Daily Papers

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.

Recurrent neural networks (RNNs) are a cornerstone of sequence modeling across various scientific and industrial applications. Owing to their versatility, numerous RNN variants have been proposed over the past decade, aiming to improve the modeling of long-term dependencies and to address challenges such as vanishing and exploding gradients. However, no central library is available to test these variations, and reimplementing diverse architectures can be time-consuming and error-prone, limiting reproducibility and exploration. Here, we introduce three open-source libraries in Julia and Python that centralize numerous recurrent cell implementations and higher-level recurrent architectures. torchrecurrent, RecurrentLayers.jl, and LuxRecurrentLayers.jl offer a consistent framework for constructing and extending RNN models, providing built-in mechanisms for customization and experimentation. All packages are available under the MIT license and actively maintained on GitHub.

The leading approaches in language modeling are all obsessed with TV shows of my youth - namely Transformers and Sesame Street. Transformers this, Transformers that, and over here a bonfire worth of GPU-TPU-neuromorphic wafer scale silicon. We opt for the lazy path of old and proven techniques with a fancy crypto inspired acronym: the Single Headed Attention RNN (SHA-RNN). The author's lone goal is to show that the entire field might have evolved a different direction if we had instead been obsessed with a slightly different acronym and slightly different result. We take a previously strong language model based only on boring LSTMs and get it to within a stone's throw of a stone's throw of state-of-the-art byte level language model results on enwik8. This work has undergone no intensive hyperparameter optimization and lived entirely on a commodity desktop machine that made the author's small studio apartment far too warm in the midst of a San Franciscan summer. The final results are achievable in plus or minus 24 hours on a single GPU as the author is impatient. The attention mechanism is also readily extended to large contexts with minimal computation. Take that Sesame Street.

Vision-Language Models (VLMs) encode images into lengthy sequences of visual tokens, leading to excessive computational overhead and limited inference efficiency. While prior efforts prune or merge tokens to address this issue, they often rely on special tokens (e.g., CLS) or require task-specific training, hindering scalability across architectures. In this paper, we propose HiPrune, a training-free and model-agnostic token Pruning framework that exploits the Hierarchical attention structure within vision encoders. We identify that middle layers attend to object-centric regions, while deep layers capture global contextual features. Based on this observation, HiPrune selects three types of informative tokens: (1) Anchor tokens with high attention in object-centric layers, (2) Buffer tokens adjacent to anchors for spatial continuity, and (3) Register tokens with strong attention in deep layers for global summarization. Our method requires no retraining and integrates seamlessly with any ViT-based VLM. Extensive experiments on LLaVA-1.5, LLaVA-NeXT, and Qwen2.5-VL demonstrate that HiPrune achieves state-of-the-art pruning performance, preserving up to 99.3% task accuracy with only 33.3% tokens, and maintaining 99.5% accuracy with just 11.1% tokens. Meanwhile, it reduces inference FLOPs and latency by up to 9times, showcasing strong generalization across models and tasks. Code is available at https://github.com/Danielement321/HiPrune.

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.

Large language models are strong sequence predictors, yet standard inference relies on immutable context histories. After making an error at generation step t, the model lacks an updatable memory mechanism that improves predictions for step t+1. We propose LLM-as-RNN, an inference-only framework that turns a frozen LLM into a recurrent predictor by representing its hidden state as natural-language memory. This state, implemented as a structured system-prompt summary, is updated at each timestep via feedback-driven text rewrites, enabling learning without parameter updates. Under a fixed token budget, LLM-as-RNN corrects errors and retains task-relevant patterns, effectively performing online learning through language. We evaluate the method on three sequential benchmarks in healthcare, meteorology, and finance across Llama, Gemma, and GPT model families. LLM-as-RNN significantly outperforms zero-shot, full-history, and MemPrompt baselines, improving predictive accuracy by 6.5% on average, while producing interpretable, human-readable learning traces absent in standard context accumulation.

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

Recurrent neural 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.

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.

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

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.

Animals ranging from rats to humans can demonstrate cognitive map capabilities. We evolved weights in a biologically plausible recurrent neural network (RNN) using an evolutionary algorithm to replicate the behavior and neural activity observed in rats during a spatial and working memory task in a triple T-maze. The rat was simulated in the Webots robot simulator and used vision, distance and accelerometer sensors to navigate a virtual maze. After evolving weights from sensory inputs to the RNN, within the RNN, and from the RNN to the robot's motors, the Webots agent successfully navigated the space to reach all four reward arms with minimal repeats before time-out. Our current findings suggest that it is the RNN dynamics that are key to performance, and that performance is not dependent on any one sensory type, which suggests that neurons in the RNN are performing mixed selectivity and conjunctive coding. Moreover, the RNN activity resembles spatial information and trajectory-dependent coding observed in the hippocampus. Collectively, the evolved RNN exhibits navigation skills, spatial memory, and working memory. Our method demonstrates how the dynamic activity in evolved RNNs can capture interesting and complex cognitive behavior and may be used to create RNN controllers for robotic applications.

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.

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.

While Transformers and other sequence-parallelizable neural network architectures seem like the current state of the art in sequence modeling, they specifically lack state-tracking capabilities. These are important for time-series tasks and logical reasoning. Traditional RNNs like LSTMs and GRUs, as well as modern variants like sLSTM do have these capabilities at the cost of strictly sequential processing. While this is often seen as a strong limitation, we show how fast these networks can get with our hardware-optimization FlashRNN in Triton and CUDA, optimizing kernels to the register level on modern GPUs. We extend traditional RNNs with a parallelization variant that processes multiple RNNs of smaller hidden state in parallel, similar to the head-wise processing in Transformers. To enable flexibility on different GPU variants, we introduce a new optimization framework for hardware-internal cache sizes, memory and compute handling. It models the hardware in a setting using polyhedral-like constraints, including the notion of divisibility. This speeds up the solution process in our ConstrINT library for general integer constraint satisfaction problems (integer CSPs). We show that our kernels can achieve 50x speed-ups over a vanilla PyTorch implementation and allow 40x larger hidden sizes compared to our Triton implementation. Our open-source kernels and the optimization library are released here to boost research in the direction of state-tracking enabled RNNs and sequence modeling: https://github.com/NX-AI/flashrnn

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

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.

State-space models (SSMs) offer a promising architecture for sequence modeling, providing an alternative to Transformers by replacing expensive self-attention with linear recurrences. In this paper, we propose a simple yet effective trick to enhance SSMs within given computational budgets by sparsifying them. Our intuition is that tokens in SSMs are highly redundant due to gradual recurrent updates, and dense recurrence operations block the delivery of past information. In particular, we observe that upper layers of SSMs tend to be more redundant as they encode global information, while lower layers encode local information. Motivated by this, we introduce Simba, a hierarchical sparsification method for SSMs based on token pruning. Simba sparsifies upper layers more than lower layers, encouraging the upper layers to behave like highways. To achieve this, we propose a novel token pruning criterion for SSMs, measuring the global impact of tokens on the final output by accumulating local recurrences. We demonstrate that Simba outperforms the baseline model, Mamba, with the same FLOPS in various natural language tasks. Moreover, we illustrate the effect of highways, showing that Simba not only enhances efficiency but also improves the information flow across long sequences. Code is available at https://github.com/woominsong/Simba.

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.

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.

The integration of Large Language Models (LLMs) into healthcare promises to transform medical diagnostics, research, and patient care. Yet, the progression of medical LLMs faces obstacles such as complex training requirements, rigorous evaluation demands, and the dominance of proprietary models that restrict academic exploration. Transparent, comprehensive access to LLM resources is essential for advancing the field, fostering reproducibility, and encouraging innovation in healthcare AI. We present Hippocrates, an open-source LLM framework specifically developed for the medical domain. In stark contrast to previous efforts, it offers unrestricted access to its training datasets, codebase, checkpoints, and evaluation protocols. This open approach is designed to stimulate collaborative research, allowing the community to build upon, refine, and rigorously evaluate medical LLMs within a transparent ecosystem. Also, we introduce Hippo, a family of 7B models tailored for the medical domain, fine-tuned from Mistral and LLaMA2 through continual pre-training, instruction tuning, and reinforcement learning from human and AI feedback. Our models outperform existing open medical LLMs models by a large-margin, even surpassing models with 70B parameters. Through Hippocrates, we aspire to unlock the full potential of LLMs not just to advance medical knowledge and patient care but also to democratize the benefits of AI research in healthcare, making them available across the globe.

We propose a one-step constrained (OSC) beam search to accelerate recurrent neural network (RNN) transducer (RNN-T) inference. The original RNN-T beam search has a while-loop leading to speed down of the decoding process. The OSC beam search eliminates this while-loop by vectorizing multiple hypotheses. This vectorization is nontrivial as the expansion of the hypotheses within the original RNN-T beam search can be different from each other. However, we found that the hypotheses expanded only once at each decoding step in most cases; thus, we constrained the maximum expansion number to one, thereby allowing vectorization of the hypotheses. For further acceleration, we assign constraints to the prefixes of the hypotheses to prune the redundant search space. In addition, OSC beam search has duplication check among hypotheses during the decoding process as duplication can undesirably shrink the search space. We achieved significant speedup compared with other RNN-T beam search methods with lower phoneme and word error rate.

Random Neural Networks (RNNs) are a class of Neural Networks (NNs) that can also be seen as a specific type of queuing network. They have been successfully used in several domains during the last 25 years, as queuing networks to analyze the performance of resource sharing in many engineering areas, as learning tools and in combinatorial optimization, where they are seen as neural systems, and also as models of neurological aspects of living beings. In this article we focus on their learning capabilities, and more specifically, we present a practical guide for using the RNN to solve supervised learning problems. We give a general description of these models using almost indistinctly the terminology of Queuing Theory and the neural one. We present the standard learning procedures used by RNNs, adapted from similar well-established improvements in the standard NN field. We describe in particular a set of learning algorithms covering techniques based on the use of first order and, then, of second order derivatives. We also discuss some issues related to these objects and present new perspectives about their use in supervised learning problems. The tutorial describes their most relevant applications, and also provides a large bibliography.

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

Recurrent neural networks are a widely used class of neural architectures. They have, however, two shortcomings. First, they are often treated as black-box models and as such it is difficult to understand what exactly they learn as well as how they arrive at a particular prediction. Second, they tend to work poorly on sequences requiring long-term memorization, despite having this capacity in principle. We aim to address both shortcomings with a class of recurrent networks that use a stochastic state transition mechanism between cell applications. This mechanism, which we term state-regularization, makes RNNs transition between a finite set of learnable states. We evaluate state-regularized RNNs on (1) regular languages for the purpose of automata extraction; (2) non-regular languages such as balanced parentheses and palindromes where external memory is required; and (3) real-word sequence learning tasks for sentiment analysis, visual object recognition and text categorisation. We show that state-regularization (a) simplifies the extraction of finite state automata that display an RNN's state transition dynamic; (b) forces RNNs to operate more like automata with external memory and less like finite state machines, which potentiality leads to a more structural memory; (c) leads to better interpretability and explainability of RNNs by leveraging the probabilistic finite state transition mechanism over time steps.

This work explores hypernetworks: an approach of using a one network, also known as a hypernetwork, to generate the weights for another network. Hypernetworks provide an abstraction that is similar to what is found in nature: the relationship between a genotype - the hypernetwork - and a phenotype - the main network. Though they are also reminiscent of HyperNEAT in evolution, our hypernetworks are trained end-to-end with backpropagation and thus are usually faster. The focus of this work is to make hypernetworks useful for deep convolutional networks and long recurrent networks, where hypernetworks can be viewed as relaxed form of weight-sharing across layers. Our main result is that hypernetworks can generate non-shared weights for LSTM and achieve near state-of-the-art results on a variety of sequence modelling tasks including character-level language modelling, handwriting generation and neural machine translation, challenging the weight-sharing paradigm for recurrent networks. Our results also show that hypernetworks applied to convolutional networks still achieve respectable results for image recognition tasks compared to state-of-the-art baseline models while requiring fewer learnable parameters.

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.

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.

Recurrent neural networks (RNNs) are central to sequence modeling tasks, yet their high computational complexity poses challenges for scalability and real-time deployment. Traditional pruning techniques, predominantly based on weight magnitudes, often overlook the intrinsic structural properties of these networks. We introduce a novel framework that models RNNs as partially ordered sets (posets) and constructs corresponding dependency lattices. By identifying meet irreducible neurons, our lattice-based pruning algorithm selectively retains critical connections while eliminating redundant ones. The method is implemented using both binary and continuous-valued adjacency matrices to capture different aspects of network connectivity. Evaluated on the MNIST dataset, our approach exhibits a clear trade-off between sparsity and classification accuracy. Moderate pruning maintains accuracy above 98%, while aggressive pruning achieves higher sparsity with only a modest performance decline. Unlike conventional magnitude-based pruning, our method leverages the structural organization of RNNs, resulting in more effective preservation of functional connectivity and improved efficiency in multilayer networks with top-down feedback. The proposed lattice-based pruning framework offers a rigorous and scalable approach for reducing RNN complexity while sustaining robust performance, paving the way for more efficient hierarchical models in both machine learning and computational neuroscience.

Large Language Models (LLMs) frequently suffer from inefficiencies, largely attributable to the discord between the requirements of auto-regressive decoding and the architecture of contemporary GPUs. Recently, regressive lightweight speculative decoding has garnered attention for its notable efficiency improvements in text generation tasks. This approach utilizes a lightweight regressive draft model, like a Recurrent Neural Network (RNN) or a single transformer decoder layer, leveraging sequential information to iteratively predict potential tokens. Specifically, RNN draft models are computationally economical but tend to deliver lower accuracy, while attention decoder layer models exhibit the opposite traits. This paper presents Clover-2, an advanced iteration of Clover, an RNN-based draft model designed to achieve comparable accuracy to that of attention decoder layer models while maintaining minimal computational overhead. Clover-2 enhances the model architecture and incorporates knowledge distillation to increase Clover's accuracy and improve overall efficiency. We conducted experiments using the open-source Vicuna 7B and LLaMA3-Instruct 8B models. The results demonstrate that Clover-2 surpasses existing methods across various model architectures, showcasing its efficacy and robustness.

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.

We present Eagle (RWKV-5) and Finch (RWKV-6), sequence models improving upon the RWKV (RWKV-4) architecture. Our architectural design advancements include multi-headed matrix-valued states and a dynamic recurrence mechanism that improve expressivity while maintaining the inference efficiency characteristics of RNNs. We introduce a new multilingual corpus with 1.12 trillion tokens and a fast tokenizer based on greedy matching for enhanced multilinguality. We trained four Eagle models, ranging from 0.46 to 7.5 billion parameters, and two Finch models with 1.6 and 3.1 billion parameters and find that they achieve competitive performance across a wide variety of benchmarks. We release all our models on HuggingFace under the Apache 2.0 license. Models at: https://huggingface.co/RWKV Training code at: https://github.com/RWKV/RWKV-LM Inference code at: https://github.com/RWKV/ChatRWKV Time-parallel training code at: https://github.com/RWKV/RWKV-infctx-trainer

Sequence models based on linear state spaces (SSMs) have recently emerged as a promising choice of architecture for modeling long range dependencies across various modalities. However, they invariably rely on discretization of a continuous state space, which complicates their presentation and understanding. In this work, we dispose of the discretization step, and propose a model based on vanilla Diagonal Linear RNNs (DLR). We empirically show that, despite being conceptually much simpler, DLR is as performant as previously-proposed SSMs on a variety of tasks and benchmarks including Long Range Arena and raw speech classification. Moreover, we characterize the expressivity of SSMs (including DLR) and attention-based models via a suite of 13 synthetic sequence-to-sequence tasks involving interactions over tens of thousands of tokens, ranging from simple operations, such as shifting an input sequence, to detecting co-dependent visual features over long spatial ranges in flattened images. We find that while SSMs report near-perfect performance on tasks that can be modeled via few convolutional kernels, they struggle on tasks requiring many such kernels and especially when the desired sequence manipulation is context-dependent. Despite these limitations, DLR reaches high performance on two higher-order reasoning tasks ListOpsSubTrees and PathfinderSegmentation-256 with input lengths 8K and 65K respectively, and gives encouraging performance on PathfinderSegmentation-512 with input length 262K for which attention is not a viable choice.

This paper presents a challenge to the community: given a large corpus of written text aligned to its normalized spoken form, train an RNN to learn the correct normalization function. We present a data set of general text where the normalizations were generated using an existing text normalization component of a text-to-speech system. This data set will be released open-source in the near future. We also present our own experiments with this data set with a variety of different RNN architectures. While some of the architectures do in fact produce very good results when measured in terms of overall accuracy, the errors that are produced are problematic, since they would convey completely the wrong message if such a system were deployed in a speech application. On the other hand, we show that a simple FST-based filter can mitigate those errors, and achieve a level of accuracy not achievable by the RNN alone. Though our conclusions are largely negative on this point, we are actually not arguing that the text normalization problem is intractable using an pure RNN approach, merely that it is not going to be something that can be solved merely by having huge amounts of annotated text data and feeding that to a general RNN model. And when we open-source our data, we will be providing a novel data set for sequence-to-sequence modeling in the hopes that the the community can find better solutions. The data used in this work have been released and are available at: https://github.com/rwsproat/text-normalization-data

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 lung radiotherapy, infrared cameras can track reflective objects on the chest to estimate tumor motion due to breathing, but treatment system latencies hinder radiation beam precision. Real-time recurrent learning (RTRL) is a potential solution that can learn patterns within non-stationary respiratory data but has high complexity. This study assesses the capabilities of resource-efficient online RNN algorithms, namely unbiased online recurrent optimization (UORO), sparse-1 step approximation (SnAp-1), and decoupled neural interfaces (DNI) to forecast respiratory motion during radiotherapy treatment accurately. We use time series containing the 3D positions of external markers on the chest of healthy subjects. We propose efficient implementations for SnAp-1 and DNI that compress the influence and immediate Jacobian matrices and accurately update the linear coefficients used in credit assignment estimation, respectively. Data was originally sampled at 10Hz; we resampled it at 3.33Hz and 30Hz to analyze the effect of the sampling rate on performance. We use UORO, SnAp-1, and DNI to forecast each marker's 3D position with horizons h<=2.1s (the time interval in advance for which the prediction is made) and compare them with RTRL, least mean squares, kernel support vector regression, and linear regression. RNNs trained online achieved similar or better accuracy than most previous works using larger training databases and deep learning, even though we used only the first minute of each sequence to predict motion within that exact sequence. SnAp-1 had the lowest normalized root mean square errors (nRMSEs) averaged over the horizon values considered, equal to 0.335 and 0.157, at 3.33Hz and 10.0Hz, respectively. Similarly, UORO had the lowest nRMSE at 30Hz, equal to 0.086. DNI's inference time (6.8ms per time step at 30Hz, Intel Core i7-13700 CPU) was the lowest among the RNN methods.

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.

In modern large language models (LLMs), increasing sequence lengths is a crucial challenge for enhancing their comprehension and coherence in handling complex tasks such as multi-modal question answering. However, handling long context sequences with LLMs is prohibitively costly due to the conventional attention mechanism's quadratic time and space complexity, and the context window size is limited by the GPU memory. Although recent works have proposed linear and sparse attention mechanisms to address this issue, their real-world applicability is often limited by the need to re-train pre-trained models. In response, we propose a novel approach, Hierarchically Pruned Attention (HiP), which simultaneously reduces the training and inference time complexity from O(T^2) to O(T log T) and the space complexity from O(T^2) to O(T). To this end, we devise a dynamic sparse attention mechanism that generates an attention mask through a novel tree-search-like algorithm for a given query on the fly. HiP is training-free as it only utilizes the pre-trained attention scores to spot the positions of the top-k most significant elements for each query. Moreover, it ensures that no token is overlooked, unlike the sliding window-based sub-quadratic attention methods, such as StreamingLLM. Extensive experiments on diverse real-world benchmarks demonstrate that HiP significantly reduces prompt (i.e., prefill) and decoding latency and memory usage while maintaining high generation performance with little or no degradation. As HiP allows pretrained LLMs to scale to millions of tokens on commodity GPUs with no additional engineering due to its easy plug-and-play deployment, we believe that our work will have a large practical impact, opening up the possibility to many long-context LLM applications previously infeasible.

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.

Transformers are highly parallel but are limited to computations in the TC^0 complexity class, excluding tasks such as entity tracking and code execution that provably require greater expressive power. Motivated by this limitation, we revisit non-linear Recurrent Neural Networks (RNNs) for language modeling and introduce Matrix-to-Matrix RNN (M^2RNN): an architecture with matrix-valued hidden states and expressive non-linear state transitions. We demonstrate that the language modeling performance of non-linear RNNs is limited by their state size. We also demonstrate how the state size expansion mechanism enables efficient use of tensor cores. Empirically, M^2RNN achieves perfect state tracking generalization at sequence lengths not seen during training. These benefits also translate to large-scale language modeling. In hybrid settings that interleave recurrent layers with attention, Hybrid M^2RNN outperforms equivalent Gated DeltaNet hybrids by 0.4-0.5 perplexity points on a 7B MoE model, while using 3times smaller state sizes for the recurrent layers. Notably, replacing even a single recurrent layer with M^2RNN in an existing hybrid architecture yields accuracy gains comparable to Hybrid M^2RNN with minimal impact on training throughput. Further, the Hybrid Gated DeltaNet models with a single M^2RNN layer also achieve superior long-context generalization, outperforming state-of-the-art hybrid linear attention architectures by up to 8 points on LongBench. Together, these results establish non-linear RNN layers as a compelling building block for efficient and scalable language models.

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.

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.

Deep Learning based models are currently dominating most state-of-the-art solutions for disease prediction. Existing works employ RNNs along with multiple levels of attention mechanisms to provide interpretability. These deep learning models, with trainable parameters running into millions, require huge amounts of compute and data to train and deploy. These requirements are sometimes so huge that they render usage of such models as unfeasible. We address these challenges by developing a simpler yet interpretable non-deep learning based model for application to EHR data. We model and showcase our work's results on the task of predicting first occurrence of a diagnosis, often overlooked in existing works. We push the capabilities of a tree based model and come up with a strong baseline for more sophisticated models. Its performance shows an improvement over deep learning based solutions (both, with and without the first-occurrence constraint) all the while maintaining interpretability.

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.

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.

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.

Recurrent neural networks are the foundation of many sequence-to-sequence models in machine learning, such as machine translation and speech synthesis. In contrast, applied quantum computing is in its infancy. Nevertheless there already exist quantum machine learning models such as variational quantum eigensolvers which have been used successfully e.g. in the context of energy minimization tasks. In this work we construct a quantum recurrent neural network (QRNN) with demonstrable performance on non-trivial tasks such as sequence learning and integer digit classification. The QRNN cell is built from parametrized quantum neurons, which, in conjunction with amplitude amplification, create a nonlinear activation of polynomials of its inputs and cell state, and allow the extraction of a probability distribution over predicted classes at each step. To study the model's performance, we provide an implementation in pytorch, which allows the relatively efficient optimization of parametrized quantum circuits with thousands of parameters. We establish a QRNN training setup by benchmarking optimization hyperparameters, and analyse suitable network topologies for simple memorisation and sequence prediction tasks from Elman's seminal paper (1990) on temporal structure learning. We then proceed to evaluate the QRNN on MNIST classification, both by feeding the QRNN each image pixel-by-pixel; and by utilising modern data augmentation as preprocessing step. Finally, we analyse to what extent the unitary nature of the network counteracts the vanishing gradient problem that plagues many existing quantum classifiers and classical RNNs.

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 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.

Linear recurrent neural networks (RNNs) and state-space models (SSMs) such as Mamba have become promising alternatives to softmax-attention as sequence mixing layers in Transformer architectures. Current models, however, do not exhibit the full state-tracking expressivity of RNNs because they rely on channel-wise (i.e. diagonal) sequence mixing. In this paper, we investigate parameterizations of a large class of dense linear RNNs as fixed-points of parallelizable diagonal linear RNNs. The resulting models can naturally trade expressivity for efficiency at a fixed number of parameters and achieve state-of-the-art results on the state-tracking benchmarks A_5 and S_5, while matching performance on copying and other tasks.

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.

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.

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.

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.

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

In order to thrive in hostile and ever-changing natural environments, mammalian brains evolved to store large amounts of knowledge about the world and continually integrate new information while avoiding catastrophic forgetting. Despite the impressive accomplishments, large language models (LLMs), even with retrieval-augmented generation (RAG), still struggle to efficiently and effectively integrate a large amount of new experiences after pre-training. In this work, we introduce HippoRAG, a novel retrieval framework inspired by the hippocampal indexing theory of human long-term memory to enable deeper and more efficient knowledge integration over new experiences. HippoRAG synergistically orchestrates LLMs, knowledge graphs, and the Personalized PageRank algorithm to mimic the different roles of neocortex and hippocampus in human memory. We compare HippoRAG with existing RAG methods on multi-hop question answering and show that our method outperforms the state-of-the-art methods remarkably, by up to 20%. Single-step retrieval with HippoRAG achieves comparable or better performance than iterative retrieval like IRCoT while being 10-30 times cheaper and 6-13 times faster, and integrating HippoRAG into IRCoT brings further substantial gains. Finally, we show that our method can tackle new types of scenarios that are out of reach of existing methods. Code and data are available at https://github.com/OSU-NLP-Group/HippoRAG.

Large-scale pre-trained models (PTMs) such as BERT and GPT have recently achieved great success in Natural Language Processing and Computer Vision domains. However, the development of PTMs on healthcare time-series data is lagging behind.This underscores the limitations of the existing transformer-based architectures, particularly their scalability to handle large-scale time series and ability to capture long-term temporal dependencies. In this study, we present Timely Generative Pre-trained Transformer (TimelyGPT). TimelyGPT employs an extrapolatable position (xPos) embedding to encode trend and periodic patterns into time-series representations. It also integrates recurrent attention and temporal convolution modules to effectively capture global-local temporal dependencies. We evaluated TimelyGPT on two large-scale healthcare time series datasets corresponding to continuous biosignals and irregularly-sampled time series, respectively. Our experiments show that during pre-training, TimelyGPT excels in learning time-series representations from continuously monitored biosignals and irregularly-sampled time series data commonly observed in longitudinal electronic health records (EHRs). In forecasting continuous biosignals, TimelyGPT achieves accurate extrapolation up to 6,000 timesteps of body temperature during the sleep stage transition, given a short look-up window (i.e., prompt) containing only 2,000 timesteps. For irregularly-sampled time series, TimelyGPT with a proposed time-specific inference demonstrates high top recall scores in predicting future diagnoses using early diagnostic records, effectively handling irregular intervals between clinical records. Together, we envision TimelyGPT to be useful in a broad spectrum of health domains, including long-term patient health state forecasting and patient risk trajectory prediction.

Currently, most multimodal studies are based on large language models (LLMs) with quadratic-complexity Transformer architectures. While linear models like RNNs enjoy low inference costs, their application has been largely limited to the text-only modality. This work explores the capabilities of modern RNN architectures in multimodal contexts. We propose ModRWKV-a decoupled multimodal framework built upon the RWKV7 architecture as its LLM backbone-which achieves multi-source information fusion through dynamically adaptable heterogeneous modality encoders. We designed the multimodal modules in ModRWKV with an extremely lightweight architecture and, through extensive experiments, identified a configuration that achieves an optimal balance between performance and computational efficiency. ModRWKV leverages the pretrained weights of the RWKV7 LLM for initialization, which significantly accelerates multimodal training. Comparative experiments with different pretrained checkpoints further demonstrate that such initialization plays a crucial role in enhancing the model's ability to understand multimodal signals. Supported by extensive experiments, we conclude that modern RNN architectures present a viable alternative to Transformers in the domain of multimodal large language models (MLLMs). Furthermore, we identify the optimal configuration of the ModRWKV architecture through systematic exploration.

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

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

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.

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

Modern Recurrent Neural Networks (RNNs), such as RWKV, are distinguished by their powerful short-range modeling capabilities and efficient fixed-size states, which constitute a core advantage over standard Transformers. However, there is a significant lack of research into their internal state as an editable knowledge representation. To fill this gap, we first explore the representational properties of the RWKV state by proposing the DREAMSTATE framework. This framework utilizes a conditional Diffusion Transformer (DiT) to directly model the probability manifold of the state, enabling its generation and editing. The structural nature of this representation is validated through t-SNE visualizations and controlled generation experiments. After successfully uncovering and modeling the state's representational potential, we further propose a novel hybrid architecture that combines the local advantages of RNNs with global context adaptability. This architecture features a parallel DiT that processes a variable-length global context to dynamically generate and adjust the core recurrent module's WKV parameters, transforming the fixed recurrence mechanism into a context-aware dynamic function. Experiments demonstrate that this hybrid model can be trained stably via a multi-objective loss, validating its design feasibility. Our work not only opens a new research direction for RNN state representation but also provides a concrete architectural reference for future model design. The code is publicly available at: https://huggingface.co/2dgx41s/DreamState.

Long Short-Term Memory (LSTM) is a recurrent neural network (RNN) architecture that has been designed to address the vanishing and exploding gradient problems of conventional RNNs. Unlike feedforward neural networks, RNNs have cyclic connections making them powerful for modeling sequences. They have been successfully used for sequence labeling and sequence prediction tasks, such as handwriting recognition, language modeling, phonetic labeling of acoustic frames. However, in contrast to the deep neural networks, the use of RNNs in speech recognition has been limited to phone recognition in small scale tasks. In this paper, we present novel LSTM based RNN architectures which make more effective use of model parameters to train acoustic models for large vocabulary speech recognition. We train and compare LSTM, RNN and DNN models at various numbers of parameters and configurations. We show that LSTM models converge quickly and give state of the art speech recognition performance for relatively small sized models.

Transformers have become the dominant architecture for sequence modeling by using self-attention to enable expressive and highly parallel processing. However, the resulting quadratic time and memory costs limit efficiency in long-context settings. Recurrent models such as LSTMs provide explicit nonlinear state updates and strong state-tracking capabilities, yet their strictly sequential computation limits parallelism. We introduce the Parallel Recursive LSTM (PR-LSTM), a hierarchical recurrent architecture that replaces left-to-right recurrence with recursive nonlinear state composition over a balanced computation tree. Tokens are first mapped independently to latent states, which are then recursively merged by a learned gated composition block. This structure uses the reduction pattern underlying parallel scans as a fixed execution schedule, rather than assuming an associative recurrence. As a result, PR-LSTM retains nonlinear gated state representations while reducing recurrent parallel depth from linear to logarithmic. Empirically, PR-LSTM achieves strong sequence-length generalization on formal-language benchmarks, solving more tasks than standard RNN, LSTM, and Transformer baselines, while avoiding the quadratic scaling of attention. These results suggest that recurrent computation can be reorganized hierarchically to expose parallelism without restricting the transition dynamics to linear or associative forms.

Recurrent Neural Networks (RNNs) are popular models of brain function. The typical training strategy is to adjust their input-output behavior so that it matches that of the biological circuit of interest. Even though this strategy ensures that the biological and artificial networks perform the same computational task, it does not guarantee that their internal activity dynamics match. This suggests that the trained RNNs might end up performing the task employing a different internal computational mechanism, which would make them a suboptimal model of the biological circuit. In this work, we introduce a novel training strategy that allows learning not only the input-output behavior of an RNN but also its internal network dynamics, based on sparse neural recordings. We test the proposed method by training an RNN to simultaneously reproduce internal dynamics and output signals of a physiologically-inspired neural model. Specifically, this model generates the multiphasic muscle-like activity patterns typically observed during the execution of reaching movements, based on the oscillatory activation patterns concurrently observed in the motor cortex. Remarkably, we show that the reproduction of the internal dynamics is successful even when the training algorithm relies on the activities of a small subset of neurons sampled from the biological network. Furthermore, we show that training the RNNs with this method significantly improves their generalization performance. Overall, our results suggest that the proposed method is suitable for building powerful functional RNN models, which automatically capture important computational properties of the biological circuit of interest from sparse neural recordings.

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.

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.

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.

Task-trained recurrent neural networks (RNNs) are widely used in neuroscience and machine learning to model dynamical computations. To gain mechanistic insight into how neural systems solve tasks, prior work often reverse-engineers individual trained networks. However, different RNNs trained on the same task and achieving similar performance can exhibit strikingly different internal solutions, a phenomenon known as solution degeneracy. Here, we develop a unified framework to systematically quantify and control solution degeneracy across three levels: behavior, neural dynamics, and weight space. We apply this framework to 3,400 RNNs trained on four neuroscience-relevant tasks: flip-flop memory, sine wave generation, delayed discrimination, and path integration, while systematically varying task complexity, learning regime, network size, and regularization. We find that higher task complexity and stronger feature learning reduce degeneracy in neural dynamics but increase it in weight space, with mixed effects on behavior. In contrast, larger networks and structural regularization reduce degeneracy at all three levels. These findings empirically validate the Contravariance Principle and provide practical guidance for researchers seeking to tune the variability of RNN solutions, either to uncover shared neural mechanisms or to model the individual variability observed in biological systems. This work provides a principled framework for quantifying and controlling solution degeneracy in task-trained RNNs, offering new tools for building more interpretable and biologically grounded models of neural computation.

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.

The RNN-Transducer (RNN-T) framework for speech recognition has been growing in popularity, particularly for deployed real-time ASR systems, because it combines high accuracy with naturally streaming recognition. One of the drawbacks of RNN-T is that its loss function is relatively slow to compute, and can use a lot of memory. Excessive GPU memory usage can make it impractical to use RNN-T loss in cases where the vocabulary size is large: for example, for Chinese character-based ASR. We introduce a method for faster and more memory-efficient RNN-T loss computation. We first obtain pruning bounds for the RNN-T recursion using a simple joiner network that is linear in the encoder and decoder embeddings; we can evaluate this without using much memory. We then use those pruning bounds to evaluate the full, non-linear joiner network.

Comprehending extended audiovisual experiences remains a fundamental challenge for computational systems. Current approaches struggle with temporal integration and cross-modal associations that humans accomplish effortlessly through hippocampal-cortical networks. We introduce HippoMM, a biologically-inspired architecture that transforms hippocampal mechanisms into computational advantages for multimodal understanding. HippoMM implements three key innovations: (i) hippocampus-inspired pattern separation and completion specifically designed for continuous audiovisual streams, (ii) short-to-long term memory consolidation that transforms perceptual details into semantic abstractions, and (iii) cross-modal associative retrieval pathways enabling modality-crossing queries. Unlike existing retrieval systems with static indexing schemes, HippoMM dynamically forms integrated episodic representations through adaptive temporal segmentation and dual-process memory encoding. Evaluations on our challenging HippoVlog benchmark demonstrate that HippoMM significantly outperforms state-of-the-art approaches (78.2% vs. 64.2% accuracy) while providing substantially faster response times (20.4s vs. 112.5s). Our results demonstrate that translating neuroscientific memory principles into computational architectures provides a promising foundation for next-generation multimodal understanding systems. The code and benchmark dataset are publicly available at https://github.com/linyueqian/HippoMM.

Large language models (LLMs) are typically trained on shuffled corpora, yielding models whose knowledge is frozen at train time and whose temporal grounding remains poorly understood. In this work, we study the impact of pre-training dynamics on the acquisition of time-sensitive factual knowledge, focusing specifically on data ordering. Our main contributions are twofold. First, we introduce a comprehensive benchmark of over 7,000 temporally grounded questions and an evaluation protocol that enables analysis of whether models correctly associate facts with their corresponding time periods. Second, we pretrain 6B-parameter models on temporally ordered Common Crawl snapshots and compare them against standard shuffled pre-training. Our results show that sequentially trained models match shuffled baselines on general language understanding and common knowledge while consistently exhibiting more up-to-date and temporally precise knowledge. Temporally ordered pre-training yields improved factual freshness, while shuffled pre-training peaks on older data, possibly due to increased factual repetition. These findings, along with the release of our code at https://github.com/kyutai-labs/kairos , checkpoints, and datasets at https://huggingface.co/collections/kyutai/kairos provide a foundation for future research on continual learning for LLMs.

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

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

Structured state space sequence (S4) models have recently achieved state-of-the-art performance on long-range sequence modeling tasks. These models also have fast inference speeds and parallelisable training, making them potentially useful in many reinforcement learning settings. We propose a modification to a variant of S4 that enables us to initialise and reset the hidden state in parallel, allowing us to tackle reinforcement learning tasks. We show that our modified architecture runs asymptotically faster than Transformers in sequence length and performs better than RNN's on a simple memory-based task. We evaluate our modified architecture on a set of partially-observable environments and find that, in practice, our model outperforms RNN's while also running over five times faster. Then, by leveraging the model's ability to handle long-range sequences, we achieve strong performance on a challenging meta-learning task in which the agent is given a randomly-sampled continuous control environment, combined with a randomly-sampled linear projection of the environment's observations and actions. Furthermore, we show the resulting model can adapt to out-of-distribution held-out tasks. Overall, the results presented in this paper show that structured state space models are fast and performant for in-context reinforcement learning tasks. We provide code at https://github.com/luchris429/popjaxrl.

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

Tabular data contains rich structural semantics and plays a crucial role in organizing and manipulating information. To better capture these structural semantics, this paper introduces the HybrId-modal Preference oPtimizatiOn (HIPPO) model, which represents tables using both text and image, and optimizes MLLMs to effectively learn more comprehensive table information from these multiple modalities. Specifically, HIPPO samples model responses from hybrid-modal table representations and designs a modality-consistent sampling strategy to enhance response diversity and mitigate modality bias during DPO training. Experimental results on table question answering and table fact verification tasks demonstrate the effectiveness of HIPPO, achieving a 4% improvement over various table reasoning models. Further analysis reveals that HIPPO not only enhances reasoning abilities based on unimodal table representations but also facilitates the extraction of crucial and distinct semantics from different modal representations. All data and codes are available at https://github.com/NEUIR/HIPPO.

Autoregressive language models are constrained by their inherently sequential nature, generating one token at a time. This paradigm limits inference speed and parallelism, especially during later stages of generation when the direction and semantics of text are relatively certain. In this work, we propose a novel framework that leverages the inherent knowledge of vanilla autoregressive language models about future tokens, combining techniques to realize this potential and enable simultaneous prediction of multiple subsequent tokens. Our approach introduces several key innovations: (1) a masked-input formulation where multiple future tokens are jointly predicted from a common prefix; (2) a gated LoRA formulation that preserves the original LLM's functionality, while equipping it for multi-token prediction; (3) a lightweight, learnable sampler module that generates coherent sequences from the predicted future tokens; (4) a set of auxiliary training losses, including a consistency loss, to enhance the coherence and accuracy of jointly generated tokens; and (5) a speculative generation strategy that expands tokens quadratically in the future while maintaining high fidelity. Our method achieves significant speedups through supervised fine-tuning on pretrained models. For example, it generates code and math nearly 5x faster, and improves general chat and knowledge tasks by almost 2.5x. These gains come without any loss in quality.

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.

How to better utilize sequential information has been extensively studied in the setting of recommender systems. To this end, architectural inductive biases such as Markov-Chains, Recurrent models, Convolutional networks and many others have demonstrated reasonable success on this task. This paper proposes a new neural architecture, multi-scale Quasi-RNN for next item Recommendation (QR-Rec) task. Our model provides the best of both worlds by exploiting multi-scale convolutional features as the compositional gating functions of a recurrent cell. The model is implemented in a multi-scale fashion, i.e., convolutional filters of various widths are implemented to capture different union-level features of input sequences which influence the compositional encoder. The key idea aims to capture the recurrent relations between different kinds of local features, which has never been studied previously in the context of recommendation. Through extensive experiments, we demonstrate that our model achieves state-of-the-art performance on 15 well-established datasets, outperforming strong competitors such as FPMC, Fossil and Caser absolutely by 0.57%-7.16% and relatively by 1.44%-17.65% in terms of MAP, Recall@10 and NDCG@10.

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.

We introduce Chronos, a simple yet effective framework for pretrained probabilistic time series models. Chronos tokenizes time series values using scaling and quantization into a fixed vocabulary and trains existing transformer-based language model architectures on these tokenized time series via the cross-entropy loss. We pretrained Chronos models based on the T5 family (ranging from 20M to 710M parameters) on a large collection of publicly available datasets, complemented by a synthetic dataset that we generated via Gaussian processes to improve generalization. In a comprehensive benchmark consisting of 42 datasets, and comprising both classical local models and deep learning methods, we show that Chronos models: (a) significantly outperform other methods on datasets that were part of the training corpus; and (b) have comparable and occasionally superior zero-shot performance on new datasets, relative to methods that were trained specifically on them. Our results demonstrate that Chronos models can leverage time series data from diverse domains to improve zero-shot accuracy on unseen forecasting tasks, positioning pretrained models as a viable tool to greatly simplify forecasting pipelines.

This abstract explores an RNN-based approach to online handwritten recognition problem. Our method uses data from an accelerometer and a gyroscope mounted on a handheld pen-like device to train and run a character pre-diction model. We have built a dataset of timestamped gyroscope and accelerometer data gathered during the manual process of handwriting Latin characters, labeled with the character being written; in total, the dataset con-sists of 1500 gyroscope and accelerometer data sequenc-es for 8 characters of the Latin alphabet from 6 different people, and 20 characters, each 1500 samples from Georgian alphabet from 5 different people. with each sequence containing the gyroscope and accelerometer data captured during the writing of a particular character sampled once every 10ms. We train an RNN-based neural network architecture on this dataset to predict the character being written. The model is optimized with categorical cross-entropy loss and RMSprop optimizer and achieves high accuracy on test data.

Linear recurrent neural networks have emerged as efficient alternatives to the original Transformer's softmax attention mechanism, thanks to their highly parallelizable training and constant memory and computation requirements at inference. Iterative refinements of these models have introduced an increasing number of architectural mechanisms, leading to increased complexity and computational costs. Nevertheless, systematic direct comparisons among these models remain limited. Existing benchmark tasks are either too simplistic to reveal substantial differences or excessively resource-intensive for experimentation. In this work, we propose a refined taxonomy of linear recurrent models and introduce SelectivBench, a set of lightweight and customizable synthetic benchmark tasks for systematically evaluating sequence models. SelectivBench specifically evaluates selectivity in sequence models at small to medium scale, such as the capacity to focus on relevant inputs while ignoring context-based distractors. It employs rule-based grammars to generate sequences with adjustable complexity, incorporating irregular gaps that intentionally violate transition rules. Evaluations of linear recurrent models on SelectivBench reveal performance patterns consistent with results from large-scale language tasks. Our analysis clarifies the roles of essential architectural features: gating and rapid forgetting mechanisms facilitate recall, in-state channel mixing is unnecessary for selectivity, but critical for generalization, and softmax attention remains dominant due to its memory capacity scaling with sequence length. Our benchmark enables targeted, efficient exploration of linear recurrent models and provides a controlled setting for studying behaviors observed in large-scale evaluations. Code is available at https://github.com/symseqbench/selectivbench

Multiple extensions of Recurrent Neural Networks (RNNs) have been proposed recently to address the difficulty of storing information over long time periods. In this paper, we experiment with the capacity of Neural Turing Machines (NTMs) to deal with these long-term dependencies on well-balanced strings of parentheses. We show that not only does the NTM emulate a stack with its heads and learn an algorithm to recognize such words, but it is also capable of strongly generalizing to much longer sequences.

Linear RNN architectures, like Mamba, can be competitive with Transformer models in language modeling while having advantageous deployment characteristics. Given the focus on training large-scale Transformer models, we consider the challenge of converting these pretrained models for deployment. We demonstrate that it is feasible to distill large Transformers into linear RNNs by reusing the linear projection weights from attention layers with academic GPU resources. The resulting hybrid model, which incorporates a quarter of the attention layers, achieves performance comparable to the original Transformer in chat benchmarks and outperforms open-source hybrid Mamba models trained from scratch with trillions of tokens in both chat benchmarks and general benchmarks. Moreover, we introduce a hardware-aware speculative decoding algorithm that accelerates the inference speed of Mamba and hybrid models. Overall we show how, with limited computation resources, we can remove many of the original attention layers and generate from the resulting model more efficiently. Our top-performing model, distilled from Llama3-8B-Instruct, achieves a 29.61 length-controlled win rate on AlpacaEval 2 against GPT-4 and 7.35 on MT-Bench, surpassing the best instruction-tuned linear RNN model.

The attention mechanism, a cornerstone of state-of-the-art neural models, faces computational hurdles in processing long sequences due to its quadratic complexity. Consequently, research efforts in the last few years focused on finding more efficient alternatives. Among them, Hyena (Poli et al., 2023) stands out for achieving competitive results in both language modeling and image classification, while offering sub-quadratic memory and computational complexity. Building on these promising results, we propose ConfHyena, a Conformer whose encoder self-attentions are replaced with an adaptation of Hyena for speech processing, where the long input sequences cause high computational costs. Through experiments in automatic speech recognition (for English) and translation (from English into 8 target languages), we show that our best ConfHyena model significantly reduces the training time by 27%, at the cost of minimal quality degradation (~1%), which, in most cases, is not statistically significant.

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

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.

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.

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

Recent advances in deep learning have relied heavily on the use of large Transformers due to their ability to learn at scale. However, the core building block of Transformers, the attention operator, exhibits quadratic cost in sequence length, limiting the amount of context accessible. Existing subquadratic methods based on low-rank and sparse approximations need to be combined with dense attention layers to match Transformers, indicating a gap in capability. In this work, we propose Hyena, a subquadratic drop-in replacement for attention constructed by interleaving implicitly parametrized long convolutions and data-controlled gating. In recall and reasoning tasks on sequences of thousands to hundreds of thousands of tokens, Hyena improves accuracy by more than 50 points over operators relying on state-spaces and other implicit and explicit methods, matching attention-based models. We set a new state-of-the-art for dense-attention-free architectures on language modeling in standard datasets (WikiText103 and The Pile), reaching Transformer quality with a 20% reduction in training compute required at sequence length 2K. Hyena operators are twice as fast as highly optimized attention at sequence length 8K, and 100x faster at sequence length 64K.

Long-sequence modeling faces a fundamental trade-off between the efficiency of compressive fixed-size memory in RNN-like models and the fidelity of lossless growing memory in attention-based Transformers. Inspired by the Multi-Store Model in cognitive science, we introduce a memory framework of artificial neural networks. Our method maintains a sliding window of the Transformer's KV cache as lossless short-term memory, while a learnable module termed Artificial Hippocampus Network (AHN) recurrently compresses out-of-window information into a fixed-size compact long-term memory. To validate this framework, we instantiate AHNs using modern RNN-like architectures, including Mamba2, DeltaNet, and Gated DeltaNet. Extensive experiments on long-context benchmarks LV-Eval and InfiniteBench demonstrate that AHN-augmented models consistently outperform sliding window baselines and achieve performance comparable or even superior to full-attention models, while substantially reducing computational and memory requirements. For instance, augmenting the Qwen2.5-3B-Instruct with AHNs reduces inference FLOPs by 40.5% and memory cache by 74.0%, while improving its average score on LV-Eval (128k sequence length) from 4.41 to 5.88. Code is available at: https://github.com/ByteDance-Seed/AHN.

We introduce WARP (Weight-space Adaptive Recurrent Prediction), a simple yet powerful model that unifies weight-space learning with linear recurrence to redefine sequence modeling. Unlike conventional recurrent neural networks (RNNs) which collapse temporal dynamics into fixed-dimensional hidden states, WARP explicitly parametrizes its hidden state as the weights and biases of a distinct auxiliary neural network, and uses input differences to drive its recurrence. This brain-inspired formulation enables efficient gradient-free adaptation of the auxiliary network at test-time, in-context learning abilities, and seamless integration of domain-specific physical priors. Empirical validation shows that WARP matches or surpasses state-of-the-art baselines on diverse classification tasks, featuring in the top three in 5 out of 6 real-world challenging datasets. Furthermore, extensive experiments across sequential image completion, multivariate time series forecasting, and dynamical system reconstruction demonstrate its expressiveness and generalisation capabilities. Remarkably, a physics-informed variant of our model outperforms the next best model by more than 10x. Ablation studies confirm the architectural necessity of key components, solidifying weight-space linear RNNs as a transformative paradigm for adaptive machine intelligence.

We present RWKV-7 "Goose", a new sequence modeling architecture, along with pre-trained language models that establish a new state-of-the-art in downstream performance at the 3 billion parameter scale on multilingual tasks, and match current SoTA English language performance despite being trained on dramatically fewer tokens than other top 3B models. Nevertheless, RWKV-7 models require only constant memory usage and constant inference time per token. RWKV-7 introduces a newly generalized formulation of the delta rule with vector-valued gating and in-context learning rates, as well as a relaxed value replacement rule. We show that RWKV-7 can perform state tracking and recognize all regular languages, while retaining parallelizability of training. This exceeds the capabilities of Transformers under standard complexity conjectures, which are limited to TC^0. To demonstrate RWKV-7's language modeling capability, we also present an extended open source 3.1 trillion token multilingual corpus, and train four RWKV-7 models ranging from 0.19 billion to 2.9 billion parameters on this dataset. To foster openness, reproduction, and adoption, we release our models and dataset component listing at https://huggingface.co/RWKV, and our training and inference code at https://github.com/RWKV/RWKV-LM all under the Apache 2.0 License.

This paper addresses the general problem of reinforcement learning (RL) in partially observable environments. In 2013, our large RL recurrent neural networks (RNNs) learned from scratch to drive simulated cars from high-dimensional video input. However, real brains are more powerful in many ways. In particular, they learn a predictive model of their initially unknown environment, and somehow use it for abstract (e.g., hierarchical) planning and reasoning. Guided by algorithmic information theory, we describe RNN-based AIs (RNNAIs) designed to do the same. Such an RNNAI can be trained on never-ending sequences of tasks, some of them provided by the user, others invented by the RNNAI itself in a curious, playful fashion, to improve its RNN-based world model. Unlike our previous model-building RNN-based RL machines dating back to 1990, the RNNAI learns to actively query its model for abstract reasoning and planning and decision making, essentially "learning to think." The basic ideas of this report can be applied to many other cases where one RNN-like system exploits the algorithmic information content of another. They are taken from a grant proposal submitted in Fall 2014, and also explain concepts such as "mirror neurons." Experimental results will be described in separate papers.

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.

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

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

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

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

In this paper, we introduce a novel fine-tuning technique for language models, which involves incorporating symmetric noise into the embedding process. This method aims to enhance the model's function by more stringently regulating its local curvature, demonstrating superior performance over the current method, NEFTune. When fine-tuning the LLaMA-2-7B model using Alpaca, standard techniques yield a 29.79% score on AlpacaEval. However, our approach, SymNoise, increases this score significantly to 69.04%, using symmetric noisy embeddings. This is a 6.7% improvement over the state-of-the-art method, NEFTune~(64.69%). Furthermore, when tested on various models and stronger baseline instruction datasets, such as Evol-Instruct, ShareGPT, OpenPlatypus, SymNoise consistently outperforms NEFTune. The current literature, including NEFTune, has underscored the importance of more in-depth research into the application of noise-based strategies in the fine-tuning of language models. Our approach, SymNoise, is another significant step towards this direction, showing notable improvement over the existing state-of-the-art method.

Training recurrent neural networks (RNNs) requires assigning credit across long sequences of computations. Standard backpropagation through time (BPTT) addresses this problem poorly: it is sequential in time, limiting parallelism, and suffers from vanishing or exploding gradients, making long-range associations difficult to learn. We propose Supervised Memory Training (SMT), a method for training nonlinear RNNs that sidesteps recurrent credit propagation entirely by reducing RNN training to supervised learning on one-step memory transition labels (m_t, x_{t+1}) rightarrow m_{t+1}. SMT acquires these memory labels by training a Transformer-based encoder on a predictive state objective--retaining only information from the past necessary to predict the future. By decoupling what to remember from how to update memory, SMT enables time-parallel RNN training with a stable O(1) length gradient path between any two tokens--without ever unrolling the RNN. We find that SMT outperforms BPTT when pretraining various RNN architectures on tasks like language modeling and pixel sequence modeling. SMT enables nonlinear RNNs to better capture long-range dependencies and train in parallel, potentially unlocking the scaling of models that build temporal abstractions of past experience.

RNN-based methods have faced challenges in the Long-term Time Series Forecasting (LTSF) domain when dealing with excessively long look-back windows and forecast horizons. Consequently, the dominance in this domain has shifted towards Transformer, MLP, and CNN approaches. The substantial number of recurrent iterations are the fundamental reasons behind the limitations of RNNs in LTSF. To address these issues, we propose two novel strategies to reduce the number of iterations in RNNs for LTSF tasks: Segment-wise Iterations and Parallel Multi-step Forecasting (PMF). RNNs that combine these strategies, namely SegRNN, significantly reduce the required recurrent iterations for LTSF, resulting in notable improvements in forecast accuracy and inference speed. Extensive experiments demonstrate that SegRNN not only outperforms SOTA Transformer-based models but also reduces runtime and memory usage by more than 78%. These achievements provide strong evidence that RNNs continue to excel in LTSF tasks and encourage further exploration of this domain with more RNN-based approaches. The source code is coming soon.

Speculative decoding has emerged as a popular method to accelerate the inference of Large Language Models (LLMs) while retaining their superior text generation performance. Previous methods either adopt a fixed speculative decoding configuration regardless of the prefix tokens, or train draft models in an offline or online manner to align them with the context. This paper proposes a training-free online learning framework to adaptively choose the configuration of the hyperparameters for speculative decoding as text is being generated. We first formulate this hyperparameter selection problem as a Multi-Armed Bandit problem and provide a general speculative decoding framework BanditSpec. Furthermore, two bandit-based hyperparameter selection algorithms, UCBSpec and EXP3Spec, are designed and analyzed in terms of a novel quantity, the stopping time regret. We upper bound this regret under both stochastic and adversarial reward settings. By deriving an information-theoretic impossibility result, it is shown that the regret performance of UCBSpec is optimal up to universal constants. Finally, extensive empirical experiments with LLaMA3 and Qwen2 demonstrate that our algorithms are effective compared to existing methods, and the throughput is close to the oracle best hyperparameter in simulated real-life LLM serving scenarios with diverse input prompts.

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

The ability to recognize and predict temporal sequences of sensory inputs is vital for survival in natural environments. Based on many known properties of cortical neurons, hierarchical temporal memory (HTM) sequence memory is recently proposed as a theoretical framework for sequence learning in the cortex. In this paper, we analyze properties of HTM sequence memory and apply it to sequence learning and prediction problems with streaming data. We show the model is able to continuously learn a large number of variable-order temporal sequences using an unsupervised Hebbian-like learning rule. The sparse temporal codes formed by the model can robustly handle branching temporal sequences by maintaining multiple predictions until there is sufficient disambiguating evidence. We compare the HTM sequence memory with other sequence learning algorithms, including statistical methods: autoregressive integrated moving average (ARIMA), feedforward neural networks: online sequential extreme learning machine (ELM), and recurrent neural networks: long short-term memory (LSTM) and echo-state networks (ESN), on sequence prediction problems with both artificial and real-world data. The HTM model achieves comparable accuracy to other state-of-the-art algorithms. The model also exhibits properties that are critical for sequence learning, including continuous online learning, the ability to handle multiple predictions and branching sequences with high order statistics, robustness to sensor noise and fault tolerance, and good performance without task-specific hyper- parameters tuning. Therefore the HTM sequence memory not only advances our understanding of how the brain may solve the sequence learning problem, but is also applicable to a wide range of real-world problems such as discrete and continuous sequence prediction, anomaly detection, and sequence classification.

Precise geocoding and time normalization for text requires that location and time phrases be identified. Many state-of-the-art geoparsers and temporal parsers suffer from low recall. Categories commonly missed by parsers are: nouns used in a non- spatiotemporal sense, adjectival and adverbial phrases, prepositional phrases, and numerical phrases. We collected and annotated data set by querying commercial web searches API with such spatiotemporal expressions as were missed by state-of-the- art parsers. Due to the high cost of sentence annotation, active learning was used to label training data, and a new strategy was designed to better select training examples to reduce labeling cost. For the learning algorithm, we applied an average perceptron trained Featurized Hidden Markov Model (FHMM). Five FHMM instances were used to create an ensemble, with the output phrase selected by voting. Our ensemble model was tested on a range of sequential labeling tasks, and has shown competitive performance. Our contributions include (1) an new dataset annotated with named entities and expanded spatiotemporal expressions; (2) a comparison of inference algorithms for ensemble models showing the superior accuracy of Belief Propagation over Viterbi Decoding; (3) a new example re-weighting method for active ensemble learning that 'memorizes' the latest examples trained; (4) a spatiotemporal parser that jointly recognizes expanded spatiotemporal expressions as well as named entities.

Respiratory motion complicates accurate irradiation of thoraco-abdominal tumors during radiotherapy, as treatment-system latency entails target-location uncertainties. This work addresses frame forecasting in chest and liver cine MRI to compensate for such delays. We investigate RNNs trained with online learning algorithms, enabling adaptation to changing respiratory patterns via on-the-fly parameter updates, and transformers, increasingly common in time-series forecasting for their ability to capture long-term dependencies. Experiments used 12 sagittal thoracic and upper-abdominal cine-MRI sequences from ETH Zürich and OvGU; the OvGU data exhibited higher motion variability, noise, and lower contrast. PCA decomposes the Lucas-Kanade optical-flow field into static deformation modes and low-dimensional, time-dependent weights. We compare various methods for forecasting these weights: linear filters, population and sequence-specific transformer encoders, and RNNs trained with real-time recurrent learning (RTRL), unbiased online recurrent optimization, decoupled neural interfaces, and sparse one-step approximation (SnAp-1). Predicted displacements were used to warp the reference frame and generate future images. Prediction accuracy decreased with the horizon h. Linear regression performed best at short horizons (1.3mm geometrical error at h=0.32s, ETH Zürich dataset), while RTRL and SnAp-1 outperformed the other algorithms at medium-to-long horizons, with geometrical errors below 1.4mm and 2.8mm on the sequences from ETH Zürich and OvGU, respectively. The sequence-specific transformer was competitive for low-to-medium horizons, but transformers remained overall limited by data scarcity and domain shift between datasets. Predicted frames visually resembled the ground truth, with notable errors occurring near the diaphragm at end-inspiration and regions affected by out-of-plane motion.

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

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.

Modern large language models (LLMs) that rely on attention mechanisms are typically trained with fixed context lengths which enforce upper limits on the length of input sequences that they can handle at evaluation time. To use these models on sequences longer than the train-time context length, one might employ techniques from the growing family of context length extrapolation methods -- most of which focus on modifying the system of positional encodings used in the attention mechanism to indicate where tokens or activations are located in the input sequence. We conduct a wide survey of existing methods of context length extrapolation on a base LLaMA or LLaMA 2 model, and introduce some of our own design as well -- in particular, a new truncation strategy for modifying the basis for the position encoding. We test these methods using three new evaluation tasks (FreeFormQA, AlteredNumericQA, and LongChat-Lines) as well as perplexity, which we find to be less fine-grained as a measure of long context performance of LLMs. We release the three tasks publicly as datasets on HuggingFace. We discover that linear scaling is the best method for extending context length, and show that further gains can be achieved by using longer scales at evaluation time. We also discover promising extrapolation capabilities in the truncated basis. To support further research in this area, we release three new 13B parameter long-context models which we call Giraffe: 4k and 16k context models trained from base LLaMA-13B, and a 32k context model trained from base LLaMA2-13B. We also release the code to replicate our results.

Hybrid sequence models that combine efficient Transformer components with linear sequence modeling blocks are a promising alternative to pure Transformers, but most are still pretrained from scratch and therefore fail to reuse existing Transformer checkpoints. We study upcycling as a practical path to convert pretrained Transformer LLMs into hybrid architectures while preserving short-context quality and improving long-context capability. We call our solution HyLo (HYbrid LOng-context): a long-context upcycling recipe that combines architectural adaptation with efficient Transformer blocks, Multi-Head Latent Attention (MLA), and linear blocks (Mamba2 or Gated DeltaNet), together with staged long-context training and teacher-guided distillation for stable optimization. HyLo extends usable context length by up to 32times through efficient post-training and reduces KV-cache memory by more than 90%, enabling up to 2M-token prefill and decoding in our vLLM inference stack, while comparable Llama baselines run out of memory beyond 64K context. Across 1B- and 3B-scale settings (Llama- and Qwen-based variants), HyLo delivers consistently strong short- and long-context performance and significantly outperforms state-of-the-art upcycled hybrid baselines on long-context evaluations such as RULER. Notably, at similar scale, HyLo-Qwen-1.7B trained on only 10B tokens significantly outperforms JetNemotron (trained on 400B tokens) on GSM8K, Lm-Harness common sense reasoning and RULER-64K.

Named entity recognition (NER) is a widely applicable natural language processing task and building block of question answering, topic modeling, information retrieval, etc. In the medical domain, NER plays a crucial role by extracting meaningful chunks from clinical notes and reports, which are then fed to downstream tasks like assertion status detection, entity resolution, relation extraction, and de-identification. Reimplementing a Bi-LSTM-CNN-Char deep learning architecture on top of Apache Spark, we present a single trainable NER model that obtains new state-of-the-art results on seven public biomedical benchmarks without using heavy contextual embeddings like BERT. This includes improving BC4CHEMD to 93.72% (4.1% gain), Species800 to 80.91% (4.6% gain), and JNLPBA to 81.29% (5.2% gain). In addition, this model is freely available within a production-grade code base as part of the open-source Spark NLP library; can scale up for training and inference in any Spark cluster; has GPU support and libraries for popular programming languages such as Python, R, Scala and Java; and can be extended to support other human languages with no code changes.

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.

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

Recurrent neural networks (RNNs) with deep test-time memorization modules, such as Titans and TTT, represent a promising, linearly-scaling paradigm distinct from Transformers. While these expressive models do not yet match the peak performance of state-of-the-art Transformers, their potential has been largely untapped due to prohibitively slow training and low hardware utilization. Existing parallelization methods force a fundamental conflict governed by the chunksize hyperparameter: large chunks boost speed but degrade performance, necessitating a fixed, suboptimal compromise. To solve this challenge, we introduce TNT, a novel training paradigm that decouples training efficiency from inference performance through a two-stage process. Stage one is an efficiency-focused pre-training phase utilizing a hierarchical memory. A global module processes large, hardware-friendly chunks for long-range context, while multiple parallel local modules handle fine-grained details. Crucially, by periodically resetting local memory states, we break sequential dependencies to enable massive context parallelization. Stage two is a brief fine-tuning phase where only the local memory modules are adapted to a smaller, high-resolution chunksize, maximizing accuracy with minimal overhead. Evaluated on Titans and TTT models, TNT achieves a substantial acceleration in training speed-up to 17 times faster than the most accurate baseline configuration - while simultaneously improving model accuracy. This improvement removes a critical scalability barrier, establishing a practical foundation for developing expressive RNNs and facilitating future work to close the performance gap with Transformers.

Although Transformers with fully connected self-attentions are powerful to model long-term dependencies, they are struggling to scale to long texts with thousands of words in language modeling. One of the solutions is to equip the model with a recurrence memory. However, existing approaches directly reuse hidden states from the previous segment that encodes contexts in a uni-directional way. As a result, this prohibits the memory to dynamically interact with the current context that provides up-to-date information for token prediction. To remedy this issue, we propose Look-Ahead Memory (LaMemo) that enhances the recurrence memory by incrementally attending to the right-side tokens, and interpolating with the old memory states to maintain long-term information in the history. LaMemo embraces bi-directional attention and segment recurrence with an additional computation overhead only linearly proportional to the memory length. Experiments on widely used language modeling benchmarks demonstrate its superiority over the baselines equipped with different types of memory.