empirically outperforms existing models for auto-regressive language modeling. Our method comes with a low-cost O(l) recurrent mode and an efficient O(l log_{2} l) parallel mode making use of highly optimized associative scan implementations. Furthermore, we derive an O(l^2) surrogate attention mode, revealing remarkable implications for Transformer and recently proposed architectures. Specifically, we prove that our approach can be interpreted as providing data-controlled relative-positional information to Attention. While many existing models solely rely on data-controlled cumulative sums for context aggregation, our findings suggest that incorporating data-controlled complex cumulative products may be a crucial step towards more powerful sequence models.

The scalability limitations of Transformers regarding sequence length have renewed interest in recurrent sequence models that are parallelizable during training. As a result, many novel recurrent architectures, such as S4, Mamba, and Aaren, have been proposed that achieve comparable performance. In this work, we revisit traditional recurrent neural networks (RNNs) from over a decade ago: LSTMs (1997) and GRUs (2014). While these models were slow due to requiring to backpropagate through time (BPTT), we show that by removing their hidden state dependencies from their input, forget, and update gates, LSTMs and GRUs no longer need to BPTT and can be efficiently trained in parallel. Building on this, we introduce minimal versions (minLSTMs and minGRUs) that (1) use significantly fewer parameters than their traditional counterparts and (2) are fully parallelizable during training (175x faster for a sequence of length 512). Lastly, we show that these stripped-down versions of decade-old RNNs match the empirical performance of recent sequence models.

Recurrent neural networks (RNNs) have recently demonstrated strong performance and faster inference than Transformers at comparable parameter budgets. However, the recursive gradient computation with the backpropagation through time (or BPTT) algorithm remains the major computational bottleneck. In this work, we propose a novel method that replaces BPTT with a fixed gradient feedback mechanism, yielding an efficient approximation of the exact gradient propagation based on the assumption of time stationarity. Our approach leverages state-space model (SSM) principles to define a structured feedback matrix that directly propagates gradients from future time steps. This formulation bypasses the need for recursive gradient backpropagation, significantly reducing training overhead while preserving the network's ability to capture long-term dependencies. The experiments on language modeling benchmarks exhibit competitive perplexity scores, while significantly reducing the training costs. These promising results suggest that designing a feedback method like an SSM can fully exploit the efficiency advantages of RNNs for many practical applications.

Recurrent Neural Networks (RNNs) offer fast inference on long sequences but are hard to optimize and slow to train. Deep state-space models (SSMs) have recently been shown to perform remarkably well on long sequence modeling tasks, and have the added benefits of fast parallelizable training and RNN-like fast inference. However, while SSMs are superficially similar to RNNs, there are important differences that make it unclear where their performance boost over RNNs comes from. In this paper, we show that careful design of deep RNNs using standard signal propagation arguments can recover the impressive performance of deep SSMs on long-range reasoning tasks, while also matching their training speed. To achieve this, we analyze and ablate a series of changes to standard RNNs including linearizing and diagonalizing the recurrence, using better parameterizations and initializations, and ensuring proper normalization of the forward pass. Our results provide new insights on the origins of the impressive performance of deep SSMs, while also introducing an RNN block called the Linear Recurrent Unit that matches both their performance on the Long Range Arena benchmark and their computational efficiency.

A central problem in learning from sequential data is representing cumulative history in an incremental fashion as more data is processed. We introduce a general framework (HiPPO) for the online compression of continuous signals and discrete time series by projection onto polynomial bases. Given a measure that specifies the importance of each time step in the past, HiPPO produces an optimal solution to a natural online function approximation problem. As special cases, our framework yields a short derivation of the recent Legendre Memory Unit (LMU) from first principles, and generalizes the ubiquitous gating mechanism of recurrent neural networks such as GRUs. This formal framework yields a new memory update mechanism (HiPPO-LegS) that scales through time to remember all history, avoiding priors on the timescale. HiPPO-LegS enjoys the theoretical benefits of timescale robustness, fast updates, and bounded gradients. By incorporating the memory dynamics into recurrent neural networks, HiPPO RNNs can empirically capture complex temporal dependencies. On the benchmark permuted MNIST dataset, HiPPO-LegS sets a new state-of-the-art accuracy of 98.3%. Finally, on a novel trajectory classification task testing robustness to out-of-distribution timescales and missing data, HiPPO-LegS outperforms RNN and neural ODE baselines by 25-40% accuracy.

We introduce the Block-Recurrent Transformer, which applies a transformer layer in a recurrent fashion along a sequence, and has linear complexity with respect to sequence length. Our recurrent cell operates on blocks of tokens rather than single tokens during training, and leverages parallel computation within a block in order to make efficient use of accelerator hardware. The cell itself is strikingly simple. It is merely a transformer layer: it uses self-attention and cross-attention to efficiently compute a recurrent function over a large set of state vectors and tokens. Our design was inspired in part by LSTM cells, and it uses LSTM-style gates, but it scales the typical LSTM cell up by several orders of magnitude. Our implementation of recurrence has the same cost in both computation time and parameter count as a conventional transformer layer, but offers dramatically improved perplexity in language modeling tasks over very long sequences. Our model out-performs a long-range Transformer XL baseline by a wide margin, while running twice as fast. We demonstrate its effectiveness on PG19 (books), arXiv papers, and GitHub source code. Our code has been released as open source.

We introduce a novel class of untrained Recurrent Neural Networks (RNNs) within the Reservoir Computing (RC) paradigm, called Residual Reservoir Memory Networks (ResRMNs). ResRMN combines a linear memory reservoir with a non-linear reservoir, where the latter is based on residual orthogonal connections along the temporal dimension for enhanced long-term propagation of the input. The resulting reservoir state dynamics are studied through the lens of linear stability analysis, and we investigate diverse configurations for the temporal residual connections. The proposed approach is empirically assessed on time-series and pixel-level 1-D classification tasks. Our experimental results highlight the advantages of the proposed approach over other conventional RC models.

We propose a novel method called Long Expressive Memory (LEM) for learning long-term sequential dependencies. LEM is gradient-based, it can efficiently process sequential tasks with very long-term dependencies, and it is sufficiently expressive to be able to learn complicated input-output maps. To derive LEM, we consider a system of multiscale ordinary differential equations, as well as a suitable time-discretization of this system. For LEM, we derive rigorous bounds to show the mitigation of the exploding and vanishing gradients problem, a well-known challenge for gradient-based recurrent sequential learning methods. We also prove that LEM can approximate a large class of dynamical systems to high accuracy. Our empirical results, ranging from image and time-series classification through dynamical systems prediction to speech recognition and language modeling, demonstrate that LEM outperforms state-of-the-art recurrent neural networks, gated recurrent units, and long short-term memory models.

Attention mechanisms have revolutionized sequence learning but suffer from quadratic computational complexity. This paper introduces Lattice, a novel recurrent neural network (RNN) mechanism that leverages the inherent low-rank structure of K-V matrices to efficiently compress the cache into a fixed number of memory slots, achieving sub-quadratic complexity. We formulate this compression as an online optimization problem and derive a dynamic memory update rule based on a single gradient descent step. The resulting recurrence features a state- and input-dependent gating mechanism, offering an interpretable memory update process. The core innovation is the orthogonal update: each memory slot is updated exclusively with information orthogonal to its current state hence incorporation of only novel, non-redundant data, which minimizes the interference with previously stored information. The experimental results show that Lattice achieves the best perplexity compared to all baselines across diverse context lengths, with performance improvement becoming more pronounced as the context length increases.

We introduce a new neural architecture to learn the conditional probability of an output sequence with elements that are discrete tokens corresponding to positions in an input sequence. Such problems cannot be trivially addressed by existent approaches such as sequence-to-sequence and Neural Turing Machines, because the number of target classes in each step of the output depends on the length of the input, which is variable. Problems such as sorting variable sized sequences, and various combinatorial optimization problems belong to this class. Our model solves the problem of variable size output dictionaries using a recently proposed mechanism of neural attention. It differs from the previous attention attempts in that, instead of using attention to blend hidden units of an encoder to a context vector at each decoder step, it uses attention as a pointer to select a member of the input sequence as the output. We call this architecture a Pointer Net (Ptr-Net). We show Ptr-Nets can be used to learn approximate solutions to three challenging geometric problems -- finding planar convex hulls, computing Delaunay triangulations, and the planar Travelling Salesman Problem -- using training examples alone. Ptr-Nets not only improve over sequence-to-sequence with input attention, but also allow us to generalize to variable size output dictionaries. We show that the learnt models generalize beyond the maximum lengths they were trained on. We hope our results on these tasks will encourage a broader exploration of neural learning for discrete problems.

Zero-shot and in-context learning enable solving tasks without model fine-tuning, making them essential for developing generative model solutions. Therefore, it is crucial to understand whether a pretrained model can be prompted to approximate any function, i.e., whether it is a universal in-context approximator. While it was recently shown that transformer models do possess this property, these results rely on their attention mechanism. Hence, these findings do not apply to fully recurrent architectures like RNNs, LSTMs, and the increasingly popular SSMs. We demonstrate that RNNs, LSTMs, GRUs, Linear RNNs, and linear gated architectures such as Mamba and Hawk/Griffin can also serve as universal in-context approximators. To streamline our argument, we introduce a programming language called LSRL that compiles to these fully recurrent architectures. LSRL may be of independent interest for further studies of fully recurrent models, such as constructing interpretability benchmarks. We also study the role of multiplicative gating and observe that architectures incorporating such gating (e.g., LSTMs, GRUs, Hawk/Griffin) can implement certain operations more stably, making them more viable candidates for practical in-context universal approximation.

The predictive learning of spatiotemporal sequences aims to generate future images by learning from the historical context, where the visual dynamics are believed to have modular structures that can be learned with compositional subsystems. This paper models these structures by presenting PredRNN, a new recurrent network, in which a pair of memory cells are explicitly decoupled, operate in nearly independent transition manners, and finally form unified representations of the complex environment. Concretely, besides the original memory cell of LSTM, this network is featured by a zigzag memory flow that propagates in both bottom-up and top-down directions across all layers, enabling the learned visual dynamics at different levels of RNNs to communicate. It also leverages a memory decoupling loss to keep the memory cells from learning redundant features. We further propose a new curriculum learning strategy to force PredRNN to learn long-term dynamics from context frames, which can be generalized to most sequence-to-sequence models. We provide detailed ablation studies to verify the effectiveness of each component. Our approach is shown to obtain highly competitive results on five datasets for both action-free and action-conditioned predictive learning scenarios.

Humans learn continually throughout their lifespan by accumulating diverse knowledge and fine-tuning it for future tasks. When presented with a similar goal, neural networks suffer from catastrophic forgetting if data distributions across sequential tasks are not stationary over the course of learning. An effective approach to address such continual learning (CL) problems is to use hypernetworks which generate task dependent weights for a target network. However, the continual learning performance of existing hypernetwork based approaches are affected by the assumption of independence of the weights across the layers in order to maintain parameter efficiency. To address this limitation, we propose a novel approach that uses a dependency preserving hypernetwork to generate weights for the target network while also maintaining the parameter efficiency. We propose to use recurrent neural network (RNN) based hypernetwork that can generate layer weights efficiently while allowing for dependencies across them. In addition, we propose novel regularisation and network growth techniques for the RNN based hypernetwork to further improve the continual learning performance. To demonstrate the effectiveness of the proposed methods, we conducted experiments on several image classification continual learning tasks and settings. We found that the proposed methods based on the RNN hypernetworks outperformed the baselines in all these CL settings and tasks.

Recurrent neural networks (RNNs), temporal convolutions, and neural differential equations (NDEs) are popular families of deep learning models for time-series data, each with unique strengths and tradeoffs in modeling power and computational efficiency. We introduce a simple sequence model inspired by control systems that generalizes these approaches while addressing their shortcomings. The Linear State-Space Layer (LSSL) maps a sequence u mapsto y by simply simulating a linear continuous-time state-space representation x = Ax + Bu, y = Cx + Du. Theoretically, we show that LSSL models are closely related to the three aforementioned families of models and inherit their strengths. For example, they generalize convolutions to continuous-time, explain common RNN heuristics, and share features of NDEs such as time-scale adaptation. We then incorporate and generalize recent theory on continuous-time memorization to introduce a trainable subset of structured matrices A that endow LSSLs with long-range memory. Empirically, stacking LSSL layers into a simple deep neural network obtains state-of-the-art results across time series benchmarks for long dependencies in sequential image classification, real-world healthcare regression tasks, and speech. On a difficult speech classification task with length-16000 sequences, LSSL outperforms prior approaches by 24 accuracy points, and even outperforms baselines that use hand-crafted features on 100x shorter sequences.

Dynamical systems (DS) theory is fundamental for many areas of science and engineering. It can provide deep insights into the behavior of systems evolving in time, as typically described by differential or recursive equations. A common approach to facilitate mathematical tractability and interpretability of DS models involves decomposing nonlinear DS into multiple linear DS separated by switching manifolds, i.e. piecewise linear (PWL) systems. PWL models are popular in engineering and a frequent choice in mathematics for analyzing the topological properties of DS. However, hand-crafting such models is tedious and only possible for very low-dimensional scenarios, while inferring them from data usually gives rise to unnecessarily complex representations with very many linear subregions. Here we introduce Almost-Linear Recurrent Neural Networks (AL-RNNs) which automatically and robustly produce most parsimonious PWL representations of DS from time series data, using as few PWL nonlinearities as possible. AL-RNNs can be efficiently trained with any SOTA algorithm for dynamical systems reconstruction (DSR), and naturally give rise to a symbolic encoding of the underlying DS that provably preserves important topological properties. We show that for the Lorenz and R\"ossler systems, AL-RNNs discover, in a purely data-driven way, the known topologically minimal PWL representations of the corresponding chaotic attractors. We further illustrate on two challenging empirical datasets that interpretable symbolic encodings of the dynamics can be achieved, tremendously facilitating mathematical and computational analysis of the underlying systems.

To cope with real-world dynamics, an intelligent system needs to incrementally acquire, update, accumulate, and exploit knowledge throughout its lifetime. This ability, known as continual learning, provides a foundation for AI systems to develop themselves adaptively. In a general sense, continual learning is explicitly limited by catastrophic forgetting, where learning a new task usually results in a dramatic performance degradation of the old tasks. Beyond this, increasingly numerous advances have emerged in recent years that largely extend the understanding and application of continual learning. The growing and widespread interest in this direction demonstrates its realistic significance as well as complexity. In this work, we present a comprehensive survey of continual learning, seeking to bridge the basic settings, theoretical foundations, representative methods, and practical applications. Based on existing theoretical and empirical results, we summarize the general objectives of continual learning as ensuring a proper stability-plasticity trade-off and an adequate intra/inter-task generalizability in the context of resource efficiency. Then we provide a state-of-the-art and elaborated taxonomy, extensively analyzing how representative methods address continual learning, and how they are adapted to particular challenges in realistic applications. Through an in-depth discussion of promising directions, we believe that such a holistic perspective can greatly facilitate subsequent exploration in this field and beyond.

Training recurrent neural networks (RNNs) is a high-dimensional process that requires updating numerous parameters. Therefore, it is often difficult to pinpoint the underlying learning mechanisms. To address this challenge, we propose to gain mechanistic insights into the phenomenon of abrupt learning by studying RNNs trained to perform diverse short-term memory tasks. In these tasks, RNN training begins with an initial search phase. Following a long period of plateau in accuracy, the values of the loss function suddenly drop, indicating abrupt learning. Analyzing the neural computation performed by these RNNs reveals geometric restructuring (GR) in their phase spaces prior to the drop. To promote these GR events, we introduce a temporal consistency regularization that accelerates (bioplausible) training, facilitates attractor formation, and enables efficient learning in strongly connected networks. Our findings offer testable predictions for neuroscientists and emphasize the need for goal-agnostic secondary mechanisms to facilitate learning in biological and artificial networks.

Neural networks are powerful and flexible models that work well for many difficult learning tasks in image, speech and natural language understanding. Despite their success, neural networks are still hard to design. In this paper, we use a recurrent network to generate the model descriptions of neural networks and train this RNN with reinforcement learning to maximize the expected accuracy of the generated architectures on a validation set. On the CIFAR-10 dataset, our method, starting from scratch, can design a novel network architecture that rivals the best human-invented architecture in terms of test set accuracy. Our CIFAR-10 model achieves a test error rate of 3.65, which is 0.09 percent better and 1.05x faster than the previous state-of-the-art model that used a similar architectural scheme. On the Penn Treebank dataset, our model can compose a novel recurrent cell that outperforms the widely-used LSTM cell, and other state-of-the-art baselines. Our cell achieves a test set perplexity of 62.4 on the Penn Treebank, which is 3.6 perplexity better than the previous state-of-the-art model. The cell can also be transferred to the character language modeling task on PTB and achieves a state-of-the-art perplexity of 1.214.

Latest insights from biology show that intelligence not only emerges from the connections between neurons but that individual neurons shoulder more computational responsibility than previously anticipated. This perspective should be critical in the context of constantly changing distinct reinforcement learning environments, yet current approaches still primarily employ static activation functions. In this work, we motivate why rationals are suitable for adaptable activation functions and why their inclusion into neural networks is crucial. Inspired by recurrence in residual networks, we derive a condition under which rational units are closed under residual connections and formulate a naturally regularised version: the recurrent-rational. We demonstrate that equipping popular algorithms with (recurrent-)rational activations leads to consistent improvements on Atari games, especially turning simple DQN into a solid approach, competitive to DDQN and Rainbow.

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

We analyze continual learning on a sequence of separable linear classification tasks with binary labels. We show theoretically that learning with weak regularization reduces to solving a sequential max-margin problem, corresponding to a special case of the Projection Onto Convex Sets (POCS) framework. We then develop upper bounds on the forgetting and other quantities of interest under various settings with recurring tasks, including cyclic and random orderings of tasks. We discuss several practical implications to popular training practices like regularization scheduling and weighting. We point out several theoretical differences between our continual classification setting and a recently studied continual regression setting.

We show that both an LSTM and a unitary-evolution recurrent neural network (URN) can achieve encouraging accuracy on two types of syntactic patterns: context-free long distance agreement, and mildly context-sensitive cross serial dependencies. This work extends recent experiments on deeply nested context-free long distance dependencies, with similar results. URNs differ from LSTMs in that they avoid non-linear activation functions, and they apply matrix multiplication to word embeddings encoded as unitary matrices. This permits them to retain all information in the processing of an input string over arbitrary distances. It also causes them to satisfy strict compositionality. URNs constitute a significant advance in the search for explainable models in deep learning applied to NLP.

Artificial neural networks (ANN) are inspired by human learning. However, unlike human education, classical ANN does not use a curriculum. Curriculum Learning (CL) refers to the process of ANN training in which examples are used in a meaningful order. When using CL, training begins with a subset of the dataset and new samples are added throughout the training, or training begins with the entire dataset and the number of samples used is reduced. With these changes in training dataset size, better results can be obtained with curriculum, anti-curriculum, or random-curriculum methods than the vanilla method. However, a generally efficient CL method for various architectures and data sets is not found. In this paper, we propose cyclical curriculum learning (CCL), in which the data size used during training changes cyclically rather than simply increasing or decreasing. Instead of using only the vanilla method or only the curriculum method, using both methods cyclically like in CCL provides more successful results. We tested the method on 18 different data sets and 15 architectures in image and text classification tasks and obtained more successful results than no-CL and existing CL methods. We also have shown theoretically that it is less erroneous to apply CL and vanilla cyclically instead of using only CL or only vanilla method. The code of Cyclical Curriculum is available at https://github.com/CyclicalCurriculum/Cyclical-Curriculum.

Chaotic dynamical systems (DS) are ubiquitous in nature and society. Often we are interested in reconstructing such systems from observed time series for prediction or mechanistic insight, where by reconstruction we mean learning geometrical and invariant temporal properties of the system in question (like attractors). However, training reconstruction algorithms like recurrent neural networks (RNNs) on such systems by gradient-descent based techniques faces severe challenges. This is mainly due to exploding gradients caused by the exponential divergence of trajectories in chaotic systems. Moreover, for (scientific) interpretability we wish to have as low dimensional reconstructions as possible, preferably in a model which is mathematically tractable. Here we report that a surprisingly simple modification of teacher forcing leads to provably strictly all-time bounded gradients in training on chaotic systems, and, when paired with a simple architectural rearrangement of a tractable RNN design, piecewise-linear RNNs (PLRNNs), allows for faithful reconstruction in spaces of at most the dimensionality of the observed system. We show on several DS that with these amendments we can reconstruct DS better than current SOTA algorithms, in much lower dimensions. Performance differences were particularly compelling on real world data with which most other methods severely struggled. This work thus led to a simple yet powerful DS reconstruction algorithm which is highly interpretable at the same time.

Learning to remember over long timescales is fundamentally challenging for recurrent neural networks (RNNs). While much prior work has explored why RNNs struggle to learn long timescales and how to mitigate this, we still lack a clear understanding of the dynamics involved when RNNs learn long timescales via gradient descent. Here we build a mathematical theory of the learning dynamics of linear RNNs trained to integrate white noise. We show that when the initial recurrent weights are small, the dynamics of learning are described by a low-dimensional system that tracks a single outlier eigenvalue of the recurrent weights. This reveals the precise manner in which the long timescale associated with white noise integration is learned. We extend our analyses to RNNs learning a damped oscillatory filter, and find rich dynamical equations for the evolution of a conjugate pair of outlier eigenvalues. Taken together, our analyses build a rich mathematical framework for studying dynamical learning problems salient for both machine learning and neuroscience.

The recent emergence of new algorithms for permuting models into functionally equivalent regions of the solution space has shed some light on the complexity of error surfaces, and some promising properties like mode connectivity. However, finding the right permutation is challenging, and current optimization techniques are not differentiable, which makes it difficult to integrate into a gradient-based optimization, and often leads to sub-optimal solutions. In this paper, we propose a Sinkhorn re-basin network with the ability to obtain the transportation plan that better suits a given objective. Unlike the current state-of-art, our method is differentiable and, therefore, easy to adapt to any task within the deep learning domain. Furthermore, we show the advantage of our re-basin method by proposing a new cost function that allows performing incremental learning by exploiting the linear mode connectivity property. The benefit of our method is compared against similar approaches from the literature, under several conditions for both optimal transport finding and linear mode connectivity. The effectiveness of our continual learning method based on re-basin is also shown for several common benchmark datasets, providing experimental results that are competitive with state-of-art results from the literature.

While Transformer-based models have demonstrated remarkable language modeling performance, their high complexities result in high costs when processing long contexts. In contrast, recurrent neural networks (RNNs) such as linear attention and state space models have gained popularity due to their constant per-token complexities. However, these recurrent models struggle with tasks that require accurate recall of contextual information from long contexts, because all contextual information is compressed into a constant-size recurrent state. Previous works have shown that recall ability is positively correlated with the recurrent state size, yet directly training RNNs with larger recurrent states results in high training costs. In this paper, we introduce StateX, a training pipeline for efficiently expanding the states of pre-trained RNNs through post-training. For two popular classes of RNNs, linear attention and state space models, we design post-training architectural modifications to scale up the state size with no or negligible increase in model parameters. Experiments on models up to 1.3B parameters demonstrate that StateX efficiently enhances the recall and in-context learning ability of RNNs without incurring high post-training costs or compromising other capabilities.

We prove an inverse approximation theorem for the approximation of nonlinear sequence-to-sequence relationships using recurrent neural networks (RNNs). This is a so-called Bernstein-type result in approximation theory, which deduces properties of a target function under the assumption that it can be effectively approximated by a hypothesis space. In particular, we show that nonlinear sequence relationships that can be stably approximated by nonlinear RNNs must have an exponential decaying memory structure - a notion that can be made precise. This extends the previously identified curse of memory in linear RNNs into the general nonlinear setting, and quantifies the essential limitations of the RNN architecture for learning sequential relationships with long-term memory. Based on the analysis, we propose a principled reparameterization method to overcome the limitations. Our theoretical results are confirmed by numerical experiments. The code has been released in https://github.com/radarFudan/Curse-of-memory

Recent architectural developments have enabled recurrent neural networks (RNNs) to reach and even surpass the performance of Transformers on certain sequence modeling tasks. These modern RNNs feature a prominent design pattern: linear recurrent layers interconnected by feedforward paths with multiplicative gating. Here, we show how RNNs equipped with these two design elements can exactly implement (linear) self-attention, the main building block of Transformers. By reverse-engineering a set of trained RNNs, we find that gradient descent in practice discovers our construction. In particular, we examine RNNs trained to solve simple in-context learning tasks on which Transformers are known to excel and find that gradient descent instills in our RNNs the same attention-based in-context learning algorithm used by Transformers. Our findings highlight the importance of multiplicative interactions in neural networks and suggest that certain RNNs might be unexpectedly implementing attention under the hood.

Continual learning can incrementally absorb new concepts without interfering with previously learned knowledge. Motivated by the characteristics of neural networks, in which information is stored in weights on connections, we investigated how to design an Innately Forgetting-Free Network (IF2Net) for continual learning context. This study proposed a straightforward yet effective learning paradigm by ingeniously keeping the weights relative to each seen task untouched before and after learning a new task. We first presented the novel representation-level learning on task sequences with random weights. This technique refers to tweaking the drifted representations caused by randomization back to their separate task-optimal working states, but the involved weights are frozen and reused (opposite to well-known layer-wise updates of weights). Then, sequential decision-making without forgetting can be achieved by projecting the output weight updates into the parsimonious orthogonal space, making the adaptations not disturb old knowledge while maintaining model plasticity. IF2Net allows a single network to inherently learn unlimited mapping rules without telling task identities at test time by integrating the respective strengths of randomization and orthogonalization. We validated the effectiveness of our approach in the extensive theoretical analysis and empirical study.

Recurrent neural networks (RNNs) are widely used throughout neuroscience as models of local neural activity. Many properties of single RNNs are well characterized theoretically, but experimental neuroscience has moved in the direction of studying multiple interacting areas, and RNN theory needs to be likewise extended. We take a constructive approach towards this problem, leveraging tools from nonlinear control theory and machine learning to characterize when combinations of stable RNNs will themselves be stable. Importantly, we derive conditions which allow for massive feedback connections between interacting RNNs. We parameterize these conditions for easy optimization using gradient-based techniques, and show that stability-constrained "networks of networks" can perform well on challenging sequential-processing benchmark tasks. Altogether, our results provide a principled approach towards understanding distributed, modular function in the brain.

In this paper, we investigate the long-term memory learning capabilities of state-space models (SSMs) from the perspective of parameterization. We prove that state-space models without any reparameterization exhibit a memory limitation similar to that of traditional RNNs: the target relationships that can be stably approximated by state-space models must have an exponential decaying memory. Our analysis identifies this "curse of memory" as a result of the recurrent weights converging to a stability boundary, suggesting that a reparameterization technique can be effective. To this end, we introduce a class of reparameterization techniques for SSMs that effectively lift its memory limitations. Besides improving approximation capabilities, we further illustrate that a principled choice of reparameterization scheme can also enhance optimization stability. We validate our findings using synthetic datasets and language models.

Memory-based meta-learning is a technique for approximating Bayes-optimal predictors. Under fairly general conditions, minimizing sequential prediction error, measured by the log loss, leads to implicit meta-learning. The goal of this work is to investigate how far this interpretation can be realized by current sequence prediction models and training regimes. The focus is on piecewise stationary sources with unobserved switching-points, which arguably capture an important characteristic of natural language and action-observation sequences in partially observable environments. We show that various types of memory-based neural models, including Transformers, LSTMs, and RNNs can learn to accurately approximate known Bayes-optimal algorithms and behave as if performing Bayesian inference over the latent switching-points and the latent parameters governing the data distribution within each segment.

Modern recurrent architectures, such as xLSTM and Mamba, have recently challenged the Transformer in language modeling. However, their structure constrains their applicability to sequences only or requires processing multi-dimensional data structures, such as images or molecular graphs, in a pre-defined sequential order. In contrast, Multi-Dimensional RNNs (MDRNNs) are well suited for data with a higher level structure, like 2D grids, trees, and directed acyclic graphs (DAGs). In this work, we extend the notion of multi-dimensionality to linear RNNs. We introduce parallelizable Linear Source Transition Mark networks (pLSTMs) using Source, Transition, and Mark gates that act on the line graph of a general DAG. This enables parallelization in analogy to parallel associative scans and the chunkwise-recurrent form of sequential linear RNNs, but for DAGs. For regular grids (1D and 2D), like images, this scheme can be efficiently implemented using einsum operations, concatenations, and padding in logarithmic time. pLSTMs tackle the vanishing/exploding activation/gradient problem for long distances in DAGs via two distinct modes: a directed propagation mode (P-mode) and a diffusive distribution mode (D-mode). To showcase the long-range capabilities of pLSTM, we introduce arrow-pointing extrapolation as a synthetic computer vision task that contains long-distance directional information. We demonstrate that pLSTMs generalize well to larger image sizes, whereas Transformers struggle to extrapolate. On established molecular graph and computer vision benchmarks, pLSTMs also show strong performance. Code and Datasets are available at: https://github.com/ml-jku/plstm_experiments.

The goal of continual learning is to find a model that solves multiple learning tasks which are presented sequentially to the learner. A key challenge in this setting is that the learner may forget how to solve a previous task when learning a new task, a phenomenon known as catastrophic forgetting. To address this challenge, many practical methods have been proposed, including memory-based, regularization-based, and expansion-based methods. However, a rigorous theoretical understanding of these methods remains elusive. This paper aims to bridge this gap between theory and practice by proposing a new continual learning framework called Ideal Continual Learner (ICL), which is guaranteed to avoid catastrophic forgetting by construction. We show that ICL unifies multiple well-established continual learning methods and gives new theoretical insights into the strengths and weaknesses of these methods. We also derive generalization bounds for ICL which allow us to theoretically quantify how rehearsal affects generalization. Finally, we connect ICL to several classic subjects and research topics of modern interest, which allows us to make historical remarks and inspire future directions.

One major obstacle towards AI is the poor ability of models to solve new problems quicker, and without forgetting previously acquired knowledge. To better understand this issue, we study the problem of continual learning, where the model observes, once and one by one, examples concerning a sequence of tasks. First, we propose a set of metrics to evaluate models learning over a continuum of data. These metrics characterize models not only by their test accuracy, but also in terms of their ability to transfer knowledge across tasks. Second, we propose a model for continual learning, called Gradient Episodic Memory (GEM) that alleviates forgetting, while allowing beneficial transfer of knowledge to previous tasks. Our experiments on variants of the MNIST and CIFAR-100 datasets demonstrate the strong performance of GEM when compared to the state-of-the-art.

We present trellis networks, a new architecture for sequence modeling. On the one hand, a trellis network is a temporal convolutional network with special structure, characterized by weight tying across depth and direct injection of the input into deep layers. On the other hand, we show that truncated recurrent networks are equivalent to trellis networks with special sparsity structure in their weight matrices. Thus trellis networks with general weight matrices generalize truncated recurrent networks. We leverage these connections to design high-performing trellis networks that absorb structural and algorithmic elements from both recurrent and convolutional models. Experiments demonstrate that trellis networks outperform the current state of the art methods on a variety of challenging benchmarks, including word-level language modeling and character-level language modeling tasks, and stress tests designed to evaluate long-term memory retention. The code is available at https://github.com/locuslab/trellisnet .

Replay methods have shown to be successful in mitigating catastrophic forgetting in continual learning scenarios despite having limited access to historical data. However, storing historical data is cheap in many real-world applications, yet replaying all historical data would be prohibited due to processing time constraints. In such settings, we propose learning the time to learn for a continual learning system, in which we learn replay schedules over which tasks to replay at different time steps. To demonstrate the importance of learning the time to learn, we first use Monte Carlo tree search to find the proper replay schedule and show that it can outperform fixed scheduling policies in terms of continual learning performance. Moreover, to improve the scheduling efficiency itself, we propose to use reinforcement learning to learn the replay scheduling policies that can generalize to new continual learning scenarios without added computational cost. In our experiments, we show the advantages of learning the time to learn, which brings current continual learning research closer to real-world needs.

In recent years, attention-like mechanisms have been used to great success in the space of large language models, unlocking scaling potential to a previously unthinkable extent. "Attention Is All You Need" famously claims RNN cells are not needed in conjunction with attention. We challenge this view. In this paper, we point to existing proofs that architectures with fully parallelizable forward or backward passes cannot represent classes of problems specifically interesting for long-running agentic tasks. We further conjecture a critical time t beyond which non-recurrence-complete models fail to aggregate inputs correctly, with concrete implications for agentic systems (e.g., software engineering agents). To address this, we introduce a recurrence-complete architecture and train it on GitHub-derived action sequences. Loss follows a power law in the trained sequence length while the parameter count remains fixed. Moreover, longer-sequence training always amortizes its linearly increasing wall-time cost, yielding lower loss as a function of wall time.

The ability to learn different tasks sequentially is essential to the development of artificial intelligence. In general, neural networks lack this capability, the major obstacle being catastrophic forgetting. It occurs when the incrementally available information from non-stationary data distributions is continually acquired, disrupting what the model has already learned. Our approach remembers old tasks by projecting the representations of new tasks close to that of old tasks while keeping the decision boundaries unchanged. We employ the center loss as a regularization penalty that enforces new tasks' features to have the same class centers as old tasks and makes the features highly discriminative. This, in turn, leads to the least forgetting of already learned information. This method is easy to implement, requires minimal computational and memory overhead, and allows the neural network to maintain high performance across many sequentially encountered tasks. We also demonstrate that using the center loss in conjunction with the memory replay outperforms other replay-based strategies. Along with standard MNIST variants for continual learning, we apply our method to continual domain adaptation scenarios with the Digits and PACS datasets. We demonstrate that our approach is scalable, effective, and gives competitive performance compared to state-of-the-art continual learning methods.

The advent of Transformers marked a significant breakthrough in sequence modelling, providing a highly performant architecture capable of leveraging GPU parallelism. However, Transformers are computationally expensive at inference time, limiting their applications, particularly in low-resource settings (e.g., mobile and embedded devices). Addressing this, we (1) begin by showing that attention can be viewed as a special Recurrent Neural Network (RNN) with the ability to compute its many-to-one RNN output efficiently. We then (2) show that popular attention-based models such as Transformers can be viewed as RNN variants. However, unlike traditional RNNs (e.g., LSTMs), these models cannot be updated efficiently with new tokens, an important property in sequence modelling. Tackling this, we (3) introduce a new efficient method of computing attention's many-to-many RNN output based on the parallel prefix scan algorithm. Building on the new attention formulation, we (4) introduce Aaren, an attention-based module that can not only (i) be trained in parallel (like Transformers) but also (ii) be updated efficiently with new tokens, requiring only constant memory for inferences (like traditional RNNs). Empirically, we show Aarens achieve comparable performance to Transformers on 38 datasets spread across four popular sequential problem settings: reinforcement learning, event forecasting, time series classification, and time series forecasting tasks while being more time and memory-efficient.

Recurrent neural networks (RNNs) in the brain and in silico excel at solving tasks with intricate temporal dependencies. Long timescales required for solving such tasks can arise from properties of individual neurons (single-neuron timescale, tau, e.g., membrane time constant in biological neurons) or recurrent interactions among them (network-mediated timescale). However, the contribution of each mechanism for optimally solving memory-dependent tasks remains poorly understood. Here, we train RNNs to solve N-parity and N-delayed match-to-sample tasks with increasing memory requirements controlled by N by simultaneously optimizing recurrent weights and taus. We find that for both tasks RNNs develop longer timescales with increasing N, but depending on the learning objective, they use different mechanisms. Two distinct curricula define learning objectives: sequential learning of a single-N (single-head) or simultaneous learning of multiple Ns (multi-head). Single-head networks increase their tau with N and are able to solve tasks for large N, but they suffer from catastrophic forgetting. However, multi-head networks, which are explicitly required to hold multiple concurrent memories, keep tau constant and develop longer timescales through recurrent connectivity. Moreover, we show that the multi-head curriculum increases training speed and network stability to ablations and perturbations, and allows RNNs to generalize better to tasks beyond their training regime. This curriculum also significantly improves training GRUs and LSTMs for large-N tasks. Our results suggest that adapting timescales to task requirements via recurrent interactions allows learning more complex objectives and improves the RNN's performance.

Which generative model is the most suitable for Continual Learning? This paper aims at evaluating and comparing generative models on disjoint sequential image generation tasks. We investigate how several models learn and forget, considering various strategies: rehearsal, regularization, generative replay and fine-tuning. We used two quantitative metrics to estimate the generation quality and memory ability. We experiment with sequential tasks on three commonly used benchmarks for Continual Learning (MNIST, Fashion MNIST and CIFAR10). We found that among all models, the original GAN performs best and among Continual Learning strategies, generative replay outperforms all other methods. Even if we found satisfactory combinations on MNIST and Fashion MNIST, training generative models sequentially on CIFAR10 is particularly instable, and remains a challenge. Our code is available online \url{https://github.com/TLESORT/Generative\_Continual\_Learning}.

Kernel continual learning by derakhshani2021kernel has recently emerged as a strong continual learner due to its non-parametric ability to tackle task interference and catastrophic forgetting. Unfortunately its success comes at the expense of an explicit memory to store samples from past tasks, which hampers scalability to continual learning settings with a large number of tasks. In this paper, we introduce generative kernel continual learning, which explores and exploits the synergies between generative models and kernels for continual learning. The generative model is able to produce representative samples for kernel learning, which removes the dependence on memory in kernel continual learning. Moreover, as we replay only on the generative model, we avoid task interference while being computationally more efficient compared to previous methods that need replay on the entire model. We further introduce a supervised contrastive regularization, which enables our model to generate even more discriminative samples for better kernel-based classification performance. We conduct extensive experiments on three widely-used continual learning benchmarks that demonstrate the abilities and benefits of our contributions. Most notably, on the challenging SplitCIFAR100 benchmark, with just a simple linear kernel we obtain the same accuracy as kernel continual learning with variational random features for one tenth of the memory, or a 10.1\% accuracy gain for the same memory budget.

In the past few years, neural networks have evolved from simple Feedforward Neural Networks to more complex neural networks, such as Convolutional Neural Networks and Recurrent Neural Networks. Where CNNs are a perfect fit for tasks where the sequence is not important such as image recognition, RNNs are useful when order is important such as machine translation. An increasing number of layers in a neural network is one way to improve its performance, but it also increases its complexity making it much more time and power-consuming to train. One way to tackle this problem is to introduce sparsity in the architecture of the neural network. Pruning is one of the many methods to make a neural network architecture sparse by clipping out weights below a certain threshold while keeping the performance near to the original. Another way is to generate arbitrary structures using random graphs and embed them between an input and output layer of an Artificial Neural Network. Many researchers in past years have focused on pruning mainly CNNs, while hardly any research is done for the same in RNNs. The same also holds in creating sparse architectures for RNNs by generating and embedding arbitrary structures. Therefore, this thesis focuses on investigating the effects of the before-mentioned two techniques on the performance of RNNs. We first describe the pruning of RNNs, its impact on the performance of RNNs, and the number of training epochs required to regain accuracy after the pruning is performed. Next, we continue with the creation and training of Sparse Recurrent Neural Networks and identify the relation between the performance and the graph properties of its underlying arbitrary structure. We perform these experiments on RNN with Tanh nonlinearity (RNN-Tanh), RNN with ReLU nonlinearity (RNN-ReLU), GRU, and LSTM. Finally, we analyze and discuss the results achieved from both the experiments.

Even when massively overparameterized, deep neural networks show a remarkable ability to generalize. Research on this phenomenon has focused on generalization within distribution, via smooth interpolation. Yet in some settings neural networks also learn to extrapolate to data far beyond the bounds of the original training set, sometimes even allowing for infinite generalization, implying that an algorithm capable of solving the task has been learned. Here we undertake a case study of the learning dynamics of recurrent neural networks (RNNs) trained on the streaming parity task in order to develop an effective theory of algorithm development. The streaming parity task is a simple but nonlinear task defined on sequences up to arbitrary length. We show that, with sufficient finite training experience, RNNs exhibit a phase transition to perfect infinite generalization. Using an effective theory for the representational dynamics, we find an implicit representational merger effect which can be interpreted as the construction of a finite automaton that reproduces the task. Overall, our results disclose one mechanism by which neural networks can generalize infinitely from finite training experience.

Natural data is redundant yet predominant architectures tile computation uniformly across their input and output space. We propose the Recurrent Interface Networks (RINs), an attention-based architecture that decouples its core computation from the dimensionality of the data, enabling adaptive computation for more scalable generation of high-dimensional data. RINs focus the bulk of computation (i.e. global self-attention) on a set of latent tokens, using cross-attention to read and write (i.e. route) information between latent and data tokens. Stacking RIN blocks allows bottom-up (data to latent) and top-down (latent to data) feedback, leading to deeper and more expressive routing. While this routing introduces challenges, this is less problematic in recurrent computation settings where the task (and routing problem) changes gradually, such as iterative generation with diffusion models. We show how to leverage recurrence by conditioning the latent tokens at each forward pass of the reverse diffusion process with those from prior computation, i.e. latent self-conditioning. RINs yield state-of-the-art pixel diffusion models for image and video generation, scaling to 1024X1024 images without cascades or guidance, while being domain-agnostic and up to 10X more efficient than 2D and 3D U-Nets.

We propose a simple technique for encouraging generative RNNs to plan ahead. We train a "backward" recurrent network to generate a given sequence in reverse order, and we encourage states of the forward model to predict cotemporal states of the backward model. The backward network is used only during training, and plays no role during sampling or inference. We hypothesize that our approach eases modeling of long-term dependencies by implicitly forcing the forward states to hold information about the longer-term future (as contained in the backward states). We show empirically that our approach achieves 9% relative improvement for a speech recognition task, and achieves significant improvement on a COCO caption generation task.

We present an architecture of a recurrent neural network (RNN) with a fully-connected deep neural network (DNN) as its feature extractor. The RNN is equipped with both causal temporal prediction and non-causal look-ahead, via auto-regression (AR) and moving-average (MA), respectively. The focus of this paper is a primal-dual training method that formulates the learning of the RNN as a formal optimization problem with an inequality constraint that provides a sufficient condition for the stability of the network dynamics. Experimental results demonstrate the effectiveness of this new method, which achieves 18.86% phone recognition error on the TIMIT benchmark for the core test set. The result approaches the best result of 17.7%, which was obtained by using RNN with long short-term memory (LSTM). The results also show that the proposed primal-dual training method produces lower recognition errors than the popular RNN methods developed earlier based on the carefully tuned threshold parameter that heuristically prevents the gradient from exploding.

The Linear Representation Hypothesis (LRH) states that neural networks learn to encode concepts as directions in activation space, and a strong version of the LRH states that models learn only such encodings. In this paper, we present a counterexample to this strong LRH: when trained to repeat an input token sequence, gated recurrent neural networks (RNNs) learn to represent the token at each position with a particular order of magnitude, rather than a direction. These representations have layered features that are impossible to locate in distinct linear subspaces. To show this, we train interventions to predict and manipulate tokens by learning the scaling factor corresponding to each sequence position. These interventions indicate that the smallest RNNs find only this magnitude-based solution, while larger RNNs have linear representations. These findings strongly indicate that interpretability research should not be confined by the LRH.

Recurrent large language models that compete with Transformers in language modeling perplexity are emerging at a rapid rate (e.g., Mamba, RWKV). Excitingly, these architectures use a constant amount of memory during inference. However, due to the limited memory, recurrent LMs cannot recall and use all the information in long contexts leading to brittle in-context learning (ICL) quality. A key challenge for efficient LMs is selecting what information to store versus discard. In this work, we observe the order in which information is shown to the LM impacts the selection difficulty. To formalize this, we show that the hardness of information recall reduces to the hardness of a problem called set disjointness (SD), a quintessential problem in communication complexity that requires a streaming algorithm (e.g., recurrent model) to decide whether inputted sets are disjoint. We empirically and theoretically show that the recurrent memory required to solve SD changes with set order, i.e., whether the smaller set appears first in-context. Our analysis suggests, to mitigate the reliance on data order, we can put information in the right order in-context or process prompts non-causally. Towards that end, we propose: (1) JRT-Prompt, where context gets repeated multiple times in the prompt, effectively showing the model all data orders. This gives 11.0 pm 1.3 points of improvement, averaged across 16 recurrent LMs and the 6 ICL tasks, with 11.9times higher throughput than FlashAttention-2 for generation prefill (length 32k, batch size 16, NVidia H100). We then propose (2) JRT-RNN, which uses non-causal prefix-linear-attention to process prompts and provides 99% of Transformer quality at 360M params., 30B tokens and 96% at 1.3B params., 50B tokens on average across the tasks, with 19.2times higher throughput for prefill than FA2.

Sequential models, such as Recurrent Neural Networks and Neural Ordinary Differential Equations, have long suffered from slow training due to their inherent sequential nature. For many years this bottleneck has persisted, as many thought sequential models could not be parallelized. We challenge this long-held belief with our parallel algorithm that accelerates GPU evaluation of sequential models by up to 3 orders of magnitude faster without compromising output accuracy. The algorithm does not need any special structure in the sequential models' architecture, making it applicable to a wide range of architectures. Using our method, training sequential models can be more than 10 times faster than the common sequential method without any meaningful difference in the training results. Leveraging this accelerated training, we discovered the efficacy of the Gated Recurrent Unit in a long time series classification problem with 17k time samples. By overcoming the training bottleneck, our work serves as the first step to unlock the potential of non-linear sequential models for long sequence problems.

Large-scale neural language models exhibit a remarkable capacity for in-context learning (ICL): they can infer novel functions from datasets provided as input. Most of our current understanding of when and how ICL arises comes from LMs trained on extremely simple learning problems like linear regression and associative recall. There remains a significant gap between these model problems and the "real" ICL exhibited by LMs trained on large text corpora, which involves not just retrieval and function approximation but free-form generation of language and other structured outputs. In this paper, we study ICL through the lens of a new family of model problems we term in context language learning (ICLL). In ICLL, LMs are presented with a set of strings from a formal language, and must generate additional strings from the same language. We focus on in-context learning of regular languages generated by random finite automata. We evaluate a diverse set of neural sequence models (including several RNNs, Transformers, and state-space model variants) on regular ICLL tasks, aiming to answer three questions: (1) Which model classes are empirically capable of ICLL? (2) What algorithmic solutions do successful models implement to perform ICLL? (3) What architectural changes can improve ICLL in less performant models? We first show that Transformers significantly outperform neural sequence models with recurrent or convolutional representations on ICLL tasks. Next, we provide evidence that their ability to do so relies on specialized "n-gram heads" (higher-order variants of induction heads) that compute input-conditional next-token distributions. Finally, we show that hard-wiring these heads into neural models improves performance not just on ICLL, but natural language modeling -- improving the perplexity of 340M-parameter models by up to 1.14 points (6.7%) on the SlimPajama dataset.

Recent shifts in the space of large language model (LLM) research have shown an increasing focus on novel architectures to compete with prototypical Transformer-based models that have long dominated this space. Linear recurrent models have proven to be a viable competitor due to their computational efficiency. However, such models still demonstrate a sizable gap compared to Transformers in terms of in-context learning among other tasks that require recalling information from a context. In this work, we introduce __Resona__, a simple and scalable framework for augmenting linear recurrent models with retrieval. __Resona__~augments models with the ability to integrate retrieved information from the provided input context, enabling tailored behavior to diverse task requirements. Experiments on a variety of linear recurrent models demonstrate that __Resona__-augmented models observe significant performance gains on a variety of synthetic as well as real-world natural language tasks, highlighting its ability to act as a general purpose method to improve the in-context learning and language modeling abilities of linear recurrent LLMs.

Irregularly sampled time series data arise naturally in many application domains including biology, ecology, climate science, astronomy, and health. Such data represent fundamental challenges to many classical models from machine learning and statistics due to the presence of non-uniform intervals between observations. However, there has been significant progress within the machine learning community over the last decade on developing specialized models and architectures for learning from irregularly sampled univariate and multivariate time series data. In this survey, we first describe several axes along which approaches to learning from irregularly sampled time series differ including what data representations they are based on, what modeling primitives they leverage to deal with the fundamental problem of irregular sampling, and what inference tasks they are designed to perform. We then survey the recent literature organized primarily along the axis of modeling primitives. We describe approaches based on temporal discretization, interpolation, recurrence, attention and structural invariance. We discuss similarities and differences between approaches and highlight primary strengths and weaknesses.

Graph generation with Machine Learning is an open problem with applications in various research fields. In this work, we propose to cast the generative process of a graph into a sequential one, relying on a node ordering procedure. We use this sequential process to design a novel generative model composed of two recurrent neural networks that learn to predict the edges of graphs: the first network generates one endpoint of each edge, while the second network generates the other endpoint conditioned on the state of the first. We test our approach extensively on five different datasets, comparing with two well-known baselines coming from graph literature, and two recurrent approaches, one of which holds state of the art performances. Evaluation is conducted considering quantitative and qualitative characteristics of the generated samples. Results show that our approach is able to yield novel, and unique graphs originating from very different distributions, while retaining structural properties very similar to those in the training sample. Under the proposed evaluation framework, our approach is able to reach performances comparable to the current state of the art on the graph generation task.

This paper investigates the gap in representation powers of Recurrent Neural Networks (RNNs) and Transformers in the context of solving algorithmic problems. We focus on understanding whether RNNs, known for their memory efficiency in handling long sequences, can match the performance of Transformers, particularly when enhanced with Chain-of-Thought (CoT) prompting. Our theoretical analysis reveals that CoT improves RNNs but is insufficient to close the gap with Transformers. A key bottleneck lies in the inability of RNNs to perfectly retrieve information from the context, even with CoT: for several tasks that explicitly or implicitly require this capability, such as associative recall and determining if a graph is a tree, we prove that RNNs are not expressive enough to solve the tasks while Transformers can solve them with ease. Conversely, we prove that adopting techniques to enhance the in-context retrieval capability of RNNs, including Retrieval-Augmented Generation (RAG) and adding a single Transformer layer, can elevate RNNs to be capable of solving all polynomial-time solvable problems with CoT, hence closing the representation gap with Transformers.

Recently, recurrent models such as state space models and linear attention have become popular due to their linear complexity in the sequence length. Thanks to their recurrent nature, in principle they can process arbitrarily long sequences, but their performance sometimes drops considerably beyond their training context lengths-i.e. they fail to length generalize. In this work, we provide comprehensive empirical and theoretical analysis to support the unexplored states hypothesis, which posits that models fail to length generalize when during training they are only exposed to a limited subset of the distribution of all attainable states (i.e. states that would be attained if the recurrence was applied to long sequences). Furthermore, we investigate simple training interventions that aim to increase the coverage of the states that the model is trained on, e.g. by initializing the state with Gaussian noise or with the final state of a different input sequence. With only 500 post-training steps (sim 0.1% of the pre-training budget), these interventions enable length generalization for sequences that are orders of magnitude longer than the training context (e.g. 2klongrightarrow 128k) and show improved performance in long context tasks, thus presenting a simple and efficient way to enable robust length generalization in general recurrent models.

In this paper we compare different types of recurrent units in recurrent neural networks (RNNs). Especially, we focus on more sophisticated units that implement a gating mechanism, such as a long short-term memory (LSTM) unit and a recently proposed gated recurrent unit (GRU). We evaluate these recurrent units on the tasks of polyphonic music modeling and speech signal modeling. Our experiments revealed that these advanced recurrent units are indeed better than more traditional recurrent units such as tanh units. Also, we found GRU to be comparable to LSTM.

Modular approaches, which use a different composition of modules for each problem and avoid forgetting by design, have been shown to be a promising direction in continual learning (CL). However, searching through the large, discrete space of possible module compositions is a challenge because evaluating a composition's performance requires a round of neural network training. To address this challenge, we develop a modular CL framework, called PICLE, that accelerates search by using a probabilistic model to cheaply compute the fitness of each composition. The model combines prior knowledge about good module compositions with dataset-specific information. Its use is complemented by splitting up the search space into subsets, such as perceptual and latent subsets. We show that PICLE is the first modular CL algorithm to achieve different types of transfer while scaling to large search spaces. We evaluate it on two benchmark suites designed to capture different desiderata of CL techniques. On these benchmarks, PICLE offers significantly better performance than state-of-the-art CL baselines.

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

The rapid advancement of generative models has enabled modern AI systems to comprehend and produce highly sophisticated content, even achieving human-level performance in specific domains. However, these models remain fundamentally constrained by catastrophic forgetting - a persistent challenge where adapting to new tasks typically leads to significant degradation in performance on previously learned tasks. To address this practical limitation, numerous approaches have been proposed to enhance the adaptability and scalability of generative models in real-world applications. In this work, we present a comprehensive survey of continual learning methods for mainstream generative models, including large language models, multimodal large language models, vision language action models, and diffusion models. Drawing inspiration from the memory mechanisms of the human brain, we systematically categorize these approaches into three paradigms: architecture-based, regularization-based, and replay-based methods, while elucidating their underlying methodologies and motivations. We further analyze continual learning setups for different generative models, including training objectives, benchmarks, and core backbones, offering deeper insights into the field. The project page of this paper is available at https://github.com/Ghy0501/Awesome-Continual-Learning-in-Generative-Models.

Structured state-space models (SSMs) such as S4, stemming from the seminal work of Gu et al., are gaining popularity as effective approaches for modeling sequential data. Deep SSMs demonstrate outstanding performance across a diverse set of domains, at a reduced training and inference cost compared to attention-based transformers. Recent developments show that if the linear recurrence powering SSMs allows for multiplicative interactions between inputs and hidden states (e.g. GateLoop, Mamba, GLA), then the resulting architecture can surpass in both in accuracy and efficiency attention-powered foundation models trained on text, at scales of billion parameters. In this paper, we give theoretical grounding to this recent finding using tools from Rough Path Theory: we show that when random linear recurrences are equipped with simple input-controlled transitions (selectivity mechanism), then the hidden state is provably a low-dimensional projection of a powerful mathematical object called the signature of the input -- capturing non-linear interactions between tokens at distinct timescales. Our theory not only motivates the success of modern selective state-space models such as Mamba but also provides a solid framework to understand the expressive power of future SSM variants.

We present sketch-rnn, a recurrent neural network (RNN) able to construct stroke-based drawings of common objects. The model is trained on thousands of crude human-drawn images representing hundreds of classes. We outline a framework for conditional and unconditional sketch generation, and describe new robust training methods for generating coherent sketch drawings in a vector format.

Developing autonomous agents that can interact with changing environments is an open challenge in machine learning. Robustness is particularly important in these settings as agents are often fit offline on expert demonstrations but deployed online where they must generalize to the closed feedback loop within the environment. In this work, we explore the application of recurrent neural networks to tasks of this nature and understand how a parameterization of their recurrent connectivity influences robustness in closed-loop settings. Specifically, we represent the recurrent connectivity as a function of rank and sparsity and show both theoretically and empirically that modulating these two variables has desirable effects on network dynamics. The proposed low-rank, sparse connectivity induces an interpretable prior on the network that proves to be most amenable for a class of models known as closed-form continuous-time neural networks (CfCs). We find that CfCs with fewer parameters can outperform their full-rank, fully-connected counterparts in the online setting under distribution shift. This yields memory-efficient and robust agents while opening a new perspective on how we can modulate network dynamics through connectivity.

Humans excel at learning abstract patterns across different sequences, filtering out irrelevant details, and transferring these generalized concepts to new sequences. In contrast, many sequence learning models lack the ability to abstract, which leads to memory inefficiency and poor transfer. We introduce a non-parametric hierarchical variable learning model (HVM) that learns chunks from sequences and abstracts contextually similar chunks as variables. HVM efficiently organizes memory while uncovering abstractions, leading to compact sequence representations. When learning on language datasets such as babyLM, HVM learns a more efficient dictionary than standard compression algorithms such as Lempel-Ziv. In a sequence recall task requiring the acquisition and transfer of variables embedded in sequences, we demonstrate HVM's sequence likelihood correlates with human recall times. In contrast, large language models (LLMs) struggle to transfer abstract variables as effectively as humans. From HVM's adjustable layer of abstraction, we demonstrate that the model realizes a precise trade-off between compression and generalization. Our work offers a cognitive model that captures the learning and transfer of abstract representations in human cognition and differentiates itself from LLMs.

Echo State Networks (ESNs) are a particular type of untrained Recurrent Neural Networks (RNNs) within the Reservoir Computing (RC) framework, popular for their fast and efficient learning. However, traditional ESNs often struggle with long-term information processing. In this paper, we introduce a novel class of deep untrained RNNs based on temporal residual connections, called Deep Residual Echo State Networks (DeepResESNs). We show that leveraging a hierarchy of untrained residual recurrent layers significantly boosts memory capacity and long-term temporal modeling. For the temporal residual connections, we consider different orthogonal configurations, including randomly generated and fixed-structure configurations, and we study their effect on network dynamics. A thorough mathematical analysis outlines necessary and sufficient conditions to ensure stable dynamics within DeepResESN. Our experiments on a variety of time series tasks showcase the advantages of the proposed approach over traditional shallow and deep RC.

Recurrent Spiking Neural Networks (RSNNs) have emerged as a computationally efficient and brain-inspired learning model. The design of sparse RSNNs with fewer neurons and synapses helps reduce the computational complexity of RSNNs. Traditionally, sparse SNNs are obtained by first training a dense and complex SNN for a target task, and, then, pruning neurons with low activity (activity-based pruning) while maintaining task performance. In contrast, this paper presents a task-agnostic methodology for designing sparse RSNNs by pruning a large randomly initialized model. We introduce a novel Lyapunov Noise Pruning (LNP) algorithm that uses graph sparsification methods and utilizes Lyapunov exponents to design a stable sparse RSNN from a randomly initialized RSNN. We show that the LNP can leverage diversity in neuronal timescales to design a sparse Heterogeneous RSNN (HRSNN). Further, we show that the same sparse HRSNN model can be trained for different tasks, such as image classification and temporal prediction. We experimentally show that, in spite of being task-agnostic, LNP increases computational efficiency (fewer neurons and synapses) and prediction performance of RSNNs compared to traditional activity-based pruning of trained dense models.

Over more than a decade there has been an extensive research effort on how to effectively utilize recurrent models and attention. While recurrent models aim to compress the data into a fixed-size memory (called hidden state), attention allows attending to the entire context window, capturing the direct dependencies of all tokens. This more accurate modeling of dependencies, however, comes with a quadratic cost, limiting the model to a fixed-length context. We present a new neural long-term memory module that learns to memorize historical context and helps attention to attend to the current context while utilizing long past information. We show that this neural memory has the advantage of fast parallelizable training while maintaining a fast inference. From a memory perspective, we argue that attention due to its limited context but accurate dependency modeling performs as a short-term memory, while neural memory due to its ability to memorize the data, acts as a long-term, more persistent, memory. Based on these two modules, we introduce a new family of architectures, called Titans, and present three variants to address how one can effectively incorporate memory into this architecture. Our experimental results on language modeling, common-sense reasoning, genomics, and time series tasks show that Titans are more effective than Transformers and recent modern linear recurrent models. They further can effectively scale to larger than 2M context window size with higher accuracy in needle-in-haystack tasks compared to baselines.

We introduce and train distributed neural architectures (DNA) in vision and language domains. DNAs are initialized with a proto-architecture that consists of (transformer, MLP, attention, etc.) modules and routers. Any token (or patch) can traverse any series of modules in any order. DNAs are a natural generalization of the sparse methods such as Mixture-of-Experts, Mixture-of-Depths, parameter sharing, etc. Computation and communication patterns of DNA modules are learnt end-to-end during training and depend on the content and context of each token (or patch). These patterns can be shaped by further requirements added to the optimization objective such as compute/memory efficiency or load balancing. We empirically show that (i) trained DNAs are competitive with the dense baselines in both domains and (ii) compute efficiency/parameter sharing can be learnt from data. Next, we analyze the emergent connectivity and computation patterns in the trained DNAs. We find that the paths that tokens take through the models are themselves distributed according to a power-law. We show that some paths (or, equivalently, groups of modules) show emergent specialization. Finally, we demonstrate that models learn to allocate compute and active parameters in an interpretable way.

In this work, we explore whether modeling recurrence into the Transformer architecture can both be beneficial and efficient, by building an extremely simple recurrent module into the Transformer. We compare our model to baselines following the training and evaluation recipe of BERT. Our results confirm that recurrence can indeed improve Transformer models by a consistent margin, without requiring low-level performance optimizations, and while keeping the number of parameters constant. For example, our base model achieves an absolute improvement of 2.1 points averaged across 10 tasks and also demonstrates increased stability in fine-tuning over a range of learning rates.

The mainstream paradigm behind continual learning has been to adapt the model parameters to non-stationary data distributions, where catastrophic forgetting is the central challenge. Typical methods rely on a rehearsal buffer or known task identity at test time to retrieve learned knowledge and address forgetting, while this work presents a new paradigm for continual learning that aims to train a more succinct memory system without accessing task identity at test time. Our method learns to dynamically prompt (L2P) a pre-trained model to learn tasks sequentially under different task transitions. In our proposed framework, prompts are small learnable parameters, which are maintained in a memory space. The objective is to optimize prompts to instruct the model prediction and explicitly manage task-invariant and task-specific knowledge while maintaining model plasticity. We conduct comprehensive experiments under popular image classification benchmarks with different challenging continual learning settings, where L2P consistently outperforms prior state-of-the-art methods. Surprisingly, L2P achieves competitive results against rehearsal-based methods even without a rehearsal buffer and is directly applicable to challenging task-agnostic continual learning. Source code is available at https://github.com/google-research/l2p.

It is an important yet challenging setting to continually learn new tasks from a few examples. Although numerous efforts have been devoted to either continual learning or few-shot learning, little work has considered this new setting of few-shot continual learning (FSCL), which needs to minimize the catastrophic forgetting to the old tasks and gradually improve the ability of few-shot generalization. In this paper, we provide a first systematic study on FSCL and present an effective solution with deep neural networks. Our solution is based on the observation that continual learning of a task sequence inevitably interferes few-shot generalization, which makes it highly nontrivial to extend few-shot learning strategies to continual learning scenarios. We draw inspirations from the robust brain system and develop a method that (1) interdependently updates a pair of fast / slow weights for continual learning and few-shot learning to disentangle their divergent objectives, inspired by the biological model of meta-plasticity and fast / slow synapse; and (2) applies a brain-inspired two-step consolidation strategy to learn a task sequence without forgetting in the fast weights while improve generalization without overfitting in the slow weights. Extensive results on various benchmarks show that our method achieves a better performance than joint training of all the tasks ever seen. The ability of few-shot generalization is also substantially improved from incoming tasks and examples.

Large language models display remarkable capabilities in logical and mathematical reasoning, allowing them to solve complex tasks. Interestingly, these abilities emerge in networks trained on the simple task of next-token prediction. In this work, we present a theoretical framework for studying auto-regressive next-token predictors. We demonstrate that even simple models such as linear next-token predictors, trained on Chain-of-Thought (CoT) data, can approximate any function efficiently computed by a Turing machine. We introduce a new complexity measure -- length complexity -- which measures the number of intermediate tokens in a CoT sequence required to approximate some target function, and analyze the interplay between length complexity and other notions of complexity. Finally, we show experimentally that simple next-token predictors, such as linear networks and shallow Multi-Layer Perceptrons (MLPs), display non-trivial performance on text generation and arithmetic tasks. Our results demonstrate that the power of language models can be attributed, to a great extent, to the auto-regressive next-token training scheme, and not necessarily to a particular choice of architecture.

Data arrives at our senses as a continuous stream, smoothly transforming from one instant to the next. These smooth transformations can be viewed as continuous symmetries of the environment that we inhabit, defining equivalence relations between stimuli over time. In machine learning, neural network architectures that respect symmetries of their data are called equivariant and have provable benefits in terms of generalization ability and sample efficiency. To date, however, equivariance has been considered only for static transformations and feed-forward networks, limiting its applicability to sequence models, such as recurrent neural networks (RNNs), and corresponding time-parameterized sequence transformations. In this work, we extend equivariant network theory to this regime of `flows' -- one-parameter Lie subgroups capturing natural transformations over time, such as visual motion. We begin by showing that standard RNNs are generally not flow equivariant: their hidden states fail to transform in a geometrically structured manner for moving stimuli. We then show how flow equivariance can be introduced, and demonstrate that these models significantly outperform their non-equivariant counterparts in terms of training speed, length generalization, and velocity generalization, on both next step prediction and sequence classification. We present this work as a first step towards building sequence models that respect the time-parameterized symmetries which govern the world around us.

Natural Language Generation (NLG) models are prone to generating repetitive utterances. In this work, we study the repetition problem for encoder-decoder models, using both recurrent neural network (RNN) and transformer architectures. To this end, we consider the chit-chat task, where the problem is more prominent than in other tasks that need encoder-decoder architectures. We first study the influence of model architectures. By using pre-attention and highway connections for RNNs, we manage to achieve lower repetition rates. However, this method does not generalize to other models such as transformers. We hypothesize that the deeper reason is that in the training corpora, there are hard tokens that are more difficult for a generative model to learn than others and, once learning has finished, hard tokens are still under-learned, so that repetitive generations are more likely to happen. Based on this hypothesis, we propose token loss dynamic reweighting (TLDR) that applies differentiable weights to individual token losses. By using higher weights for hard tokens and lower weights for easy tokens, NLG models are able to learn individual tokens at different paces. Experiments on chit-chat benchmark datasets show that TLDR is more effective in repetition reduction for both RNN and transformer architectures than baselines using different weighting functions.

Graph neural networks (GNNs) have been shown to be highly sensitive to the choice of aggregation function. While summing over a node's neighbours can approximate any permutation-invariant function over discrete inputs, Cohen-Karlik et al. [2020] proved there are set-aggregation problems for which summing cannot generalise to unbounded inputs, proposing recurrent neural networks regularised towards permutation-invariance as a more expressive aggregator. We show that these results carry over to the graph domain: GNNs equipped with recurrent aggregators are competitive with state-of-the-art permutation-invariant aggregators, on both synthetic benchmarks and real-world problems. However, despite the benefits of recurrent aggregators, their O(V) depth makes them both difficult to parallelise and harder to train on large graphs. Inspired by the observation that a well-behaved aggregator for a GNN is a commutative monoid over its latent space, we propose a framework for constructing learnable, commutative, associative binary operators. And with this, we construct an aggregator of O(log V) depth, yielding exponential improvements for both parallelism and dependency length while achieving performance competitive with recurrent aggregators. Based on our empirical observations, our proposed learnable commutative monoid (LCM) aggregator represents a favourable tradeoff between efficient and expressive aggregators.

Parameter generation has struggled to scale up for a long time, significantly limiting its range of applications. In this study, we introduce Recurrent diffusion for large-scale Parameter Generation, called RPG. We first divide the trained parameters into non-overlapping parts, after which a recurrent model is proposed to learn their relationships. The recurrent model's outputs, as conditions, are then fed into a diffusion model to generate the neural network parameters. Using only a single GPU, recurrent diffusion enables us to generate popular vision and language models such as ConvNeXt-L and LoRA parameters of LLaMA-7B. Meanwhile, across various architectures and tasks, the generated parameters consistently perform comparable results over trained networks. Notably, our approach also shows the potential to generate models for handling unseen tasks, which largely increases the practicality of parameter generation. Our code is available https://github.com/NUS-HPC-AI-Lab/Recurrent-Parameter-Generation{here}.

Standard artificial neural networks suffer from the well-known issue of catastrophic forgetting, making continual or lifelong learning difficult for machine learning. In recent years, numerous methods have been proposed for continual learning, but due to differences in evaluation protocols it is difficult to directly compare their performance. To enable more structured comparisons, we describe three continual learning scenarios based on whether at test time task identity is provided and--in case it is not--whether it must be inferred. Any sequence of well-defined tasks can be performed according to each scenario. Using the split and permuted MNIST task protocols, for each scenario we carry out an extensive comparison of recently proposed continual learning methods. We demonstrate substantial differences between the three scenarios in terms of difficulty and in terms of how efficient different methods are. In particular, when task identity must be inferred (i.e., class incremental learning), we find that regularization-based approaches (e.g., elastic weight consolidation) fail and that replaying representations of previous experiences seems required for solving this scenario.

Despite the remarkable success achieved by neural networks, particularly those represented by MLP and Transformer, we reveal that they exhibit potential flaws in the modeling and reasoning of periodicity, i.e., they tend to memorize the periodic data rather than genuinely understanding the underlying principles of periodicity. However, periodicity is a crucial trait in various forms of reasoning and generalization, underpinning predictability across natural and engineered systems through recurring patterns in observations. In this paper, we propose FAN, a novel network architecture based on Fourier Analysis, which empowers the ability to efficiently model and reason about periodic phenomena. By introducing Fourier Series, the periodicity is naturally integrated into the structure and computational processes of the neural network, thus achieving a more accurate expression and prediction of periodic patterns. As a promising substitute to multi-layer perceptron (MLP), FAN can seamlessly replace MLP in various models with fewer parameters and FLOPs. Through extensive experiments, we demonstrate the effectiveness of FAN in modeling and reasoning about periodic functions, and the superiority and generalizability of FAN across a range of real-world tasks, including symbolic formula representation, time series forecasting, and language modeling.

In this paper, we tackle the important yet under-investigated problem of making long-horizon prediction of event sequences. Existing state-of-the-art models do not perform well at this task due to their autoregressive structure. We propose HYPRO, a hybridly normalized probabilistic model that naturally fits this task: its first part is an autoregressive base model that learns to propose predictions; its second part is an energy function that learns to reweight the proposals such that more realistic predictions end up with higher probabilities. We also propose efficient training and inference algorithms for this model. Experiments on multiple real-world datasets demonstrate that our proposed HYPRO model can significantly outperform previous models at making long-horizon predictions of future events. We also conduct a range of ablation studies to investigate the effectiveness of each component of our proposed methods.

Designing efficient and effective architectural backbones has been in the core of research efforts to enhance the capability of foundation models. Inspired by the human cognitive phenomenon of attentional bias-the natural tendency to prioritize certain events or stimuli-we reconceptualize neural architectures, including Transformers, Titans, and modern linear recurrent neural networks as associative memory modules that learn a mapping of keys and values using an internal objective, referred to as attentional bias. Surprisingly, we observed that most existing sequence models leverage either (1) dot-product similarity, or (2) L2 regression objectives as their attentional bias. Going beyond these objectives, we present a set of alternative attentional bias configurations along with their effective approximations to stabilize their training procedure. We then reinterpret forgetting mechanisms in modern deep learning architectures as a form of retention regularization, providing a novel set of forget gates for sequence models. Building upon these insights, we present Miras, a general framework to design deep learning architectures based on four choices of: (i) associative memory architecture, (ii) attentional bias objective, (iii) retention gate, and (iv) memory learning algorithm. We present three novel sequence models-Moneta, Yaad, and Memora-that go beyond the power of existing linear RNNs while maintaining a fast parallelizable training process. Our experiments show different design choices in Miras yield models with varying strengths. For example, certain instances of Miras achieve exceptional performance in special tasks such as language modeling, commonsense reasoning, and recall intensive tasks, even outperforming Transformers and other modern linear recurrent models.

Recent work on large language models relies on the intuition that most natural language processing tasks can be described via natural language instructions. Language models trained on these instructions show strong zero-shot performance on several standard datasets. However, these models even though impressive still perform poorly on a wide range of tasks outside of their respective training and evaluation sets. To address this limitation, we argue that a model should be able to keep extending its knowledge and abilities, without forgetting previous skills. In spite of the limited success of Continual Learning we show that Language Models can be continual learners. We empirically investigate the reason for this success and conclude that Continual Learning emerges from self-supervision pre-training. Our resulting model Continual-T0 (CT0) is able to learn diverse new tasks, while still maintaining good performance on previous tasks, spanning remarkably through 70 datasets in total. Finally, we show that CT0 is able to combine instructions in ways it was never trained for, demonstrating some compositionality.

Instruction tuning is vital for aligning large language models (LLMs) with human intent, but current methods typically rely on costly human-annotated seed data or powerful external teacher models. While instruction back-translation techniques reduce this dependency, they remain fundamentally tethered to an initial seed set, which limits full automation, introduces biases, and can lead to inefficient use of unlabeled corpora. In this paper, we propose Cycle-Instruct, a novel framework that achieves fully seed-free instruction tuning. Inspired by cycle consistency, Cycle-Instruct employs a dual self-training loop where two models-an answer generator and a question generator-are bootstrapped solely from raw, unlabeled text. These models mutually supervise each other by reconstructing original text segments from their counterpart's generated pseudo-labels, effectively learning from the intrinsic structure of the data without any human-provided seeds. We demonstrate Cycle-Instruct's efficacy across four diverse data tracks, including general instruction-following, domain-specific tasks, dialogue logs, and plain text. Our extensive experiments show that Cycle-Instruct not only outperforms seed-driven back-translation baselines but also achieves performance comparable to strongly supervised methods.

Sequential dynamics are a key feature of many modern recommender systems, which seek to capture the `context' of users' activities on the basis of actions they have performed recently. To capture such patterns, two approaches have proliferated: Markov Chains (MCs) and Recurrent Neural Networks (RNNs). Markov Chains assume that a user's next action can be predicted on the basis of just their last (or last few) actions, while RNNs in principle allow for longer-term semantics to be uncovered. Generally speaking, MC-based methods perform best in extremely sparse datasets, where model parsimony is critical, while RNNs perform better in denser datasets where higher model complexity is affordable. The goal of our work is to balance these two goals, by proposing a self-attention based sequential model (SASRec) that allows us to capture long-term semantics (like an RNN), but, using an attention mechanism, makes its predictions based on relatively few actions (like an MC). At each time step, SASRec seeks to identify which items are `relevant' from a user's action history, and use them to predict the next item. Extensive empirical studies show that our method outperforms various state-of-the-art sequential models (including MC/CNN/RNN-based approaches) on both sparse and dense datasets. Moreover, the model is an order of magnitude more efficient than comparable CNN/RNN-based models. Visualizations on attention weights also show how our model adaptively handles datasets with various density, and uncovers meaningful patterns in activity sequences.

Large language models (LLMs) suffer from catastrophic forgetting during continual learning. Conventional rehearsal-based methods rely on previous training data to retain the model's ability, which may not be feasible in real-world applications. When conducting continual learning based on a publicly-released LLM checkpoint, the availability of the original training data may be non-existent. To address this challenge, we propose a framework called Self-Synthesized Rehearsal (SSR) that uses the LLM to generate synthetic instances for rehearsal. Concretely, we first employ the base LLM for in-context learning to generate synthetic instances. Subsequently, we utilize the latest LLM to refine the instance outputs based on the synthetic inputs, preserving its acquired ability. Finally, we select diverse high-quality synthetic instances for rehearsal in future stages. Experimental results demonstrate that SSR achieves superior or comparable performance compared to conventional rehearsal-based approaches while being more data-efficient. Besides, SSR effectively preserves the generalization capabilities of LLMs in general domains.

Continual learning aims to enable a single model to learn a sequence of tasks without catastrophic forgetting. Top-performing methods usually require a rehearsal buffer to store past pristine examples for experience replay, which, however, limits their practical value due to privacy and memory constraints. In this work, we present a simple yet effective framework, DualPrompt, which learns a tiny set of parameters, called prompts, to properly instruct a pre-trained model to learn tasks arriving sequentially without buffering past examples. DualPrompt presents a novel approach to attach complementary prompts to the pre-trained backbone, and then formulates the objective as learning task-invariant and task-specific "instructions". With extensive experimental validation, DualPrompt consistently sets state-of-the-art performance under the challenging class-incremental setting. In particular, DualPrompt outperforms recent advanced continual learning methods with relatively large buffer sizes. We also introduce a more challenging benchmark, Split ImageNet-R, to help generalize rehearsal-free continual learning research. Source code is available at https://github.com/google-research/l2p.

Language models with recurrent depth, also referred to as universal or looped when considering transformers, are defined by the capacity to increase their computation through the repetition of layers. Recent efforts in pretraining have demonstrated that these architectures can scale to modern language modeling tasks while exhibiting advantages in reasoning tasks. In this work, we examine the relationship between recurrent-depth models and diffusion language models. Building on their similarities, we develop a new diffusion forcing sampler for these models to accelerate generation. The sampler advances by decoding new tokens at every forward pass of the model, while the latent states of these tokens can be further refined in parallel through recurrence. Theoretically, generation with our sampler is strictly more expressive than the baseline autoregressive generation using the same time budget on modern hardware. Moreover, this sampler, based on principles from diffusion literature, can be directly applied to existing 3.5B recurrent-depth transformers without any tuning, leading to up to a 5x speedup. Consequently, our findings not only provide an efficient mechanism for parallelizing the extra computation in recurrent-depth models at inference, but also suggest that such models can be naturally viewed as strong continuous, though causal, diffusion language models.

In this paper, we propose a novel neural network model called RNN Encoder-Decoder that consists of two recurrent neural networks (RNN). One RNN encodes a sequence of symbols into a fixed-length vector representation, and the other decodes the representation into another sequence of symbols. The encoder and decoder of the proposed model are jointly trained to maximize the conditional probability of a target sequence given a source sequence. The performance of a statistical machine translation system is empirically found to improve by using the conditional probabilities of phrase pairs computed by the RNN Encoder-Decoder as an additional feature in the existing log-linear model. Qualitatively, we show that the proposed model learns a semantically and syntactically meaningful representation of linguistic phrases.

Nearly all real world tasks are inherently partially observable, necessitating the use of memory in Reinforcement Learning (RL). Most model-free approaches summarize the trajectory into a latent Markov state using memory models borrowed from Supervised Learning (SL), even though RL tends to exhibit different training and efficiency characteristics. Addressing this discrepancy, we introduce Fast and Forgetful Memory, an algorithm-agnostic memory model designed specifically for RL. Our approach constrains the model search space via strong structural priors inspired by computational psychology. It is a drop-in replacement for recurrent neural networks (RNNs) in recurrent RL algorithms, achieving greater reward than RNNs across various recurrent benchmarks and algorithms without changing any hyperparameters. Moreover, Fast and Forgetful Memory exhibits training speeds two orders of magnitude faster than RNNs, attributed to its logarithmic time and linear space complexity. Our implementation is available at https://github.com/proroklab/ffm.

The continual learning capability of large language models (LLMs) is crucial for advancing artificial general intelligence. However, continual fine-tuning LLMs across various domains often suffers from catastrophic forgetting, characterized by: 1) significant forgetting of their general capabilities, and 2) sharp performance declines in previously learned tasks. To simultaneously address both issues in a simple yet stable manner, we propose General Sample Replay (GeRe), a framework that use usual pretraining texts for efficient anti-forgetting. Beyond revisiting the most prevalent replay-based practices under GeRe, we further leverage neural states to introduce a enhanced activation states constrained optimization method using threshold-based margin (TM) loss, which maintains activation state consistency during replay learning. We are the first to validate that a small, fixed set of pre-collected general replay samples is sufficient to resolve both concerns--retaining general capabilities while promoting overall performance across sequential tasks. Indeed, the former can inherently facilitate the latter. Through controlled experiments, we systematically compare TM with different replay strategies under the GeRe framework, including vanilla label fitting, logit imitation via KL divergence and feature imitation via L1/L2 losses. Results demonstrate that TM consistently improves performance and exhibits better robustness. Our work paves the way for efficient replay of LLMs for the future. Our code and data are available at https://github.com/Qznan/GeRe.

We present methodology for using dynamic evaluation to improve neural sequence models. Models are adapted to recent history via a gradient descent based mechanism, causing them to assign higher probabilities to re-occurring sequential patterns. Dynamic evaluation outperforms existing adaptation approaches in our comparisons. Dynamic evaluation improves the state-of-the-art word-level perplexities on the Penn Treebank and WikiText-2 datasets to 51.1 and 44.3 respectively, and the state-of-the-art character-level cross-entropies on the text8 and Hutter Prize datasets to 1.19 bits/char and 1.08 bits/char respectively.

In this paper we propose a novel model for unconditional audio generation based on generating one audio sample at a time. We show that our model, which profits from combining memory-less modules, namely autoregressive multilayer perceptrons, and stateful recurrent neural networks in a hierarchical structure is able to capture underlying sources of variations in the temporal sequences over very long time spans, on three datasets of different nature. Human evaluation on the generated samples indicate that our model is preferred over competing models. We also show how each component of the model contributes to the exhibited performance.

We describe a new class of learning models called memory networks. Memory networks reason with inference components combined with a long-term memory component; they learn how to use these jointly. The long-term memory can be read and written to, with the goal of using it for prediction. We investigate these models in the context of question answering (QA) where the long-term memory effectively acts as a (dynamic) knowledge base, and the output is a textual response. We evaluate them on a large-scale QA task, and a smaller, but more complex, toy task generated from a simulated world. In the latter, we show the reasoning power of such models by chaining multiple supporting sentences to answer questions that require understanding the intension of verbs.

We present an approach for estimating the period with which an action is repeated in a video. The crux of the approach lies in constraining the period prediction module to use temporal self-similarity as an intermediate representation bottleneck that allows generalization to unseen repetitions in videos in the wild. We train this model, called Repnet, with a synthetic dataset that is generated from a large unlabeled video collection by sampling short clips of varying lengths and repeating them with different periods and counts. This combination of synthetic data and a powerful yet constrained model, allows us to predict periods in a class-agnostic fashion. Our model substantially exceeds the state of the art performance on existing periodicity (PERTUBE) and repetition counting (QUVA) benchmarks. We also collect a new challenging dataset called Countix (~90 times larger than existing datasets) which captures the challenges of repetition counting in real-world videos. Project webpage: https://sites.google.com/view/repnet .

This paper shows how Long Short-term Memory recurrent neural networks can be used to generate complex sequences with long-range structure, simply by predicting one data point at a time. The approach is demonstrated for text (where the data are discrete) and online handwriting (where the data are real-valued). It is then extended to handwriting synthesis by allowing the network to condition its predictions on a text sequence. The resulting system is able to generate highly realistic cursive handwriting in a wide variety of styles.

In Continual learning (CL) balancing effective adaptation while combating catastrophic forgetting is a central challenge. Many of the recent best-performing methods utilize various forms of prior task data, e.g. a replay buffer, to tackle the catastrophic forgetting problem. Having access to previous task data can be restrictive in many real-world scenarios, for example when task data is sensitive or proprietary. To overcome the necessity of using previous tasks' data, in this work, we start with strong representation learning methods that have been shown to be less prone to forgetting. We propose a holistic approach to jointly learn the representation and class prototypes while maintaining the relevance of old class prototypes and their embedded similarities. Specifically, samples are mapped to an embedding space where the representations are learned using a supervised contrastive loss. Class prototypes are evolved continually in the same latent space, enabling learning and prediction at any point. To continually adapt the prototypes without keeping any prior task data, we propose a novel distillation loss that constrains class prototypes to maintain relative similarities as compared to new task data. This method yields state-of-the-art performance in the task-incremental setting, outperforming methods relying on large amounts of data, and provides strong performance in the class-incremental setting without using any stored data points.

Constructing states from sequences of observations is an important component of reinforcement learning agents. One solution for state construction is to use recurrent neural networks. Back-propagation through time (BPTT), and real-time recurrent learning (RTRL) are two popular gradient-based methods for recurrent learning. BPTT requires complete trajectories of observations before it can compute the gradients and is unsuitable for online updates. RTRL can do online updates but scales poorly to large networks. In this paper, we propose two constraints that make RTRL scalable. We show that by either decomposing the network into independent modules or learning the network in stages, we can make RTRL scale linearly with the number of parameters. Unlike prior scalable gradient estimation algorithms, such as UORO and Truncated-BPTT, our algorithms do not add noise or bias to the gradient estimate. Instead, they trade off the functional capacity of the network for computationally efficient learning. We demonstrate the effectiveness of our approach over Truncated-BPTT on a prediction benchmark inspired by animal learning and by doing policy evaluation of pre-trained policies for Atari 2600 games.

This paper explores the potential of recurrent neural networks (RNNs) and other subquadratic architectures as competitive alternatives to transformer-based models in low-resource language modeling scenarios. We utilize HGRN2 (Qin et al., 2024), a recently proposed RNN-based architecture, and comparatively evaluate its effectiveness against transformer-based baselines and other subquadratic architectures (LSTM, xLSTM, Mamba). Our experimental results show that BABYHGRN, our HGRN2 language model, outperforms transformer-based models in both the 10M and 100M word tracks of the challenge, as measured by their performance on the BLiMP, EWoK, GLUE and BEAR benchmarks. Further, we show the positive impact of knowledge distillation. Our findings challenge the prevailing focus on transformer architectures and indicate the viability of RNN-based models, particularly in resource-constrained environments.

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

This paper introduces Graph Convolutional Recurrent Network (GCRN), a deep learning model able to predict structured sequences of data. Precisely, GCRN is a generalization of classical recurrent neural networks (RNN) to data structured by an arbitrary graph. Such structured sequences can represent series of frames in videos, spatio-temporal measurements on a network of sensors, or random walks on a vocabulary graph for natural language modeling. The proposed model combines convolutional neural networks (CNN) on graphs to identify spatial structures and RNN to find dynamic patterns. We study two possible architectures of GCRN, and apply the models to two practical problems: predicting moving MNIST data, and modeling natural language with the Penn Treebank dataset. Experiments show that exploiting simultaneously graph spatial and dynamic information about data can improve both precision and learning speed.

State-of-the-art solutions in the areas of "Language Modelling & Generating Text", "Speech Recognition", "Generating Image Descriptions" or "Video Tagging" have been using Recurrent Neural Networks as the foundation for their approaches. Understanding the underlying concepts is therefore of tremendous importance if we want to keep up with recent or upcoming publications in those areas. In this work we give a short overview over some of the most important concepts in the realm of Recurrent Neural Networks which enables readers to easily understand the fundamentals such as but not limited to "Backpropagation through Time" or "Long Short-Term Memory Units" as well as some of the more recent advances like the "Attention Mechanism" or "Pointer Networks". We also give recommendations for further reading regarding more complex topics where it is necessary.

Continual learning aims to equip models with the ability to retain previously learned knowledge like a human. Recent work incorporating Parameter-Efficient Fine-Tuning has revitalized the field by introducing lightweight extension modules. However, existing methods usually overlook the issue of information leakage caused by the fact that the experiment data have been used in pre-trained models. Once these duplicate data are removed in the pre-training phase, their performance can be severely affected. In this paper, we propose a new LoRA-based rehearsal-free method named DESIRE. Our method avoids imposing additional constraints during training to mitigate catastrophic forgetting, thereby maximizing the learning of new classes. To integrate knowledge from old and new tasks, we propose two efficient post-processing modules. On the one hand, we retain only two sets of LoRA parameters for merging and propose dynamic representation consolidation to calibrate the merged feature representation. On the other hand, we propose decision boundary refinement to address classifier bias when training solely on new class data. Extensive experiments demonstrate that our method achieves state-of-the-art performance on multiple datasets and strikes an effective balance between stability and plasticity. Our code will be publicly available.

In Recurrent Neural Networks (RNNs), encoding information in a suboptimal or erroneous way can impact the quality of representations based on later elements in the sequence and subsequently lead to wrong predictions and a worse model performance. In humans, challenging cases like garden path sentences (an instance of this being the infamous "The horse raced past the barn fell") can lead their language understanding astray. However, they are still able to correct their representation accordingly and recover when new information is encountered. Inspired by this, I propose an augmentation to standard RNNs in form of a gradient-based correction mechanism: This way I hope to enable such models to dynamically adapt their inner representation of a sentence, adding a way to correct deviations as soon as they occur. This could therefore lead to more robust models using more flexible representations, even during inference time. I conduct different experiments in the context of language modeling, where the impact of using such a mechanism is examined in detail. To this end, I look at modifications based on different kinds of time-dependent error signals and how they influence the model performance. Furthermore, this work contains a study of the model's confidence in its predictions during training and for challenging test samples and the effect of the manipulation thereof. Lastly, I also study the difference in behavior of these novel models compared to a standard LSTM baseline and investigate error cases in detail to identify points of future research. I show that while the proposed approach comes with promising theoretical guarantees and an appealing intuition, it is only able to produce minor improvements over the baseline due to challenges in its practical application and the efficacy of the tested model variants.

We present Probabilistic Structure Integration (PSI), a system for learning richly controllable and flexibly promptable world models from data. PSI consists of a three-step cycle. The first step, Probabilistic prediction, involves building a probabilistic graphical model Psi of the data, in the form of a random-access autoregressive sequence model. Psi supports a complete set of learned conditional distributions describing the dependence of any variables in the data on any other set of variables. In step 2, Structure extraction, we show how to extract underlying low-dimensional properties in the data, corresponding to a diverse set of meaningful "intermediate structures", in a zero-shot fashion via causal inference on Psi. Step 3, Integration, completes the cycle by converting these structures into new token types that are then continually mixed back into the training diet as conditioning signals and prediction targets. Each such cycle augments the capabilities of Psi, both allowing it to model the underlying data better, and creating new control handles -- akin to an LLM-like universal prompting language. We train an instance of Psi on 1.4 trillion tokens of internet video data; we use it to perform a variety of useful video prediction and understanding inferences; we extract state-of-the-art optical flow, self-supervised depth and object segmentation; and we use these structures to support a full cycle of predictive improvements.

In this paper, we present a novel approach for incorporating external knowledge in Recurrent Neural Networks (RNNs). We propose the integration of lexicon features into the self-attention mechanism of RNN-based architectures. This form of conditioning on the attention distribution, enforces the contribution of the most salient words for the task at hand. We introduce three methods, namely attentional concatenation, feature-based gating and affine transformation. Experiments on six benchmark datasets show the effectiveness of our methods. Attentional feature-based gating yields consistent performance improvement across tasks. Our approach is implemented as a simple add-on module for RNN-based models with minimal computational overhead and can be adapted to any deep neural architecture.

In this report we review memory-based meta-learning as a tool for building sample-efficient strategies that learn from past experience to adapt to any task within a target class. Our goal is to equip the reader with the conceptual foundations of this tool for building new, scalable agents that operate on broad domains. To do so, we present basic algorithmic templates for building near-optimal predictors and reinforcement learners which behave as if they had a probabilistic model that allowed them to efficiently exploit task structure. Furthermore, we recast memory-based meta-learning within a Bayesian framework, showing that the meta-learned strategies are near-optimal because they amortize Bayes-filtered data, where the adaptation is implemented in the memory dynamics as a state-machine of sufficient statistics. Essentially, memory-based meta-learning translates the hard problem of probabilistic sequential inference into a regression problem.

This paper investigates the ability of transformer-based models to learn structural recursion from examples. Recursion is a universal concept in both natural and formal languages. Structural recursion is central to the programming language and formal mathematics tasks where symbolic tools currently excel beyond neural models, such as inferring semantic relations between datatypes and emulating program behavior. We introduce a general framework that nicely connects the abstract concepts of structural recursion in the programming language domain to concrete sequence modeling problems and learned models' behavior. The framework includes a representation that captures the general syntax of structural recursion, coupled with two different frameworks for understanding their semantics -- one that is more natural from a programming languages perspective and one that helps bridge that perspective with a mechanistic understanding of the underlying transformer architecture. With our framework as a powerful conceptual tool, we identify different issues under various set-ups. The models trained to emulate recursive computations cannot fully capture the recursion yet instead fit short-cut algorithms and thus cannot solve certain edge cases that are under-represented in the training distribution. In addition, it is difficult for state-of-the-art large language models (LLMs) to mine recursive rules from in-context demonstrations. Meanwhile, these LLMs fail in interesting ways when emulating reduction (step-wise computation) of the recursive function.

In real-world environments, continual learning is essential for machine learning models, as they need to acquire new knowledge incrementally without forgetting what they have already learned. While pretrained language models have shown impressive capabilities on various static tasks, applying them to continual learning poses significant challenges, including avoiding catastrophic forgetting, facilitating knowledge transfer, and maintaining parameter efficiency. In this paper, we introduce MoCL-P, a novel lightweight continual learning method that addresses these challenges simultaneously. Unlike traditional approaches that continuously expand parameters for newly arriving tasks, MoCL-P integrates task representation-guided module composition with adaptive pruning, effectively balancing knowledge integration and computational overhead. Our evaluation across three continual learning benchmarks with up to 176 tasks shows that MoCL-P achieves state-of-the-art performance and improves parameter efficiency by up to three times, demonstrating its potential for practical applications where resource requirements are constrained.

Transformer models have established new benchmarks in natural language processing; however, their increasing depth results in substantial growth in parameter counts. While existing recurrent transformer methods address this issue by reprocessing layers multiple times, they often apply recurrence indiscriminately across entire blocks of layers. In this work, we investigate Intra-Layer Recurrence (ILR), a more targeted approach that applies recurrence selectively to individual layers within a single forward pass. Our experiments show that allocating more iterations to earlier layers yields optimal results. These findings suggest that ILR offers a promising direction for optimizing recurrent structures in transformer architectures.

Sentence-level representations are necessary for various NLP tasks. Recurrent neural networks have proven to be very effective in learning distributed representations and can be trained efficiently on natural language inference tasks. We build on top of one such model and propose a hierarchy of BiLSTM and max pooling layers that implements an iterative refinement strategy and yields state of the art results on the SciTail dataset as well as strong results for SNLI and MultiNLI. We can show that the sentence embeddings learned in this way can be utilized in a wide variety of transfer learning tasks, outperforming InferSent on 7 out of 10 and SkipThought on 8 out of 9 SentEval sentence embedding evaluation tasks. Furthermore, our model beats the InferSent model in 8 out of 10 recently published SentEval probing tasks designed to evaluate sentence embeddings' ability to capture some of the important linguistic properties of sentences.

This work explores the in-context learning capabilities of State Space Models (SSMs) and presents, to the best of our knowledge, the first theoretical explanation of a possible underlying mechanism. We introduce a novel weight construction for SSMs, enabling them to predict the next state of any dynamical system after observing previous states without parameter fine-tuning. This is accomplished by extending the HiPPO framework to demonstrate that continuous SSMs can approximate the derivative of any input signal. Specifically, we find an explicit weight construction for continuous SSMs and provide an asymptotic error bound on the derivative approximation. The discretization of this continuous SSM subsequently yields a discrete SSM that predicts the next state. Finally, we demonstrate the effectiveness of our parameterization empirically. This work should be an initial step toward understanding how sequence models based on SSMs learn in context.

Several variants of the Long Short-Term Memory (LSTM) architecture for recurrent neural networks have been proposed since its inception in 1995. In recent years, these networks have become the state-of-the-art models for a variety of machine learning problems. This has led to a renewed interest in understanding the role and utility of various computational components of typical LSTM variants. In this paper, we present the first large-scale analysis of eight LSTM variants on three representative tasks: speech recognition, handwriting recognition, and polyphonic music modeling. The hyperparameters of all LSTM variants for each task were optimized separately using random search, and their importance was assessed using the powerful fANOVA framework. In total, we summarize the results of 5400 experimental runs (approx 15 years of CPU time), which makes our study the largest of its kind on LSTM networks. Our results show that none of the variants can improve upon the standard LSTM architecture significantly, and demonstrate the forget gate and the output activation function to be its most critical components. We further observe that the studied hyperparameters are virtually independent and derive guidelines for their efficient adjustment.

We introduce Sundial, a family of native, flexible, and scalable time series foundation models. To predict the next-patch's distribution, we propose a TimeFlow Loss based on flow-matching, which facilitates native pre-training of Transformers on time series without discrete tokenization. Conditioned on arbitrary-length time series, our model is pre-trained without specifying any prior distribution and can generate multiple probable predictions, achieving flexibility in representation learning beyond using parametric densities. Towards time series foundation models, we leverage minimal but crucial adaptations of Transformers and curate TimeBench with 1 trillion time points, comprising mostly real-world datasets and synthetic data. By mitigating mode collapse through TimeFlow Loss, we pre-train a family of Sundial models on TimeBench, which exhibit unprecedented model capacity and generalization performance on zero-shot forecasting. In addition to presenting good scaling behavior, Sundial achieves new state-of-the-art on both point forecasting and probabilistic forecasting benchmarks. We believe that Sundial's pioneering generative paradigm will facilitate a wide variety of forecasting scenarios.

In this paper, we propose a method to partially mimic natural intelligence for the problem of lifelong learning representations that are compatible. We take the perspective of a learning agent that is interested in recognizing object instances in an open dynamic universe in a way in which any update to its internal feature representation does not render the features in the gallery unusable for visual search. We refer to this learning problem as Compatible Lifelong Learning Representations (CL2R) as it considers compatible representation learning within the lifelong learning paradigm. We identify stationarity as the property that the feature representation is required to hold to achieve compatibility and propose a novel training procedure that encourages local and global stationarity on the learned representation. Due to stationarity, the statistical properties of the learned features do not change over time, making them interoperable with previously learned features. Extensive experiments on standard benchmark datasets show that our CL2R training procedure outperforms alternative baselines and state-of-the-art methods. We also provide novel metrics to specifically evaluate compatible representation learning under catastrophic forgetting in various sequential learning tasks. Code at https://github.com/NiccoBiondi/CompatibleLifelongRepresentation.

Recurrent connectivity in the visual cortex is believed to aid object recognition for challenging conditions such as occlusion. Here we investigate if and how artificial neural networks also benefit from recurrence. We compare architectures composed of bottom-up, lateral and top-down connections and evaluate their performance using two novel stereoscopic occluded object datasets. We find that classification accuracy is significantly higher for recurrent models when compared to feedforward models of matched parametric complexity. Additionally we show that for challenging stimuli, the recurrent feedback is able to correctly revise the initial feedforward guess.

No free lunch theorems for supervised learning state that no learner can solve all problems or that all learners achieve exactly the same accuracy on average over a uniform distribution on learning problems. Accordingly, these theorems are often referenced in support of the notion that individual problems require specially tailored inductive biases. While virtually all uniformly sampled datasets have high complexity, real-world problems disproportionately generate low-complexity data, and we argue that neural network models share this same preference, formalized using Kolmogorov complexity. Notably, we show that architectures designed for a particular domain, such as computer vision, can compress datasets on a variety of seemingly unrelated domains. Our experiments show that pre-trained and even randomly initialized language models prefer to generate low-complexity sequences. Whereas no free lunch theorems seemingly indicate that individual problems require specialized learners, we explain how tasks that often require human intervention such as picking an appropriately sized model when labeled data is scarce or plentiful can be automated into a single learning algorithm. These observations justify the trend in deep learning of unifying seemingly disparate problems with an increasingly small set of machine learning models.

The chain-structured long short-term memory (LSTM) has showed to be effective in a wide range of problems such as speech recognition and machine translation. In this paper, we propose to extend it to tree structures, in which a memory cell can reflect the history memories of multiple child cells or multiple descendant cells in a recursive process. We call the model S-LSTM, which provides a principled way of considering long-distance interaction over hierarchies, e.g., language or image parse structures. We leverage the models for semantic composition to understand the meaning of text, a fundamental problem in natural language understanding, and show that it outperforms a state-of-the-art recursive model by replacing its composition layers with the S-LSTM memory blocks. We also show that utilizing the given structures is helpful in achieving a performance better than that without considering the structures.

Koopman representations aim to learn features of nonlinear dynamical systems (NLDS) which lead to linear dynamics in the latent space. Theoretically, such features can be used to simplify many problems in modeling and control of NLDS. In this work we study autoencoder formulations of this problem, and different ways they can be used to model dynamics, specifically for future state prediction over long horizons. We discover several limitations of predicting future states in the latent space and propose an inference-time mechanism, which we refer to as Periodic Reencoding, for faithfully capturing long term dynamics. We justify this method both analytically and empirically via experiments in low and high dimensional NLDS.

Hierarchically gated linear RNN (HGRN,Qin et al. 2023) has demonstrated competitive training speed and performance in language modeling, while offering efficient inference. However, the recurrent state size of HGRN remains relatively small, which limits its expressiveness.To address this issue, inspired by linear attention, we introduce a simple outer-product-based state expansion mechanism so that the recurrent state size can be significantly enlarged without introducing any additional parameters. The linear attention form also allows for hardware-efficient training.Our extensive experiments verify the advantage of HGRN2 over HGRN1 in language modeling, image classification, and Long Range Arena.Our largest 3B HGRN2 model slightly outperforms Mamba and LLaMa Architecture Transformer for language modeling in a controlled experiment setting; and performs competitively with many open-source 3B models in downstream evaluation while using much fewer total training tokens.

The role of hidden units in recurrent neural networks is typically seen as modeling memory, with research focusing on enhancing information retention through gating mechanisms. A less explored perspective views hidden units as active participants in the computation performed by the network, rather than passive memory stores. In this work, we revisit bi-linear operations, which involve multiplicative interactions between hidden units and input embeddings. We demonstrate theoretically and empirically that they constitute a natural inductive bias for representing the evolution of hidden states in state tracking tasks. These are the simplest type of task that require hidden units to actively contribute to the behavior of the network. We also show that bi-linear state updates form a natural hierarchy corresponding to state tracking tasks of increasing complexity, with popular linear recurrent networks such as Mamba residing at the lowest-complexity center of that hierarchy.

In this paper, we propose a recurrent framework for Joint Unsupervised LEarning (JULE) of deep representations and image clusters. In our framework, successive operations in a clustering algorithm are expressed as steps in a recurrent process, stacked on top of representations output by a Convolutional Neural Network (CNN). During training, image clusters and representations are updated jointly: image clustering is conducted in the forward pass, while representation learning in the backward pass. Our key idea behind this framework is that good representations are beneficial to image clustering and clustering results provide supervisory signals to representation learning. By integrating two processes into a single model with a unified weighted triplet loss and optimizing it end-to-end, we can obtain not only more powerful representations, but also more precise image clusters. Extensive experiments show that our method outperforms the state-of-the-art on image clustering across a variety of image datasets. Moreover, the learned representations generalize well when transferred to other tasks.

Convolutional neural networks show remarkable results in classification but struggle with learning new things on the fly. We present a novel rehearsal-free approach, where a deep neural network is continually learning new unseen object categories without saving any data of prior sequences. Our approach is called RECALL, as the network recalls categories by calculating logits for old categories before training new ones. These are then used during training to avoid changing the old categories. For each new sequence, a new head is added to accommodate the new categories. To mitigate forgetting, we present a regularization strategy where we replace the classification with a regression. Moreover, for the known categories, we propose a Mahalanobis loss that includes the variances to account for the changing densities between known and unknown categories. Finally, we present a novel dataset for continual learning, especially suited for object recognition on a mobile robot (HOWS-CL-25), including 150,795 synthetic images of 25 household object categories. Our approach RECALL outperforms the current state of the art on CORe50 and iCIFAR-100 and reaches the best performance on HOWS-CL-25.

A recent trend in LLMs is developing recurrent sub-quadratic models that improve long-context processing efficiency. We investigate leading large long-context models, focusing on how their fixed-size recurrent memory affects their performance. Our experiments reveal that, even when these models are trained for extended contexts, their use of long contexts remains underutilized. Specifically, we demonstrate that a chunk-based inference procedure, which identifies and processes only the most relevant portion of the input can mitigate recurrent memory failures and be effective for many long-context tasks: On LongBench, our method improves the overall performance of Falcon3-Mamba-Inst-7B by 14%, Falcon-Mamba-Inst-7B by 28%, RecurrentGemma-IT-9B by 50%, and RWKV6-Finch-7B by 51%. Surprisingly, this simple approach also leads to state-of-the-art results in the challenging LongBench v2 benchmark, showing competitive performance with equivalent size Transformers. Furthermore, our findings raise questions about whether recurrent models genuinely exploit long-range dependencies, as our single-chunk strategy delivers stronger performance - even in tasks that presumably require cross-context relations.

Most of the dominant approaches to continual learning are based on either memory replay, parameter isolation, or regularization techniques that require task boundaries to calculate task statistics. We propose a static architecture-based method that doesn't use any of these. We show that we can improve the continual learning performance by replacing the final layer of our networks with our pairwise interaction layer. The pairwise interaction layer uses sparse representations from a Winner-take-all style activation function to find the relevant correlations in the hidden layer representations. The networks using this architecture show competitive performance in MNIST and FashionMNIST-based continual image classification experiments. We demonstrate this in an online streaming continual learning setup where the learning system cannot access task labels or boundaries.

Continual learning and few-shot learning are important frontiers in progress towards broader Machine Learning (ML) capabilities. There is a growing body of work in both, but few works combining the two. One exception is the Continual few-shot Learning (CFSL) framework of Antoniou et al. arXiv:2004.11967. In this study, we extend CFSL in two ways that capture a broader range of challenges, important for intelligent agent behaviour in real-world conditions. First, we modify CFSL to make it more comparable to standard continual learning experiments, where usually a much larger number of classes are presented. Second, we introduce an 'instance test' which requires recognition of specific instances of classes -- a capability of animal cognition that is usually neglected in ML. For an initial exploration of ML model performance under these conditions, we selected representative baseline models from the original CFSL work and added a model variant with replay. As expected, learning more classes is more difficult than the original CFSL experiments, and interestingly, the way in which image instances and classes are presented affects classification performance. Surprisingly, accuracy in the baseline instance test is comparable to other classification tasks, but poor given significant occlusion and noise. The use of replay for consolidation improves performance substantially for both types of tasks, but particularly the instance test.

Spatio-temporal predictive learning is a learning paradigm that enables models to learn spatial and temporal patterns by predicting future frames from given past frames in an unsupervised manner. Despite remarkable progress in recent years, a lack of systematic understanding persists due to the diverse settings, complex implementation, and difficult reproducibility. Without standardization, comparisons can be unfair and insights inconclusive. To address this dilemma, we propose OpenSTL, a comprehensive benchmark for spatio-temporal predictive learning that categorizes prevalent approaches into recurrent-based and recurrent-free models. OpenSTL provides a modular and extensible framework implementing various state-of-the-art methods. We conduct standard evaluations on datasets across various domains, including synthetic moving object trajectory, human motion, driving scenes, traffic flow and weather forecasting. Based on our observations, we provide a detailed analysis of how model architecture and dataset properties affect spatio-temporal predictive learning performance. Surprisingly, we find that recurrent-free models achieve a good balance between efficiency and performance than recurrent models. Thus, we further extend the common MetaFormers to boost recurrent-free spatial-temporal predictive learning. We open-source the code and models at https://github.com/chengtan9907/OpenSTL.

Continual Learning (CL) aims at incrementally learning new tasks without forgetting the knowledge acquired from old ones. Experience Replay (ER) is a simple and effective rehearsal-based strategy, which optimizes the model with current training data and a subset of old samples stored in a memory buffer. To further reduce forgetting, recent approaches extend ER with various techniques, such as model regularization and memory sampling. However, the prediction consistency between the new model and the old one on current training data has been seldom explored, resulting in less knowledge preserved when few previous samples are available. To address this issue, we propose a CL method with Strong Experience Replay (SER), which additionally utilizes future experiences mimicked on the current training data, besides distilling past experience from the memory buffer. In our method, the updated model will produce approximate outputs as its original ones, which can effectively preserve the acquired knowledge. Experimental results on multiple image classification datasets show that our SER method surpasses the state-of-the-art methods by a noticeable margin.

We explore the properties of byte-level recurrent language models. When given sufficient amounts of capacity, training data, and compute time, the representations learned by these models include disentangled features corresponding to high-level concepts. Specifically, we find a single unit which performs sentiment analysis. These representations, learned in an unsupervised manner, achieve state of the art on the binary subset of the Stanford Sentiment Treebank. They are also very data efficient. When using only a handful of labeled examples, our approach matches the performance of strong baselines trained on full datasets. We also demonstrate the sentiment unit has a direct influence on the generative process of the model. Simply fixing its value to be positive or negative generates samples with the corresponding positive or negative sentiment.

Time series analysis is a fundamental task in various application domains, and deep learning approaches have demonstrated remarkable performance in this area. However, many real-world time series data exhibit significant periodic or quasi-periodic dynamics that are often not adequately captured by existing deep learning-based solutions. This results in an incomplete representation of the underlying dynamic behaviors of interest. To address this gap, we propose an unsupervised method called Floss that automatically regularizes learned representations in the frequency domain. The Floss method first automatically detects major periodicities from the time series. It then employs periodic shift and spectral density similarity measures to learn meaningful representations with periodic consistency. In addition, Floss can be easily incorporated into both supervised, semi-supervised, and unsupervised learning frameworks. We conduct extensive experiments on common time series classification, forecasting, and anomaly detection tasks to demonstrate the effectiveness of Floss. We incorporate Floss into several representative deep learning solutions to justify our design choices and demonstrate that it is capable of automatically discovering periodic dynamics and improving state-of-the-art deep learning models.

Can a pretrained neural network adapt its architecture to different inputs without any finetuning? Do we need all layers for simple tasks, and are they adequate for challenging tasks? We found that the layers of a pretrained large language model (LLM) can be manipulated as separate modules to build a better and even shallower model customized for each test sample. In particular, each layer from the pretrained model can be skipped/pruned or repeated multiple times as recurrent neural networks (RNN), and stacked with others in arbitrary orders, yielding a chain-of-layers (CoLa) per sample. This compositional space greatly expands the scope of existing works on looped/recurrent pretrained modules, layer pruning, or early-exit networks. We develop a Monte Carlo Tree Search (MCTS) protocol to explore and identify the optimal CoLa for each sample from math and commonsense reasoning benchmarks. Compared to a static model of a fixed depth, CoLa allows shortcut paths (fast thinking), recurrence of the same layer(s) (slow thinking), and combining both, offering more flexible, dynamic architectures for different inputs. We conduct an extensive analysis of the MCTS-optimized CoLa, which leads to two key findings: (1) For >75% of samples with correct predictions by the original LLM, we can find shorter CoLa, suggesting a large space for improving inference efficiency; (2) For >60% of samples with originally incorrect predictions, we can identify CoLa achieving correct predictions, suggesting a large space of performance enhancement. Our results highlight the shortcomings of using a fixed architecture of pre-trained LLMs for inference on different samples and pave the way to unlock the generalization power of test-time depth adaptation.

The recent success of large language models (LLMs) trained on static, pre-collected, general datasets has sparked numerous research directions and applications. One such direction addresses the non-trivial challenge of integrating pre-trained LLMs into dynamic data distributions, task structures, and user preferences. Pre-trained LLMs, when tailored for specific needs, often experience significant performance degradation in previous knowledge domains -- a phenomenon known as "catastrophic forgetting". While extensively studied in the continual learning (CL) community, it presents new manifestations in the realm of LLMs. In this survey, we provide a comprehensive overview of the current research progress on LLMs within the context of CL. This survey is structured into four main sections: we first describe an overview of continually learning LLMs, consisting of two directions of continuity: vertical continuity (or vertical continual learning), i.e., continual adaptation from general to specific capabilities, and horizontal continuity (or horizontal continual learning), i.e., continual adaptation across time and domains (Section 3). We then summarize three stages of learning LLMs in the context of modern CL: Continual Pre-Training (CPT), Domain-Adaptive Pre-training (DAP), and Continual Fine-Tuning (CFT) (Section 4). Then we provide an overview of evaluation protocols for continual learning with LLMs, along with the current available data sources (Section 5). Finally, we discuss intriguing questions pertaining to continual learning for LLMs (Section 6). The full list of papers examined in this survey is available at https://github.com/Wang-ML-Lab/llm-continual-learning-survey.

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.

The success of large-scale language models like GPT can be attributed to their ability to efficiently predict the next token in a sequence. However, these models rely on constant computational effort regardless of the complexity of the token they are predicting, lacking the capacity for iterative refinement. In this paper, we introduce a novel Loop-Residual Neural Network, which achieves better performance by utilizing longer computational time without increasing the model size. Our approach revisits the input multiple times, refining the prediction by iteratively looping over a subset of the model with residual connections. We demonstrate the effectiveness of this method through experiments comparing versions of GPT-2 with our Loop-Residual models, showing improved performance in language modeling tasks while maintaining similar parameter counts. Importantly, these improvements are achieved without the need for extra training data.

We present significant extensions to diffusion-based sequence generation models, blurring the line with autoregressive language models. We introduce hyperschedules, which assign distinct noise schedules to individual token positions, generalizing both autoregressive models (e.g., GPT) and conventional diffusion models (e.g., SEDD, MDLM) as special cases. Second, we propose two hybrid token-wise noising processes that interpolate between absorbing and uniform processes, enabling the model to fix past mistakes, and we introduce a novel inference algorithm that leverages this new feature in a simplified context inspired from MDLM. To support efficient training and inference, we design attention masks compatible with KV-caching. Our methods achieve state-of-the-art perplexity and generate diverse, high-quality sequences across standard benchmarks, suggesting a promising path for autoregressive diffusion-based sequence generation.

The ever-growing availability of unlabeled data presents both opportunities and challenges for training artificial intelligence systems. While self-supervised learning (SSL) has emerged as a powerful paradigm for extracting meaningful representations from vast amounts of unlabeled data, existing methods still struggle to adapt to the non-stationary, non-IID nature of real-world data streams without forgetting previously learned knowledge. Recent works have adopted a repeated cosine annealing schedule for large-scale continual pre-training; however, these schedules (1) inherently cause forgetting during the re-warming phase and (2) have not been systematically compared to existing continual SSL methods. In this work, we systematically compare the widely used cosine schedule with the recently proposed infinite learning rate schedule and empirically find the latter to be a more effective alternative. Our extensive empirical evaluation across diverse image and language datasets demonstrates that the infinite learning rate schedule consistently enhances continual pre-training performance compared to a repeated cosine decay without being restricted to a fixed iteration budget. For instance, in a small-scale MAE pre-training setup, it outperforms several strong baselines from the literature. We then scale up our experiments to larger MAE pre-training and autoregressive language model pre-training. Our results show that the infinite learning rate schedule remains effective at scale, surpassing repeated cosine decay for both MAE pre-training and zero-shot LM benchmarks.

Discovering the underlying relationships among variables from temporal observations has been a longstanding challenge in numerous scientific disciplines, including biology, finance, and climate science. The dynamics of such systems are often best described using continuous-time stochastic processes. Unfortunately, most existing structure learning approaches assume that the underlying process evolves in discrete-time and/or observations occur at regular time intervals. These mismatched assumptions can often lead to incorrect learned structures and models. In this work, we introduce a novel structure learning method, SCOTCH, which combines neural stochastic differential equations (SDE) with variational inference to infer a posterior distribution over possible structures. This continuous-time approach can naturally handle both learning from and predicting observations at arbitrary time points. Theoretically, we establish sufficient conditions for an SDE and SCOTCH to be structurally identifiable, and prove its consistency under infinite data limits. Empirically, we demonstrate that our approach leads to improved structure learning performance on both synthetic and real-world datasets compared to relevant baselines under regular and irregular sampling intervals.

We reformulate the problem of encoding a multi-scale representation of a sequence in a language model by casting it in a continuous learning framework. We propose a hierarchical multi-scale language model in which short time-scale dependencies are encoded in the hidden state of a lower-level recurrent neural network while longer time-scale dependencies are encoded in the dynamic of the lower-level network by having a meta-learner update the weights of the lower-level neural network in an online meta-learning fashion. We use elastic weights consolidation as a higher-level to prevent catastrophic forgetting in our continuous learning framework.

This paper introduces the counter-intuitive generalization results of overfitting pre-trained large language models (LLMs) on very small datasets. In the setting of open-ended text generation, it is well-documented that LLMs tend to generate repetitive and dull sequences, a phenomenon that is especially apparent when generating using greedy decoding. This issue persists even with state-of-the-art LLMs containing billions of parameters, trained via next-token prediction on large datasets. We find that by further fine-tuning these models to achieve a near-zero training loss on a small set of samples -- a process we refer to as hyperfitting -- the long-sequence generative capabilities are greatly enhanced. Greedy decoding with these Hyperfitted models even outperform Top-P sampling over long-sequences, both in terms of diversity and human preferences. This phenomenon extends to LLMs of various sizes, different domains, and even autoregressive image generation. We further find this phenomena to be distinctly different from that of Grokking and double descent. Surprisingly, our experiments indicate that hyperfitted models rarely fall into repeating sequences they were trained on, and even explicitly blocking these sequences results in high-quality output. All hyperfitted models produce extremely low-entropy predictions, often allocating nearly all probability to a single token.

Incremental learning aims to overcome catastrophic forgetting when learning deep networks from sequential tasks. With impressive learning efficiency and performance, prompt-based methods adopt a fixed backbone to sequential tasks by learning task-specific prompts. However, existing prompt-based methods heavily rely on strong pretraining (typically trained on ImageNet-21k), and we find that their models could be trapped if the potential gap between the pretraining task and unknown future tasks is large. In this work, we develop a learnable Adaptive Prompt Generator (APG). The key is to unify the prompt retrieval and prompt learning processes into a learnable prompt generator. Hence, the whole prompting process can be optimized to reduce the negative effects of the gap between tasks effectively. To make our APG avoid learning ineffective knowledge, we maintain a knowledge pool to regularize APG with the feature distribution of each class. Extensive experiments show that our method significantly outperforms advanced methods in exemplar-free incremental learning without (strong) pretraining. Besides, under strong retraining, our method also has comparable performance to existing prompt-based models, showing that our method can still benefit from pretraining. Codes can be found at https://github.com/TOM-tym/APG

A recurrent neural network (RNN) is a widely used deep-learning network for dealing with sequential data. Imitating a dynamical system, an infinite-width RNN can approximate any open dynamical system in a compact domain. In general, deep networks with bounded widths are more effective than wide networks in practice; however, the universal approximation theorem for deep narrow structures has yet to be extensively studied. In this study, we prove the universality of deep narrow RNNs and show that the upper bound of the minimum width for universality can be independent of the length of the data. Specifically, we show that a deep RNN with ReLU activation can approximate any continuous function or L^p function with the widths d_x+d_y+2 and max{d_x+1,d_y}, respectively, where the target function maps a finite sequence of vectors in R^{d_x} to a finite sequence of vectors in R^{d_y}. We also compute the additional width required if the activation function is tanh or more. In addition, we prove the universality of other recurrent networks, such as bidirectional RNNs. Bridging a multi-layer perceptron and an RNN, our theory and proof technique can be an initial step toward further research on deep RNNs.

Subgraph GNNs are provably expressive neural architectures that learn graph representations from sets of subgraphs. Unfortunately, their applicability is hampered by the computational complexity associated with performing message passing on many subgraphs. In this paper, we consider the problem of learning to select a small subset of the large set of possible subgraphs in a data-driven fashion. We first motivate the problem by proving that there are families of WL-indistinguishable graphs for which there exist efficient subgraph selection policies: small subsets of subgraphs that can already identify all the graphs within the family. We then propose a new approach, called Policy-Learn, that learns how to select subgraphs in an iterative manner. We prove that, unlike popular random policies and prior work addressing the same problem, our architecture is able to learn the efficient policies mentioned above. Our experimental results demonstrate that Policy-Learn outperforms existing baselines across a wide range of datasets.

Multivariate time series forecasting is an important machine learning problem across many domains, including predictions of solar plant energy output, electricity consumption, and traffic jam situation. Temporal data arise in these real-world applications often involves a mixture of long-term and short-term patterns, for which traditional approaches such as Autoregressive models and Gaussian Process may fail. In this paper, we proposed a novel deep learning framework, namely Long- and Short-term Time-series network (LSTNet), to address this open challenge. LSTNet uses the Convolution Neural Network (CNN) and the Recurrent Neural Network (RNN) to extract short-term local dependency patterns among variables and to discover long-term patterns for time series trends. Furthermore, we leverage traditional autoregressive model to tackle the scale insensitive problem of the neural network model. In our evaluation on real-world data with complex mixtures of repetitive patterns, LSTNet achieved significant performance improvements over that of several state-of-the-art baseline methods. All the data and experiment codes are available online.

While differentiable logic gates have shown promise in feedforward networks, their application to sequential modeling remains unexplored. This paper presents the first implementation of Recurrent Deep Differentiable Logic Gate Networks (RDDLGN), combining Boolean operations with recurrent architectures for sequence-to-sequence learning. Evaluated on WMT'14 English-German translation, RDDLGN achieves 5.00 BLEU and 30.9\% accuracy during training, approaching GRU performance (5.41 BLEU) and graceful degradation (4.39 BLEU) during inference. This work establishes recurrent logic-based neural computation as viable, opening research directions for FPGA acceleration in sequential modeling and other recursive network architectures.

Inspired by Regularized Lottery Ticket Hypothesis (RLTH), which hypothesizes that there exist smooth (non-binary) subnetworks within a dense network that achieve the competitive performance of the dense network, we propose a few-shot class incremental learning (FSCIL) method referred to as Soft-SubNetworks (SoftNet). Our objective is to learn a sequence of sessions incrementally, where each session only includes a few training instances per class while preserving the knowledge of the previously learned ones. SoftNet jointly learns the model weights and adaptive non-binary soft masks at a base training session in which each mask consists of the major and minor subnetwork; the former aims to minimize catastrophic forgetting during training, and the latter aims to avoid overfitting to a few samples in each new training session. We provide comprehensive empirical validations demonstrating that our SoftNet effectively tackles the few-shot incremental learning problem by surpassing the performance of state-of-the-art baselines over benchmark datasets.

Recently, continual learning (CL) has gained significant interest because it enables deep learning models to acquire new knowledge without forgetting previously learnt information. However, most existing works require knowing the task identities and boundaries, which is not realistic in a real context. In this paper, we address a more challenging and realistic setting in CL, namely the Task-Free Continual Learning (TFCL) in which a model is trained on non-stationary data streams with no explicit task information. To address TFCL, we introduce an evolved mixture model whose network architecture is dynamically expanded to adapt to the data distribution shift. We implement this expansion mechanism by evaluating the probability distance between the knowledge stored in each mixture model component and the current memory buffer using the Hilbert Schmidt Independence Criterion (HSIC). We further introduce two simple dropout mechanisms to selectively remove stored examples in order to avoid memory overload while preserving memory diversity. Empirical results demonstrate that the proposed approach achieves excellent performance.

Recent work has proposed the linear representation hypothesis: that language models perform computation by manipulating one-dimensional representations of concepts ("features") in activation space. In contrast, we explore whether some language model representations may be inherently multi-dimensional. We begin by developing a rigorous definition of irreducible multi-dimensional features based on whether they can be decomposed into either independent or non-co-occurring lower-dimensional features. Motivated by these definitions, we design a scalable method that uses sparse autoencoders to automatically find multi-dimensional features in GPT-2 and Mistral 7B. These auto-discovered features include strikingly interpretable examples, e.g. circular features representing days of the week and months of the year. We identify tasks where these exact circles are used to solve computational problems involving modular arithmetic in days of the week and months of the year. Finally, we provide evidence that these circular features are indeed the fundamental unit of computation in these tasks with intervention experiments on Mistral 7B and Llama 3 8B, and we find further circular representations by breaking down the hidden states for these tasks into interpretable components.