Daily Papers

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.

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.

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.

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.

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.

Many machine learning tasks can be expressed as the transformation---or transduction---of input sequences into output sequences: speech recognition, machine translation, protein secondary structure prediction and text-to-speech to name but a few. One of the key challenges in sequence transduction is learning to represent both the input and output sequences in a way that is invariant to sequential distortions such as shrinking, stretching and translating. Recurrent neural networks (RNNs) are a powerful sequence learning architecture that has proven capable of learning such representations. However RNNs traditionally require a pre-defined alignment between the input and output sequences to perform transduction. This is a severe limitation since finding the alignment is the most difficult aspect of many sequence transduction problems. Indeed, even determining the length of the output sequence is often challenging. This paper introduces an end-to-end, probabilistic sequence transduction system, based entirely on RNNs, that is in principle able to transform any input sequence into any finite, discrete output sequence. Experimental results for phoneme recognition are provided on the TIMIT speech corpus.

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.

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.

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.

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.

Discrete event sequences are ubiquitous, such as an ordered event series of process interactions in Information and Communication Technology systems. Recent years have witnessed increasing efforts in detecting anomalies with discrete-event sequences. However, it still remains an extremely difficult task due to several intrinsic challenges including data imbalance issues, the discrete property of the events, and sequential nature of the data. To address these challenges, in this paper, we propose OC4Seq, a multi-scale one-class recurrent neural network for detecting anomalies in discrete event sequences. Specifically, OC4Seq integrates the anomaly detection objective with recurrent neural networks (RNNs) to embed the discrete event sequences into latent spaces, where anomalies can be easily detected. In addition, given that an anomalous sequence could be caused by either individual events, subsequences of events, or the whole sequence, we design a multi-scale RNN framework to capture different levels of sequential patterns simultaneously. Experimental results on three benchmark datasets show that OC4Seq consistently outperforms various representative baselines by a large margin. Moreover, through both quantitative and qualitative analysis, the importance of capturing multi-scale sequential patterns for event anomaly detection is verified.

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.

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.

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

Breaking domain names such as openresearch into component words open and research is important for applications like Text-to-Speech synthesis and web search. We link this problem to the classic problem of Chinese word segmentation and show the effectiveness of a tagging model based on Recurrent Neural Networks (RNNs) using characters as input. To compensate for the lack of training data, we propose a pre-training method on concatenated entity names in a large knowledge database. Pre-training improves the model by 33% and brings the sequence accuracy to 85%.

Machine learning architectures, including transformers and recurrent neural networks (RNNs) have revolutionized forecasting in applications ranging from text processing to extreme weather. Notably, advanced network architectures, tuned for applications such as natural language processing, are transferable to other tasks such as spatiotemporal forecasting tasks. However, there is a scarcity of ablation studies to illustrate the key components that enable this forecasting accuracy. The absence of such studies, although explainable due to the associated computational cost, intensifies the belief that these models ought to be considered as black boxes. In this work, we decompose the key architectural components of the most powerful neural architectures, namely gating and recurrence in RNNs, and attention mechanisms in transformers. Then, we synthesize and build novel hybrid architectures from the standard blocks, performing ablation studies to identify which mechanisms are effective for each task. The importance of considering these components as hyper-parameters that can augment the standard architectures is exhibited on various forecasting datasets, from the spatiotemporal chaotic dynamics of the multiscale Lorenz 96 system, the Kuramoto-Sivashinsky equation, as well as standard real world time-series benchmarks. A key finding is that neural gating and attention improves the performance of all standard RNNs in most tasks, while the addition of a notion of recurrence in transformers is detrimental. Furthermore, our study reveals that a novel, sparsely used, architecture which integrates Recurrent Highway Networks with neural gating and attention mechanisms, emerges as the best performing architecture in high-dimensional spatiotemporal forecasting of dynamical systems.

Softmax attention is the principle backbone of foundation models for various artificial intelligence applications, yet its quadratic complexity in sequence length can limit its inference throughput in long-context settings. To address this challenge, alternative architectures such as linear attention, State Space Models (SSMs), and Recurrent Neural Networks (RNNs) have been considered as more efficient alternatives. While connections between these approaches exist, such models are commonly developed in isolation and there is a lack of theoretical understanding of the shared principles underpinning these architectures and their subtle differences, greatly influencing performance and scalability. In this paper, we introduce the Dynamical Systems Framework (DSF), which allows a principled investigation of all these architectures in a common representation. Our framework facilitates rigorous comparisons, providing new insights on the distinctive characteristics of each model class. For instance, we compare linear attention and selective SSMs, detailing their differences and conditions under which both are equivalent. We also provide principled comparisons between softmax attention and other model classes, discussing the theoretical conditions under which softmax attention can be approximated. Additionally, we substantiate these new insights with empirical validations and mathematical arguments. This shows the DSF's potential to guide the systematic development of future more efficient and scalable foundation models.

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 present a simple regularization technique for Recurrent Neural Networks (RNNs) with Long Short-Term Memory (LSTM) units. Dropout, the most successful technique for regularizing neural networks, does not work well with RNNs and LSTMs. In this paper, we show how to correctly apply dropout to LSTMs, and show that it substantially reduces overfitting on a variety of tasks. These tasks include language modeling, speech recognition, image caption generation, and machine translation.

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

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.

Deep Learning has revolutionized vision via convolutional neural networks (CNNs) and natural language processing via recurrent neural networks (RNNs). However, success stories of Deep Learning with standard feed-forward neural networks (FNNs) are rare. FNNs that perform well are typically shallow and, therefore cannot exploit many levels of abstract representations. We introduce self-normalizing neural networks (SNNs) to enable high-level abstract representations. While batch normalization requires explicit normalization, neuron activations of SNNs automatically converge towards zero mean and unit variance. The activation function of SNNs are "scaled exponential linear units" (SELUs), which induce self-normalizing properties. Using the Banach fixed-point theorem, we prove that activations close to zero mean and unit variance that are propagated through many network layers will converge towards zero mean and unit variance -- even under the presence of noise and perturbations. This convergence property of SNNs allows to (1) train deep networks with many layers, (2) employ strong regularization, and (3) to make learning highly robust. Furthermore, for activations not close to unit variance, we prove an upper and lower bound on the variance, thus, vanishing and exploding gradients are impossible. We compared SNNs on (a) 121 tasks from the UCI machine learning repository, on (b) drug discovery benchmarks, and on (c) astronomy tasks with standard FNNs and other machine learning methods such as random forests and support vector machines. SNNs significantly outperformed all competing FNN methods at 121 UCI tasks, outperformed all competing methods at the Tox21 dataset, and set a new record at an astronomy data set. The winning SNN architectures are often very deep. Implementations are available at: github.com/bioinf-jku/SNNs.

Humans can understand and produce new utterances effortlessly, thanks to their compositional skills. Once a person learns the meaning of a new verb "dax," he or she can immediately understand the meaning of "dax twice" or "sing and dax." In this paper, we introduce the SCAN domain, consisting of a set of simple compositional navigation commands paired with the corresponding action sequences. We then test the zero-shot generalization capabilities of a variety of recurrent neural networks (RNNs) trained on SCAN with sequence-to-sequence methods. We find that RNNs can make successful zero-shot generalizations when the differences between training and test commands are small, so that they can apply "mix-and-match" strategies to solve the task. However, when generalization requires systematic compositional skills (as in the "dax" example above), RNNs fail spectacularly. We conclude with a proof-of-concept experiment in neural machine translation, suggesting that lack of systematicity might be partially responsible for neural networks' notorious training data thirst.

Since its introduction, softmax attention has become the backbone of modern transformer architectures due to its expressiveness and scalability across a wide range of tasks. However, the main drawback of softmax attention is the quadratic memory requirement and computational complexity with respect to the sequence length. By replacing the softmax nonlinearity, linear attention and similar methods have been introduced to avoid the quadratic bottleneck of softmax attention. Despite these linear forms of attention being derived from the original softmax formulation, they typically lag in terms of downstream accuracy. While strong intuition of the softmax nonlinearity on the query and key inner product suggests that it has desirable properties compared to other nonlinearities, the question of why this discrepancy exists still remains unanswered. This work demonstrates that linear attention is an approximation of softmax attention by deriving the recurrent form of softmax attention. Using this form, each part of softmax attention can be described in the language of recurrent neural networks (RNNs). Describing softmax attention as an RNN allows for the ablation of the components of softmax attention to understand the importance of each part and how they interact. In this way, our work helps explain why softmax attention is more expressive than its counterparts.

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) provide a powerful approach in neuroscience to infer latent dynamics in neural populations and to generate hypotheses about the neural computations underlying behavior. However, past work has focused on relatively simple, input-driven, and largely deterministic behaviors - little is known about the mechanisms that would allow RNNs to generate the richer, spontaneous, and potentially stochastic behaviors observed in natural settings. Modeling with Hidden Markov Models (HMMs) has revealed a segmentation of natural behaviors into discrete latent states with stochastic transitions between them, a type of dynamics that may appear at odds with the continuous state spaces implemented by RNNs. Here we first show that RNNs can replicate HMM emission statistics and then reverse-engineer the trained networks to uncover the mechanisms they implement. In the absence of inputs, the activity of trained RNNs collapses towards a single fixed point. When driven by stochastic input, trajectories instead exhibit noise-sustained dynamics along closed orbits. Rotation along these orbits modulates the emission probabilities and is governed by transitions between regions of slow, noise-driven dynamics connected by fast, deterministic transitions. The trained RNNs develop highly structured connectivity, with a small set of "kick neurons" initiating transitions between these regions. This mechanism emerges during training as the network shifts into a regime of stochastic resonance, enabling it to perform probabilistic computations. Analyses across multiple HMM architectures - fully connected, cyclic, and linear-chain - reveal that this solution generalizes through the modular reuse of the same dynamical motif, suggesting a compositional principle by which RNNs can emulate complex discrete latent dynamics.

Recurrent Neural Networks (RNNs) have revolutionized many areas of machine learning, particularly in natural language and data sequence processing. Long Short-Term Memory (LSTM) has demonstrated its ability to capture long-term dependencies in sequential data. Inspired by the Kolmogorov-Arnold Networks (KANs) a promising alternatives to Multi-Layer Perceptrons (MLPs), we proposed a new neural networks architecture inspired by KAN and the LSTM, the Temporal Kolomogorov-Arnold Networks (TKANs). TKANs combined the strenght of both networks, it is composed of Recurring Kolmogorov-Arnold Networks (RKANs) Layers embedding memory management. This innovation enables us to perform multi-step time series forecasting with enhanced accuracy and efficiency. By addressing the limitations of traditional models in handling complex sequential patterns, the TKAN architecture offers significant potential for advancements in fields requiring more than one step ahead forecasting.

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.

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.

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.

Neural architectures such as Recurrent Neural Networks (RNNs), Transformers, and State-Space Models have shown great success in handling sequential data by learning temporal dependencies. Decision Trees (DTs), on the other hand, remain a widely used class of models for structured tabular data but are typically not designed to capture sequential patterns directly. Instead, DT-based approaches for time-series data often rely on feature engineering, such as manually incorporating lag features, which can be suboptimal for capturing complex temporal dependencies. To address this limitation, we introduce ReMeDe Trees, a novel recurrent DT architecture that integrates an internal memory mechanism, similar to RNNs, to learn long-term dependencies in sequential data. Our model learns hard, axis-aligned decision rules for both output generation and state updates, optimizing them efficiently via gradient descent. We provide a proof-of-concept study on synthetic benchmarks to demonstrate the effectiveness of our approach.

Our previously proposed MossFormer has achieved promising performance in monaural speech separation. However, it predominantly adopts a self-attention-based MossFormer module, which tends to emphasize longer-range, coarser-scale dependencies, with a deficiency in effectively modelling finer-scale recurrent patterns. In this paper, we introduce a novel hybrid model that provides the capabilities to model both long-range, coarse-scale dependencies and fine-scale recurrent patterns by integrating a recurrent module into the MossFormer framework. Instead of applying the recurrent neural networks (RNNs) that use traditional recurrent connections, we present a recurrent module based on a feedforward sequential memory network (FSMN), which is considered "RNN-free" recurrent network due to the ability to capture recurrent patterns without using recurrent connections. Our recurrent module mainly comprises an enhanced dilated FSMN block by using gated convolutional units (GCU) and dense connections. In addition, a bottleneck layer and an output layer are also added for controlling information flow. The recurrent module relies on linear projections and convolutions for seamless, parallel processing of the entire sequence. The integrated MossFormer2 hybrid model demonstrates remarkable enhancements over MossFormer and surpasses other state-of-the-art methods in WSJ0-2/3mix, Libri2Mix, and WHAM!/WHAMR! benchmarks.

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.

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.

Transformers have revolutionized almost all natural language processing (NLP) tasks but suffer from memory and computational complexity that scales quadratically with sequence length. In contrast, recurrent neural networks (RNNs) exhibit linear scaling in memory and computational requirements but struggle to match the same performance as Transformers due to limitations in parallelization and scalability. We propose a novel model architecture, Receptance Weighted Key Value (RWKV), that combines the efficient parallelizable training of Transformers with the efficient inference of RNNs. Our approach leverages a linear attention mechanism and allows us to formulate the model as either a Transformer or an RNN, which parallelizes computations during training and maintains constant computational and memory complexity during inference, leading to the first non-transformer architecture to be scaled to tens of billions of parameters. Our experiments reveal that RWKV performs on par with similarly sized Transformers, suggesting that future work can leverage this architecture to create more efficient models. This work presents a significant step towards reconciling the trade-offs between computational efficiency and model performance in sequence processing tasks.

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.

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.

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.

Transformers are considered conceptually different compared to the previous generation of state-of-the-art NLP models - recurrent neural networks (RNNs). In this work, we demonstrate that decoder-only transformers can in fact be conceptualized as infinite multi-state RNNs - an RNN variant with unlimited hidden state size. We further show that pretrained transformers can be converted into finite multi-state RNNs by fixing the size of their hidden state. We observe that several existing transformers cache compression techniques can be framed as such conversion policies, and introduce a novel policy, TOVA, which is simpler compared to these policies. Our experiments with several long range tasks indicate that TOVA outperforms all other baseline policies, while being nearly on par with the full (infinite) model, and using in some cases only 1{8} of the original cache size. Our results indicate that transformer decoder LLMs often behave in practice as RNNs. They also lay out the option of mitigating one of their most painful computational bottlenecks - the size of their cache memory. We publicly release our code at https://github.com/schwartz-lab-NLP/TOVA.

State-space models (SSMs) and transformers dominate the language modeling landscape. However, they are constrained to a lower computational complexity than classical recurrent neural networks (RNNs), limiting their expressivity. In contrast, RNNs lack parallelization during training, raising fundamental questions about the trade off between parallelization and expressivity. We propose implicit SSMs, which iterate a transformation until convergence to a fixed point. Theoretically, we show that implicit SSMs implement the non-linear state-transitions of RNNs. Empirically, we find that only approximate fixed-point convergence suffices, enabling the design of a scalable training curriculum that largely retains parallelization, with full convergence required only for a small subset of tokens. Our approach demonstrates superior state-tracking capabilities on regular languages, surpassing transformers and SSMs. We further scale implicit SSMs to natural language reasoning tasks and pretraining of large-scale language models up to 1.3B parameters on 207B tokens - representing, to our knowledge, the largest implicit model trained to date. Notably, our implicit models outperform their explicit counterparts on standard benchmarks.

Foundation models for zero-shot time series forecasting face challenges in efficient long-horizon prediction and reproducibility, with existing synthetic-only approaches underperforming on challenging benchmarks. This paper presents TempoPFN, a univariate time series foundation model based on linear Recurrent Neural Networks (RNNs) pre-trained exclusively on synthetic data. The model uses a GatedDeltaProduct architecture with state-weaving for fully parallelizable training across sequence lengths, eliminating the need for windowing or summarization techniques while maintaining robust temporal state-tracking. Our comprehensive synthetic data pipeline unifies diverse generators, including stochastic differential equations, Gaussian processes, and audio synthesis, with novel augmentations. In zero-shot evaluations on the Gift-Eval benchmark, TempoPFN achieves top-tier competitive performance, outperforming all existing synthetic-only approaches and surpassing the vast majority of models trained on real-world data, while being more efficient than existing baselines by leveraging fully parallelizable training and inference. We open-source our complete data generation pipeline and training code, providing a reproducible foundation for future research.

Skeleton-based action recognition task is entangled with complex spatio-temporal variations of skeleton joints, and remains challenging for Recurrent Neural Networks (RNNs). In this work, we propose a temporal-then-spatial recalibration scheme to alleviate such complex variations, resulting in an end-to-end Memory Attention Networks (MANs) which consist of a Temporal Attention Recalibration Module (TARM) and a Spatio-Temporal Convolution Module (STCM). Specifically, the TARM is deployed in a residual learning module that employs a novel attention learning network to recalibrate the temporal attention of frames in a skeleton sequence. The STCM treats the attention calibrated skeleton joint sequences as images and leverages the Convolution Neural Networks (CNNs) to further model the spatial and temporal information of skeleton data. These two modules (TARM and STCM) seamlessly form a single network architecture that can be trained in an end-to-end fashion. MANs significantly boost the performance of skeleton-based action recognition and achieve the best results on four challenging benchmark datasets: NTU RGB+D, HDM05, SYSU-3D and UT-Kinect.

Although end-to-end neural text-to-speech (TTS) methods (such as Tacotron2) are proposed and achieve state-of-the-art performance, they still suffer from two problems: 1) low efficiency during training and inference; 2) hard to model long dependency using current recurrent neural networks (RNNs). Inspired by the success of Transformer network in neural machine translation (NMT), in this paper, we introduce and adapt the multi-head attention mechanism to replace the RNN structures and also the original attention mechanism in Tacotron2. With the help of multi-head self-attention, the hidden states in the encoder and decoder are constructed in parallel, which improves the training efficiency. Meanwhile, any two inputs at different times are connected directly by self-attention mechanism, which solves the long range dependency problem effectively. Using phoneme sequences as input, our Transformer TTS network generates mel spectrograms, followed by a WaveNet vocoder to output the final audio results. Experiments are conducted to test the efficiency and performance of our new network. For the efficiency, our Transformer TTS network can speed up the training about 4.25 times faster compared with Tacotron2. For the performance, rigorous human tests show that our proposed model achieves state-of-the-art performance (outperforms Tacotron2 with a gap of 0.048) and is very close to human quality (4.39 vs 4.44 in MOS).

World models are a fundamental component in model-based reinforcement learning (MBRL). To perform temporally extended and consistent simulations of the future in partially observable environments, world models need to possess long-term memory. However, state-of-the-art MBRL agents, such as Dreamer, predominantly employ recurrent neural networks (RNNs) as their world model backbone, which have limited memory capacity. In this paper, we seek to explore alternative world model backbones for improving long-term memory. In particular, we investigate the effectiveness of Transformers and Structured State Space Sequence (S4) models, motivated by their remarkable ability to capture long-range dependencies in low-dimensional sequences and their complementary strengths. We propose S4WM, the first world model compatible with parallelizable SSMs including S4 and its variants. By incorporating latent variable modeling, S4WM can efficiently generate high-dimensional image sequences through latent imagination. Furthermore, we extensively compare RNN-, Transformer-, and S4-based world models across four sets of environments, which we have tailored to assess crucial memory capabilities of world models, including long-term imagination, context-dependent recall, reward prediction, and memory-based reasoning. Our findings demonstrate that S4WM outperforms Transformer-based world models in terms of long-term memory, while exhibiting greater efficiency during training and imagination. These results pave the way for the development of stronger MBRL agents.

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.

One essential advantage of recurrent neural networks (RNNs) over transformer-based language models is their linear computational complexity concerning the sequence length, which makes them much faster in handling long sequences during inference. However, most publicly available RNNs (e.g., Mamba and RWKV) are trained on sequences with less than 10K tokens, and their effectiveness in longer contexts remains largely unsatisfying so far. In this paper, we study the cause of the inability to process long context for RNNs and suggest critical mitigations. We examine two practical concerns when applying state-of-the-art RNNs to long contexts: (1) the inability to extrapolate to inputs longer than the training length and (2) the upper bound of memory capacity. Addressing the first concern, we first investigate *state collapse* (SC), a phenomenon that causes severe performance degradation on sequence lengths not encountered during training. With controlled experiments, we attribute this to overfitting due to the recurrent state being overparameterized for the training length. For the second concern, we train a series of Mamba-2 models on long documents to empirically estimate the recurrent state capacity in language modeling and passkey retrieval. Then, three SC mitigation methods are proposed to improve Mamba-2's length generalizability, allowing the model to process more than 1M tokens without SC. We also find that the recurrent state capacity in passkey retrieval scales exponentially to the state size, and we empirically train a Mamba-2 370M with near-perfect passkey retrieval accuracy on 256K context length. This suggests a promising future for RNN-based long-context modeling.

Sequence modeling is a crucial area across various domains, including Natural Language Processing (NLP), speech recognition, time series forecasting, music generation, and bioinformatics. Recurrent Neural Networks (RNNs) and Long Short Term Memory Networks (LSTMs) have historically dominated sequence modeling tasks like Machine Translation, Named Entity Recognition (NER), etc. However, the advancement of transformers has led to a shift in this paradigm, given their superior performance. Yet, transformers suffer from O(N^2) attention complexity and challenges in handling inductive bias. Several variations have been proposed to address these issues which use spectral networks or convolutions and have performed well on a range of tasks. However, they still have difficulty in dealing with long sequences. State Space Models(SSMs) have emerged as promising alternatives for sequence modeling paradigms in this context, especially with the advent of S4 and its variants, such as S4nd, Hippo, Hyena, Diagnol State Spaces (DSS), Gated State Spaces (GSS), Linear Recurrent Unit (LRU), Liquid-S4, Mamba, etc. In this survey, we categorize the foundational SSMs based on three paradigms namely, Gating architectures, Structural architectures, and Recurrent architectures. This survey also highlights diverse applications of SSMs across domains such as vision, video, audio, speech, language (especially long sequence modeling), medical (including genomics), chemical (like drug design), recommendation systems, and time series analysis, including tabular data. Moreover, we consolidate the performance of SSMs on benchmark datasets like Long Range Arena (LRA), WikiText, Glue, Pile, ImageNet, Kinetics-400, sstv2, as well as video datasets such as Breakfast, COIN, LVU, and various time series datasets. The project page for Mamba-360 work is available on this webpage.https://github.com/badripatro/mamba360.

Recurrent neural networks (RNNs) sequentially process data by updating their state with each new data point, and have long been the de facto choice for sequence modeling tasks. However, their inherently sequential computation makes them slow to train. Feed-forward and convolutional architectures have recently been shown to achieve superior results on some sequence modeling tasks such as machine translation, with the added advantage that they concurrently process all inputs in the sequence, leading to easy parallelization and faster training times. Despite these successes, however, popular feed-forward sequence models like the Transformer fail to generalize in many simple tasks that recurrent models handle with ease, e.g. copying strings or even simple logical inference when the string or formula lengths exceed those observed at training time. We propose the Universal Transformer (UT), a parallel-in-time self-attentive recurrent sequence model which can be cast as a generalization of the Transformer model and which addresses these issues. UTs combine the parallelizability and global receptive field of feed-forward sequence models like the Transformer with the recurrent inductive bias of RNNs. We also add a dynamic per-position halting mechanism and find that it improves accuracy on several tasks. In contrast to the standard Transformer, under certain assumptions, UTs can be shown to be Turing-complete. Our experiments show that UTs outperform standard Transformers on a wide range of algorithmic and language understanding tasks, including the challenging LAMBADA language modeling task where UTs achieve a new state of the art, and machine translation where UTs achieve a 0.9 BLEU improvement over Transformers on the WMT14 En-De dataset.

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.

Recurrent Neural Networks (RNNs) have long been the dominant architecture in sequence-to-sequence learning. RNNs, however, are inherently sequential models that do not allow parallelization of their computations. Transformers are emerging as a natural alternative to standard RNNs, replacing recurrent computations with a multi-head attention mechanism. In this paper, we propose the SepFormer, a novel RNN-free Transformer-based neural network for speech separation. The SepFormer learns short and long-term dependencies with a multi-scale approach that employs transformers. The proposed model achieves state-of-the-art (SOTA) performance on the standard WSJ0-2/3mix datasets. It reaches an SI-SNRi of 22.3 dB on WSJ0-2mix and an SI-SNRi of 19.5 dB on WSJ0-3mix. The SepFormer inherits the parallelization advantages of Transformers and achieves a competitive performance even when downsampling the encoded representation by a factor of 8. It is thus significantly faster and it is less memory-demanding than the latest speech separation systems with comparable performance.

Learning latent representations from long text sequences is an important first step in many natural language processing applications. Recurrent Neural Networks (RNNs) have become a cornerstone for this challenging task. However, the quality of sentences during RNN-based decoding (reconstruction) decreases with the length of the text. We propose a sequence-to-sequence, purely convolutional and deconvolutional autoencoding framework that is free of the above issue, while also being computationally efficient. The proposed method is simple, easy to implement and can be leveraged as a building block for many applications. We show empirically that compared to RNNs, our framework is better at reconstructing and correcting long paragraphs. Quantitative evaluation on semi-supervised text classification and summarization tasks demonstrate the potential for better utilization of long unlabeled text data.

Recurrent neural networks (RNNs), such as long short-term memory networks (LSTMs), serve as a fundamental building block for many sequence learning tasks, including machine translation, language modeling, and question answering. In this paper, we consider the specific problem of word-level language modeling and investigate strategies for regularizing and optimizing LSTM-based models. We propose the weight-dropped LSTM which uses DropConnect on hidden-to-hidden weights as a form of recurrent regularization. Further, we introduce NT-ASGD, a variant of the averaged stochastic gradient method, wherein the averaging trigger is determined using a non-monotonic condition as opposed to being tuned by the user. Using these and other regularization strategies, we achieve state-of-the-art word level perplexities on two data sets: 57.3 on Penn Treebank and 65.8 on WikiText-2. In exploring the effectiveness of a neural cache in conjunction with our proposed model, we achieve an even lower state-of-the-art perplexity of 52.8 on Penn Treebank and 52.0 on WikiText-2.

A key advantage of Recurrent Neural Networks (RNNs) over Transformers is their linear computational and space complexity enables faster training and inference for long sequences. However, RNNs are fundamentally unable to randomly access historical context, and simply integrating attention mechanisms may undermine their efficiency advantages. To overcome this limitation, we propose Hierarchical Sparse Attention (HSA), a novel attention mechanism that enhances RNNs with long-range random access flexibility while preserving their merits in efficiency and length generalization. HSA divides inputs into chunks, selecting the top-k chunks and hierarchically aggregates information. The core innovation lies in learning token-to-chunk relevance based on fine-grained token-level information inside each chunk. This approach enhances the precision of chunk selection across both in-domain and out-of-domain context lengths. To make HSA efficient, we further introduce a hardware-aligned kernel design. By combining HSA with Mamba, we introduce RAMba, which achieves perfect accuracy in passkey retrieval across 64 million contexts despite pre-training on only 4K-length contexts, and significant improvements on various downstream tasks, with nearly constant memory footprint. These results show RAMba's huge potential in long-context modeling.

Recent progress in using recurrent neural networks (RNNs) for image description has motivated the exploration of their application for video description. However, while images are static, working with videos requires modeling their dynamic temporal structure and then properly integrating that information into a natural language description. In this context, we propose an approach that successfully takes into account both the local and global temporal structure of videos to produce descriptions. First, our approach incorporates a spatial temporal 3-D convolutional neural network (3-D CNN) representation of the short temporal dynamics. The 3-D CNN representation is trained on video action recognition tasks, so as to produce a representation that is tuned to human motion and behavior. Second we propose a temporal attention mechanism that allows to go beyond local temporal modeling and learns to automatically select the most relevant temporal segments given the text-generating RNN. Our approach exceeds the current state-of-art for both BLEU and METEOR metrics on the Youtube2Text dataset. We also present results on a new, larger and more challenging dataset of paired video and natural language descriptions.

Transformer is a deep neural network that employs a self-attention mechanism to comprehend the contextual relationships within sequential data. Unlike conventional neural networks or updated versions of Recurrent Neural Networks (RNNs) such as Long Short-Term Memory (LSTM), transformer models excel in handling long dependencies between input sequence elements and enable parallel processing. As a result, transformer-based models have attracted substantial interest among researchers in the field of artificial intelligence. This can be attributed to their immense potential and remarkable achievements, not only in Natural Language Processing (NLP) tasks but also in a wide range of domains, including computer vision, audio and speech processing, healthcare, and the Internet of Things (IoT). Although several survey papers have been published highlighting the transformer's contributions in specific fields, architectural differences, or performance evaluations, there is still a significant absence of a comprehensive survey paper encompassing its major applications across various domains. Therefore, we undertook the task of filling this gap by conducting an extensive survey of proposed transformer models from 2017 to 2022. Our survey encompasses the identification of the top five application domains for transformer-based models, namely: NLP, Computer Vision, Multi-Modality, Audio and Speech Processing, and Signal Processing. We analyze the impact of highly influential transformer-based models in these domains and subsequently classify them based on their respective tasks using a proposed taxonomy. Our aim is to shed light on the existing potential and future possibilities of transformers for enthusiastic researchers, thus contributing to the broader understanding of this groundbreaking technology.

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.

Convolutional Neural Networks (CNN) have shown promising results for the task of Handwritten Text Recognition (HTR) but they still fall behind Recurrent Neural Networks (RNNs)/Transformer based models in terms of performance. In this paper, we propose a CNN based architecture that bridges this gap. Our work, Easter2.0, is composed of multiple layers of 1D Convolution, Batch Normalization, ReLU, Dropout, Dense Residual connection, Squeeze-and-Excitation module and make use of Connectionist Temporal Classification (CTC) loss. In addition to the Easter2.0 architecture, we propose a simple and effective data augmentation technique 'Tiling and Corruption (TACO)' relevant for the task of HTR/OCR. Our work achieves state-of-the-art results on IAM handwriting database when trained using only publicly available training data. In our experiments, we also present the impact of TACO augmentations and Squeeze-and-Excitation (SE) on text recognition accuracy. We further show that Easter2.0 is suitable for few-shot learning tasks and outperforms current best methods including Transformers when trained on limited amount of annotated data. Code and model is available at: https://github.com/kartikgill/Easter2

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.

Long short-term memory (LSTM) models are a particular type of recurrent neural networks (RNNs) that are central to sequential modeling tasks in domains such as urban telecommunication forecasting, where temporal correlations and nonlinear dependencies dominate. However, conventional LSTMs suffer from high parameter redundancy and limited nonlinear expressivity. In this work, we propose the Quantum-inspired Kolmogorov-Arnold Long Short-Term Memory (QKAN-LSTM), which integrates Data Re-Uploading Activation (DARUAN) modules into the gating structure of LSTMs. Each DARUAN acts as a quantum variational activation function (QVAF), enhancing frequency adaptability and enabling an exponentially enriched spectral representation without multi-qubit entanglement. The resulting architecture preserves quantum-level expressivity while remaining fully executable on classical hardware. Empirical evaluations on three datasets, Damped Simple Harmonic Motion, Bessel Function, and Urban Telecommunication, demonstrate that QKAN-LSTM achieves superior predictive accuracy and generalization with a 79% reduction in trainable parameters compared to classical LSTMs. We extend the framework to the Jiang-Huang-Chen-Goan Network (JHCG Net), which generalizes KAN to encoder-decoder structures, and then further use QKAN to realize the latent KAN, thereby creating a Hybrid QKAN (HQKAN) for hierarchical representation learning. The proposed HQKAN-LSTM thus provides a scalable and interpretable pathway toward quantum-inspired sequential modeling in real-world data environments.

Most frame-based learned video codecs can be interpreted as recurrent neural networks (RNNs) propagating reference information along the temporal dimension. This work revisits the limitations of the current approaches from an RNN perspective. The output-recurrence methods, which propagate decoded frames, are intuitive but impose dual constraints on the output decoded frames, leading to suboptimal rate-distortion performance. In contrast, the hidden-to-hidden connection approaches, which propagate latent features within the RNN, offer greater flexibility but require large buffer sizes. To address these issues, we propose HyTIP, a learned video coding framework that combines both mechanisms. Our hybrid buffering strategy uses explicit decoded frames and a small number of implicit latent features to achieve competitive coding performance. Experimental results show that our HyTIP outperforms the sole use of either output-recurrence or hidden-to-hidden approaches. Furthermore, it achieves comparable performance to state-of-the-art methods but with a much smaller buffer size, and outperforms VTM 17.0 (Low-delay B) in terms of PSNR-RGB and MS-SSIM-RGB. The source code of HyTIP is available at https://github.com/NYCU-MAPL/HyTIP.

In real-world applications of natural language generation, there are often constraints on the target sentences in addition to fluency and naturalness requirements. Existing language generation techniques are usually based on recurrent neural networks (RNNs). However, it is non-trivial to impose constraints on RNNs while maintaining generation quality, since RNNs generate sentences sequentially (or with beam search) from the first word to the last. In this paper, we propose CGMH, a novel approach using Metropolis-Hastings sampling for constrained sentence generation. CGMH allows complicated constraints such as the occurrence of multiple keywords in the target sentences, which cannot be handled in traditional RNN-based approaches. Moreover, CGMH works in the inference stage, and does not require parallel corpora for training. We evaluate our method on a variety of tasks, including keywords-to-sentence generation, unsupervised sentence paraphrasing, and unsupervised sentence error correction. CGMH achieves high performance compared with previous supervised methods for sentence generation. Our code is released at https://github.com/NingMiao/CGMH

Linear transformers have emerged as a subquadratic-time alternative to softmax attention and have garnered significant interest due to their fixed-size recurrent state that lowers inference cost. However, their original formulation suffers from poor scaling and underperforms compute-matched transformers. Recent linear models such as RWKV and Mamba have attempted to address these shortcomings by proposing novel time-mixing and gating architectures, but pre-training large language models requires significant data and compute investments. Thus, the search for subquadratic architectures is limited by the availability of compute and quality pre-training datasets. As a cost-effective alternative to pre-training linear transformers, we propose Scalable UPtraining for Recurrent Attention (SUPRA). We present a method to uptrain existing large pre-trained transformers into Recurrent Neural Networks (RNNs) with a modest compute budget. This allows us to leverage the strong pre-training data and performance of existing transformer LLMs, while requiring 5% of the training cost. We find that our linearization technique leads to competitive performance on standard benchmarks, but we identify persistent in-context learning and long-context modeling shortfalls for even the largest linear models. Our code and models can be found at https://github.com/TRI-ML/linear_open_lm.

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.

This report introduces PixelBytes Embedding, a novel approach for unified multimodal representation learning. Our method captures diverse inputs in a single, cohesive representation, enabling emergent properties for multimodal sequence generation, particularly for text and pixelated images. Inspired by state-of-the-art sequence models such as Image Transformers, PixelCNN, and Mamba-Bytes, PixelBytes aims to address the challenges of integrating different data types. We explore various model architectures, including Recurrent Neural Networks (RNNs), State Space Models (SSMs), and Attention-based models, focusing on bidirectional processing and our innovative PxBy embedding technique. Our experiments, conducted on a specialized PixelBytes Pok{\'e}mon dataset, demonstrate that bidirectional sequence models with PxBy embedding and convolutional layers can generate coherent multimodal sequences. This work contributes to the advancement of integrated AI models capable of understanding and generating multimodal data in a unified manner.

Music source separation (MSS) aims to separate a music recording into multiple musically distinct stems, such as vocals, bass, drums, and more. Recently, deep learning approaches such as convolutional neural networks (CNNs) and recurrent neural networks (RNNs) have been used, but the improvement is still limited. In this paper, we propose a novel frequency-domain approach based on a Band-Split RoPE Transformer (called BS-RoFormer). BS-RoFormer relies on a band-split module to project the input complex spectrogram into subband-level representations, and then arranges a stack of hierarchical Transformers to model the inner-band as well as inter-band sequences for multi-band mask estimation. To facilitate training the model for MSS, we propose to use the Rotary Position Embedding (RoPE). The BS-RoFormer system trained on MUSDB18HQ and 500 extra songs ranked the first place in the MSS track of Sound Demixing Challenge (SDX23). Benchmarking a smaller version of BS-RoFormer on MUSDB18HQ, we achieve state-of-the-art result without extra training data, with 9.80 dB of average SDR.

This report presents PixelBytes, an approach for unified multimodal representation learning. Drawing inspiration from sequence models like Image Transformers, PixelCNN, and Mamba-Bytes, we explore integrating text, audio, action-state, and pixelated images (sprites) into a cohesive representation. We conducted experiments on a PixelBytes Pokemon dataset and an Optimal-Control dataset. Our investigation covered various model architectures, including Recurrent Neural Networks (RNNs), State Space Models (SSMs), and Attention-based models, with a focus on bidirectional processing and our PxBy embedding technique. We evaluated models based on data reduction strategies and autoregressive learning, specifically examining Long Short-Term Memory (LSTM) networks in predictive and autoregressive modes. Our results indicate that autoregressive models perform better than predictive models in this context. Additionally, we found that diffusion models can be applied to control problems and parallelized generation. PixelBytes aims to contribute to the development of foundation models for multimodal data processing and generation. The project's code, models, and datasets are available online.

Bilevel optimization is an important formulation for many machine learning problems. Current bilevel optimization algorithms assume that the gradient of the upper-level function is Lipschitz. However, recent studies reveal that certain neural networks such as recurrent neural networks (RNNs) and long-short-term memory networks (LSTMs) exhibit potential unbounded smoothness, rendering conventional bilevel optimization algorithms unsuitable. In this paper, we design a new bilevel optimization algorithm, namely BO-REP, to address this challenge. This algorithm updates the upper-level variable using normalized momentum and incorporates two novel techniques for updating the lower-level variable: initialization refinement and periodic updates. Specifically, once the upper-level variable is initialized, a subroutine is invoked to obtain a refined estimate of the corresponding optimal lower-level variable, and the lower-level variable is updated only after every specific period instead of each iteration. When the upper-level problem is nonconvex and unbounded smooth, and the lower-level problem is strongly convex, we prove that our algorithm requires mathcal{O}(1/epsilon^4) iterations to find an epsilon-stationary point in the stochastic setting, where each iteration involves calling a stochastic gradient or Hessian-vector product oracle. Notably, this result matches the state-of-the-art complexity results under the bounded smoothness setting and without mean-squared smoothness of the stochastic gradient, up to logarithmic factors. Our proof relies on novel technical lemmas for the periodically updated lower-level variable, which are of independent interest. Our experiments on hyper-representation learning, hyperparameter optimization, and data hyper-cleaning for text classification tasks demonstrate the effectiveness of our proposed algorithm.

Recently Transformer and Convolution neural network (CNN) based models have shown promising results in Automatic Speech Recognition (ASR), outperforming Recurrent neural networks (RNNs). Transformer models are good at capturing content-based global interactions, while CNNs exploit local features effectively. In this work, we achieve the best of both worlds by studying how to combine convolution neural networks and transformers to model both local and global dependencies of an audio sequence in a parameter-efficient way. To this regard, we propose the convolution-augmented transformer for speech recognition, named Conformer. Conformer significantly outperforms the previous Transformer and CNN based models achieving state-of-the-art accuracies. On the widely used LibriSpeech benchmark, our model achieves WER of 2.1%/4.3% without using a language model and 1.9%/3.9% with an external language model on test/testother. We also observe competitive performance of 2.7%/6.3% with a small model of only 10M parameters.

To enable learning on edge devices with fast convergence and low memory, we present a novel backpropagation-free optimization algorithm dubbed Target Projection Stochastic Gradient Descent (tpSGD). tpSGD generalizes direct random target projection to work with arbitrary loss functions and extends target projection for training recurrent neural networks (RNNs) in addition to feedforward networks. tpSGD uses layer-wise stochastic gradient descent (SGD) and local targets generated via random projections of the labels to train the network layer-by-layer with only forward passes. tpSGD doesn't require retaining gradients during optimization, greatly reducing memory allocation compared to SGD backpropagation (BP) methods that require multiple instances of the entire neural network weights, input/output, and intermediate results. Our method performs comparably to BP gradient-descent within 5% accuracy on relatively shallow networks of fully connected layers, convolutional layers, and recurrent layers. tpSGD also outperforms other state-of-the-art gradient-free algorithms in shallow models consisting of multi-layer perceptrons, convolutional neural networks (CNNs), and RNNs with competitive accuracy and less memory and time. We evaluate the performance of tpSGD in training deep neural networks (e.g. VGG) and extend the approach to multi-layer RNNs. These experiments highlight new research directions related to optimized layer-based adaptor training for domain-shift using tpSGD at the edge.

Managing long texts is challenging for large language models (LLMs) due to limited context window sizes. This study introduces UIO-LLMs, an unbiased incremental optimization approach for memory-enhanced transformers under long-context settings. We initially conceptualize the process as a streamlined encoder-decoder framework where the weights-shared encoder and decoder respectively encapsulate a context segment into memories and leverage these memories to predict outputs of the subsequent segment. Subsequently, by treating our memory-enhanced transformers as fully-connected recurrent neural networks (RNNs), we refine the training process using the Truncated Backpropagation Through Time (TBPTT) algorithm, which incorporates innovative incremental optimization techniques. These techniques not only diminish time complexity but also address the bias in gradient computation through an unbiased optimization process. UIO-LLMs successfully handle long context, such as extending the context window of Llama2-7b-chat from 4K to 100K tokens with minimal 2% additional parameters, while keeping the inference cost nearly linear as context length increases.

This review presents a comprehensive exploration of hybrid and ensemble deep learning models within Natural Language Processing (NLP), shedding light on their transformative potential across diverse tasks such as Sentiment Analysis, Named Entity Recognition, Machine Translation, Question Answering, Text Classification, Generation, Speech Recognition, Summarization, and Language Modeling. The paper systematically introduces each task, delineates key architectures from Recurrent Neural Networks (RNNs) to Transformer-based models like BERT, and evaluates their performance, challenges, and computational demands. The adaptability of ensemble techniques is emphasized, highlighting their capacity to enhance various NLP applications. Challenges in implementation, including computational overhead, overfitting, and model interpretation complexities, are addressed alongside the trade-off between interpretability and performance. Serving as a concise yet invaluable guide, this review synthesizes insights into tasks, architectures, and challenges, offering a holistic perspective for researchers and practitioners aiming to advance language-driven applications through ensemble deep learning in NLP.

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.

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.

Recent advancements in sequence modeling have led to the emergence of Structured State Space Models (SSMs) as an efficient alternative to Recurrent Neural Networks (RNNs) and Transformers, addressing challenges in long-range dependency modeling and computational efficiency. While RNNs suffer from vanishing gradients and sequential inefficiencies, and Transformers face quadratic complexity, SSMs leverage structured recurrence and state-space representations to achieve superior long-sequence processing with linear or near-linear complexity. This survey provides a comprehensive review of SSMs, tracing their evolution from the foundational S4 model to its successors like Mamba, Simplified Structured State Space Sequence Model (S5), and Jamba, highlighting their improvements in computational efficiency, memory optimization, and inference speed. By comparing SSMs with traditional sequence models across domains such as natural language processing (NLP), speech recognition, vision, and time-series forecasting, we demonstrate their advantages in handling long-range dependencies while reducing computational overhead. Despite their potential, challenges remain in areas such as training optimization, hybrid modeling, and interpretability. This survey serves as a structured guide for researchers and practitioners, detailing the advancements, trade-offs, and future directions of SSM-based architectures in AI and deep learning.

Semantic representation and inference is essential for Natural Language Processing (NLP). The state of the art for semantic representation and inference is deep learning, and particularly Recurrent Neural Networks (RNNs), Convolutional Neural Networks (CNNs), and transformer Self-Attention models. This thesis investigates the use of deep learning for novel semantic representation and inference, and makes contributions in the following three areas: creating training data, improving semantic representations and extending inference learning. In terms of creating training data, we contribute the largest publicly available dataset of real-life factual claims for the purpose of automatic claim verification (MultiFC), and we present a novel inference model composed of multi-scale CNNs with different kernel sizes that learn from external sources to infer fact checking labels. In terms of improving semantic representations, we contribute a novel model that captures non-compositional semantic indicators. By definition, the meaning of a non-compositional phrase cannot be inferred from the individual meanings of its composing words (e.g., hot dog). Motivated by this, we operationalize the compositionality of a phrase contextually by enriching the phrase representation with external word embeddings and knowledge graphs. Finally, in terms of inference learning, we propose a series of novel deep learning architectures that improve inference by using syntactic dependencies, by ensembling role guided attention heads, incorporating gating layers, and concatenating multiple heads in novel and effective ways. This thesis consists of seven publications (five published and two under review).

Transformer-based large language models (LLMs) excel in modeling complex language patterns but face significant computational costs during inference, especially with long inputs due to the attention mechanism's memory overhead. We observe that certain attention heads exhibit a distribution where the attention weights concentrate on tokens near the query token, termed as recency aware, which focuses on local and short-range dependencies. Leveraging this insight, we propose RecurFormer, a novel architecture that replaces these attention heads with linear recurrent neural networks (RNNs), specifically the Mamba architecture. This replacement reduces the cache size without evicting tokens, thus maintaining generation quality. RecurFormer retains the ability to model long-range dependencies through the remaining attention heads and allows for reusing pre-trained Transformer-based LLMs weights with continual training. Experiments demonstrate that RecurFormer matches the original model's performance while significantly enhancing inference efficiency. Our approach provides a practical solution to the computational challenges of Transformer-based LLMs inference, making it highly attractive for tasks involving long inputs.

State-space models (SSMs) have emerged as a potential alternative architecture for building large language models (LLMs) compared to the previously ubiquitous transformer architecture. One theoretical weakness of transformers is that they cannot express certain kinds of sequential computation and state tracking (Merrill and Sabharwal, 2023), which SSMs are explicitly designed to address via their close architectural similarity to recurrent neural networks (RNNs). But do SSMs truly have an advantage (over transformers) in expressive power for state tracking? Surprisingly, the answer is no. Our analysis reveals that the expressive power of SSMs is limited very similarly to transformers: SSMs cannot express computation outside the complexity class TC^0. In particular, this means they cannot solve simple state-tracking problems like permutation composition. It follows that SSMs are provably unable to accurately track chess moves with certain notation, evaluate code, or track entities in a long narrative. To supplement our formal analysis, we report experiments showing that Mamba-style SSMs indeed struggle with state tracking. Thus, despite its recurrent formulation, the "state" in an SSM is an illusion: SSMs have similar expressiveness limitations to non-recurrent models like transformers, which may fundamentally limit their ability to solve real-world state-tracking problems.

Face presentation attacks (PA), also known as spoofing attacks, pose a substantial threat to biometric systems that rely on facial recognition systems, such as access control systems, mobile payments, and identity verification systems. To mitigate the spoofing risk, several video-based methods have been presented in the literature that analyze facial motion in successive video frames. However, estimating the motion between adjacent frames is a challenging task and requires high computational cost. In this paper, we rephrase the face anti-spoofing task as a motion prediction problem and introduce a deep ensemble learning model with a frame skipping mechanism. In particular, the proposed frame skipping adopts a uniform sampling approach by dividing the original video into video clips of fixed size. By doing so, every nth frame of the clip is selected to ensure that the temporal patterns can easily be perceived during the training of three different recurrent neural networks (RNNs). Motivated by the performance of individual RNNs, a meta-model is developed to improve the overall detection performance by combining the prediction of individual RNNs. Extensive experiments were performed on four datasets, and state-of-the-art performance is reported on MSU-MFSD (3.12%), Replay-Attack (11.19%), and OULU-NPU (12.23%) databases by using half total error rates (HTERs) in the most challenging cross-dataset testing scenario.

Sequential VAEs have been successfully considered for many high-dimensional time series modelling problems, with many variant models relying on discrete-time mechanisms such as recurrent neural networks (RNNs). On the other hand, continuous-time methods have recently gained attraction, especially in the context of irregularly-sampled time series, where they can better handle the data than discrete-time methods. One such class are Gaussian process variational autoencoders (GPVAEs), where the VAE prior is set as a Gaussian process (GP). However, a major limitation of GPVAEs is that it inherits the cubic computational cost as GPs, making it unattractive to practioners. In this work, we leverage the equivalent discrete state space representation of Markovian GPs to enable linear time GPVAE training via Kalman filtering and smoothing. We show on a variety of high-dimensional temporal and spatiotemporal tasks that our method performs favourably compared to existing approaches whilst being computationally highly scalable.

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

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.

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.

There is a growing body of studies on applying deep learning to biometrics analysis. Certain circumstances, however, could impair the objective measures and accuracy of the proposed biometric data analysis methods. For instance, people with chronic pain (CP) unconsciously adapt specific body movements to protect themselves from injury or additional pain. Because there is no dedicated benchmark database to analyse this correlation, we considered one of the specific circumstances that potentially influence a person's biometrics during daily activities in this study and classified pain level and pain-related behaviour in the EmoPain database. To achieve this, we proposed a sparsely-connected recurrent neural networks (s-RNNs) ensemble with the gated recurrent unit (GRU) that incorporates multiple autoencoders using a shared training framework. This architecture is fed by multidimensional data collected from inertial measurement unit (IMU) and surface electromyography (sEMG) sensors. Furthermore, to compensate for variations in the temporal dimension that may not be perfectly represented in the latent space of s-RNNs, we fused hand-crafted features derived from information-theoretic approaches with represented features in the shared hidden state. We conducted several experiments which indicate that the proposed method outperforms the state-of-the-art approaches in classifying both pain level and pain-related behaviour.

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.

This paper studies the emotion recognition from musical tracks in the 2-dimensional valence-arousal (V-A) emotional space. We propose a method based on convolutional (CNN) and recurrent neural networks (RNN), having significantly fewer parameters compared with the state-of-the-art method for the same task. We utilize one CNN layer followed by two branches of RNNs trained separately for arousal and valence. The method was evaluated using the 'MediaEval2015 emotion in music' dataset. We achieved an RMSE of 0.202 for arousal and 0.268 for valence, which is the best result reported on this dataset.

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

Analog In-memory Computing (IMC) has demonstrated energy-efficient and low latency implementation of convolution and fully-connected layers in deep neural networks (DNN) by using physics for computing in parallel resistive memory arrays. However, recurrent neural networks (RNN) that are widely used for speech-recognition and natural language processing have tasted limited success with this approach. This can be attributed to the significant time and energy penalties incurred in implementing nonlinear activation functions that are abundant in such models. In this work, we experimentally demonstrate the implementation of a non-linear activation function integrated with a ramp analog-to-digital conversion (ADC) at the periphery of the memory to improve in-memory implementation of RNNs. Our approach uses an extra column of memristors to produce an appropriately pre-distorted ramp voltage such that the comparator output directly approximates the desired nonlinear function. We experimentally demonstrate programming different nonlinear functions using a memristive array and simulate its incorporation in RNNs to solve keyword spotting and language modelling tasks. Compared to other approaches, we demonstrate manifold increase in area-efficiency, energy-efficiency and throughput due to the in-memory, programmable ramp generator that removes digital processing overhead.

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

In this work, we model abstractive text summarization using Attentional Encoder-Decoder Recurrent Neural Networks, and show that they achieve state-of-the-art performance on two different corpora. We propose several novel models that address critical problems in summarization that are not adequately modeled by the basic architecture, such as modeling key-words, capturing the hierarchy of sentence-to-word structure, and emitting words that are rare or unseen at training time. Our work shows that many of our proposed models contribute to further improvement in performance. We also propose a new dataset consisting of multi-sentence summaries, and establish performance benchmarks for further research.

We present a comprehensive study of deep bidirectional long short-term memory (LSTM) recurrent neural network (RNN) based acoustic models for automatic speech recognition (ASR). We study the effect of size and depth and train models of up to 8 layers. We investigate the training aspect and study different variants of optimization methods, batching, truncated backpropagation, different regularization techniques such as dropout and L_2 regularization, and different gradient clipping variants. The major part of the experimental analysis was performed on the Quaero corpus. Additional experiments also were performed on the Switchboard corpus. Our best LSTM model has a relative improvement in word error rate of over 14\% compared to our best feed-forward neural network (FFNN) baseline on the Quaero task. On this task, we get our best result with an 8 layer bidirectional LSTM and we show that a pretraining scheme with layer-wise construction helps for deep LSTMs. Finally we compare the training calculation time of many of the presented experiments in relation with recognition performance. All the experiments were done with RETURNN, the RWTH extensible training framework for universal recurrent neural networks in combination with RASR, the RWTH ASR toolkit.

In this paper we present two deep-learning systems that competed at SemEval-2018 Task 3 "Irony detection in English tweets". We design and ensemble two independent models, based on recurrent neural networks (Bi-LSTM), which operate at the word and character level, in order to capture both the semantic and syntactic information in tweets. Our models are augmented with a self-attention mechanism, in order to identify the most informative words. The embedding layer of our word-level model is initialized with word2vec word embeddings, pretrained on a collection of 550 million English tweets. We did not utilize any handcrafted features, lexicons or external datasets as prior information and our models are trained end-to-end using back propagation on constrained data. Furthermore, we provide visualizations of tweets with annotations for the salient tokens of the attention layer that can help to interpret the inner workings of the proposed models. We ranked 2nd out of 42 teams in Subtask A and 2nd out of 31 teams in Subtask B. However, post-task-completion enhancements of our models achieve state-of-the-art results ranking 1st for both subtasks.

This paper presents a way of doing large scale audio understanding without traditional state of the art neural architectures. Ever since the introduction of deep learning for understanding audio signals in the past decade, convolutional architectures have been able to achieve state of the art results surpassing traditional hand-crafted features. In the recent past, there has been a similar shift away from traditional convolutional and recurrent neural networks towards purely end-to-end Transformer architectures. We, in this work, explore an approach, based on Bag-of-Words model. Our approach does not have any convolutions, recurrence, attention, transformers or other approaches such as BERT. We utilize micro and macro level clustered vanilla embeddings, and use a MLP head for classification. We only use feed-forward encoder-decoder models to get the bottlenecks of spectral envelops, spectral patches and slices as well as multi-resolution spectra. A classification head (a feed-forward layer), similar to the approach in SimCLR is trained on a learned representation. Using simple codes learned on latent representations, we show how we surpass traditional convolutional neural network architectures, and come strikingly close to outperforming powerful Transformer architectures. This work hopefully would pave way for exciting advancements in the field of representation learning without massive, end-to-end neural architectures.

Recent advances in artificial neural networks for machine learning, and language modeling in particular, have established a family of recurrent neural network (RNN) architectures that, unlike conventional RNNs with vector-form hidden states, use two-dimensional (2D) matrix-form hidden states. Such 2D-state RNNs, known as Fast Weight Programmers (FWPs), can be interpreted as a neural network whose synaptic weights (called fast weights) dynamically change over time as a function of input observations, and serve as short-term memory storage; corresponding synaptic weight modifications are controlled or programmed by another network (the programmer) whose parameters are trained (e.g., by gradient descent). In this Primer, we review the technical foundations of FWPs, their computational characteristics, and their connections to transformers and state space models. We also discuss connections between FWPs and models of synaptic plasticity in the brain, suggesting a convergence of natural and artificial intelligence.

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.

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.

Neural architecture search (NAS) has allowed for the automatic creation of new and effective neural network architectures, offering an alternative to the laborious process of manually designing complex architectures. However, traditional NAS algorithms are slow and require immense amounts of computing power. Recent research has investigated training-free NAS metrics for image classification architectures, drastically speeding up search algorithms. In this paper, we investigate training-free NAS metrics for recurrent neural network (RNN) and BERT-based transformer architectures, targeted towards language modeling tasks. First, we develop a new training-free metric, named hidden covariance, that predicts the trained performance of an RNN architecture and significantly outperforms existing training-free metrics. We experimentally evaluate the effectiveness of the hidden covariance metric on the NAS-Bench-NLP benchmark. Second, we find that the current search space paradigm for transformer architectures is not optimized for training-free neural architecture search. Instead, a simple qualitative analysis can effectively shrink the search space to the best performing architectures. This conclusion is based on our investigation of existing training-free metrics and new metrics developed from recent transformer pruning literature, evaluated on our own benchmark of trained BERT architectures. Ultimately, our analysis shows that the architecture search space and the training-free metric must be developed together in order to achieve effective results.

Recent advances in recurrent neural network architectures, such as Mamba and RWKV, have enabled RNNs to match or exceed the performance of equal-size transformers in terms of language modeling perplexity and downstream evaluations, suggesting that future systems may be built on completely new architectures. In this paper, we examine if selected interpretability methods originally designed for transformer language models will transfer to these up-and-coming recurrent architectures. Specifically, we focus on steering model outputs via contrastive activation addition, on eliciting latent predictions via the tuned lens, and eliciting latent knowledge from models fine-tuned to produce false outputs under certain conditions. Our results show that most of these techniques are effective when applied to RNNs, and we show that it is possible to improve some of them by taking advantage of RNNs' compressed state.

Transformers achieve remarkable performance in several tasks but due to their quadratic complexity, with respect to the input's length, they are prohibitively slow for very long sequences. To address this limitation, we express the self-attention as a linear dot-product of kernel feature maps and make use of the associativity property of matrix products to reduce the complexity from Oleft(N^2right) to Oleft(Nright), where N is the sequence length. We show that this formulation permits an iterative implementation that dramatically accelerates autoregressive transformers and reveals their relationship to recurrent neural networks. Our linear transformers achieve similar performance to vanilla transformers and they are up to 4000x faster on autoregressive prediction of very long sequences.

We introduce the concept of multiple temporal perspectives, a novel approach applicable to Recurrent Neural Network (RNN) architectures for enhancing their understanding of sequential data. This method involves maintaining diverse temporal views of previously encountered text, significantly enriching the language models' capacity to interpret context. To show the efficacy of this approach, we incorporate it into the Receptance Weighted Key Value (RWKV) architecture, addressing its inherent challenge of retaining all historical information within a single hidden state. Notably, this improvement is achieved with a minimal increase in the number of parameters --even as little as 0.04% of the original number of parameters. Further, the additional parameters necessary for the multiple temporal perspectives are fine-tuned with minimal computational overhead, avoiding the need for a full pre-training. The resulting model maintains linear computational complexity during prompt inference, ensuring consistent efficiency across various sequence lengths. The empirical results and ablation studies included in our research validate the effectiveness of our approach, showcasing improved performance across multiple benchmarks. The code, model weights and datasets are open-sourced at: https://github.com/RazvanDu/TemporalRNNs.

Traveling waves of neural activity have been observed throughout the brain at a diversity of regions and scales; however, their precise computational role is still debated. One physically inspired hypothesis suggests that the cortical sheet may act like a wave-propagating system capable of invertibly storing a short-term memory of sequential stimuli through induced waves traveling across the cortical surface, and indeed many experimental results from neuroscience correlate wave activity with memory tasks. To date, however, the computational implications of this idea have remained hypothetical due to the lack of a simple recurrent neural network architecture capable of exhibiting such waves. In this work, we introduce a model to fill this gap, which we denote the Wave-RNN (wRNN), and demonstrate how such an architecture indeed efficiently encodes the recent past through a suite of synthetic memory tasks where wRNNs learn faster and reach significantly lower error than wave-free counterparts. We further explore the implications of this memory storage system on more complex sequence modeling tasks such as sequential image classification and find that wave-based models not only again outperform comparable wave-free RNNs while using significantly fewer parameters, but additionally perform comparably to more complex gated architectures such as LSTMs and GRUs.

In this paper we present an end-to-end speech recognition model with Transformer encoders that can be used in a streaming speech recognition system. Transformer computation blocks based on self-attention are used to encode both audio and label sequences independently. The activations from both audio and label encoders are combined with a feed-forward layer to compute a probability distribution over the label space for every combination of acoustic frame position and label history. This is similar to the Recurrent Neural Network Transducer (RNN-T) model, which uses RNNs for information encoding instead of Transformer encoders. The model is trained with the RNN-T loss well-suited to streaming decoding. We present results on the LibriSpeech dataset showing that limiting the left context for self-attention in the Transformer layers makes decoding computationally tractable for streaming, with only a slight degradation in accuracy. We also show that the full attention version of our model beats the-state-of-the art accuracy on the LibriSpeech benchmarks. Our results also show that we can bridge the gap between full attention and limited attention versions of our model by attending to a limited number of future frames.

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).

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.

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.

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.

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.

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.

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.

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.

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.

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.

This paper describes a novel text-to-speech (TTS) technique based on deep convolutional neural networks (CNN), without use of any recurrent units. Recurrent neural networks (RNN) have become a standard technique to model sequential data recently, and this technique has been used in some cutting-edge neural TTS techniques. However, training RNN components often requires a very powerful computer, or a very long time, typically several days or weeks. Recent other studies, on the other hand, have shown that CNN-based sequence synthesis can be much faster than RNN-based techniques, because of high parallelizability. The objective of this paper is to show that an alternative neural TTS based only on CNN alleviate these economic costs of training. In our experiment, the proposed Deep Convolutional TTS was sufficiently trained overnight (15 hours), using an ordinary gaming PC equipped with two GPUs, while the quality of the synthesized speech was almost acceptable.

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.

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.

This paper presents a comprehensive study on stock price prediction, leveragingadvanced machine learning (ML) and deep learning (DL) techniques to improve financial forecasting accuracy. The research evaluates the performance of various recurrent neural network (RNN) architectures, including Long Short-Term Memory (LSTM) networks, Gated Recurrent Units (GRU), and attention-based models. These models are assessed for their ability to capture complex temporal dependencies inherent in stock market data. Our findings show that attention-based models outperform other architectures, achieving the highest accuracy by capturing both short and long-term dependencies. This study contributes valuable insights into AI-driven financial forecasting, offering practical guidance for developing more accurate and efficient trading systems.

Deep learning has gained much success in sentence-level relation classification. For example, convolutional neural networks (CNN) have delivered competitive performance without much effort on feature engineering as the conventional pattern-based methods. Thus a lot of works have been produced based on CNN structures. However, a key issue that has not been well addressed by the CNN-based method is the lack of capability to learn temporal features, especially long-distance dependency between nominal pairs. In this paper, we propose a simple framework based on recurrent neural networks (RNN) and compare it with CNN-based model. To show the limitation of popular used SemEval-2010 Task 8 dataset, we introduce another dataset refined from MIMLRE(Angeli et al., 2014). Experiments on two different datasets strongly indicates that the RNN-based model can deliver better performance on relation classification, and it is particularly capable of learning long-distance relation patterns. This makes it suitable for real-world applications where complicated expressions are often involved.

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.

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.

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.

A Recurrent Neural Network (RNN) was used to perform video frame prediction of microbial growth for a population of two mutants of Pseudomonas aeruginosa. The RNN was trained on videos of 20 frames that were acquired using fluorescence microscopy and microfluidics. The network predicted the last 10 frames of each video, and the accuracy's of the predictions was assessed by comparing raw images, population curves, and the number and size of individual colonies. Overall, we found the predictions to be accurate using this approach. The implications this result has on designing autonomous experiments in microbiology, and the steps that can be taken to make the predictions even more accurate, are discussed.