Daily Papers

For sequence models with large vocabularies, a majority of network parameters lie in the input and output layers. In this work, we describe a new method, DeFINE, for learning deep token representations efficiently. Our architecture uses a hierarchical structure with novel skip-connections which allows for the use of low dimensional input and output layers, reducing total parameters and training time while delivering similar or better performance versus existing methods. DeFINE can be incorporated easily in new or existing sequence models. Compared to state-of-the-art methods including adaptive input representations, this technique results in a 6% to 20% drop in perplexity. On WikiText-103, DeFINE reduces the total parameters of Transformer-XL by half with minimal impact on performance. On the Penn Treebank, DeFINE improves AWD-LSTM by 4 points with a 17% reduction in parameters, achieving comparable performance to state-of-the-art methods with fewer parameters. For machine translation, DeFINE improves the efficiency of the Transformer model by about 1.4 times while delivering similar performance.

This paper introduces a novel model for semantic role labeling that makes use of neural sequence modeling techniques. Our approach is motivated by the observation that complex syntactic structures and related phenomena, such as nested subordinations and nominal predicates, are not handled well by existing models. Our model treats such instances as sub-sequences of lexicalized dependency paths and learns suitable embedding representations. We experimentally demonstrate that such embeddings can improve results over previous state-of-the-art semantic role labelers, and showcase qualitative improvements obtained by our method.

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.

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.

Transformers have reached remarkable success in sequence modeling. However, these models have efficiency issues as they need to store all the history token-level representations as memory. We present Memformer, an efficient neural network for sequence modeling, that utilizes an external dynamic memory to encode and retrieve past information. Our model achieves linear time complexity and constant memory space complexity when processing long sequences. We also propose a new optimization scheme, memory replay back-propagation (MRBP), which promotes long-range back-propagation through time with a significantly reduced memory requirement. Experimental results show that Memformer has achieved comparable performance compared to the baselines by using 8.1x less memory space and 3.2x faster on inference. Analysis of the attention pattern shows that our external memory slots can encode and retain important information through timesteps.

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

Alzheimer's Disease (AD) is marked by significant inter-individual variability in its progression, complicating accurate prognosis and personalized care planning. This heterogeneity underscores the critical need for predictive models capable of forecasting patient-specific disease trajectories. Artificial Intelligence (AI) offers powerful tools to address this challenge by analyzing complex, multi-modal, and longitudinal patient data. This paper provides a comprehensive survey of AI methodologies applied to personalized AD progression prediction. We review key approaches including state-space models for capturing temporal dynamics, deep learning techniques like Recurrent Neural Networks for sequence modeling, Graph Neural Networks (GNNs) for leveraging network structures, and the emerging concept of AI-driven digital twins for individualized simulation. Recognizing that data limitations often impede progress, we examine common challenges such as high dimensionality, missing data, and dataset imbalance. We further discuss AI-driven mitigation strategies, with a specific focus on synthetic data generation using Variational Autoencoders (VAEs) and Generative Adversarial Networks (GANs) to augment and balance datasets. The survey synthesizes the strengths and limitations of current approaches, emphasizing the trend towards multimodal integration and the persistent need for model interpretability and generalizability. Finally, we identify critical open challenges, including robust external validation, clinical integration, and ethical considerations, and outline promising future research directions such as hybrid models, causal inference, and federated learning. This review aims to consolidate current knowledge and guide future efforts in developing clinically relevant AI tools for personalized AD prognostication.

Existing sequence models, including RNNs, LSTMs, continuous-time networks, and Transformers, share a common structural principle: layer-wise dynamics, where all neurons in the same layer co-evolve through a shared parameterized operator, leaving individual neurons no freedom to evolve independently. Yet in many complex dynamical systems, rich global behavior emerges precisely from locally evolving units interacting through structured connectivity. Inspired by this principle, we introduce Topological Neural Dynamics (TND), a sequence modeling framework that shifts computation from layer-wise to neuron-wise dynamics. TND represents a neural system as a directed neuron graph, an interaction operator, and a local dynamics function, where each neuron evolves independently and collective computation emerges from interactions through the explicit graph topology. We instantiate TND as a discrete-time graph-coupled dynamical system and evaluate it as a case study on a behavior cloning task in single-player Pong. Compared with Vanilla RNN, Sparse RNN, LSTM, Closed-form continuous-time neural network (CfC), and Transformer baselines, TND achieves the best catch rate and a mean of 17.47 consecutive catches per round, more than three times that of the strongest baseline. These results suggest that shifting from layer-wise to neuron-wise dynamics provides an effective inductive bias for sequence modeling.

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

Numerical simulation of non-linear partial differential equations plays a crucial role in modeling physical science and engineering phenomena, such as weather, climate, and aerodynamics. Recent Machine Learning (ML) models trained on low-resolution spatio-temporal signals have shown new promises in capturing important dynamics in high-resolution signals, under the condition that the models can effectively recover the missing details. However, this study shows that significant information is often lost in the low-resolution down-sampled features. To address such issues, we propose a new approach, namely Temporal Stencil Modeling (TSM), which combines the strengths of advanced time-series sequence modeling (with the HiPPO features) and state-of-the-art neural PDE solvers (with learnable stencil modeling). TSM aims to recover the lost information from the PDE trajectories and can be regarded as a temporal generalization of classic finite volume methods such as WENO. Our experimental results show that TSM achieves the new state-of-the-art simulation accuracy for 2-D incompressible Navier-Stokes turbulent flows: it significantly outperforms the previously reported best results by 19.9% in terms of the highly-correlated duration time and reduces the inference latency into 80%. We also show a strong generalization ability of the proposed method to various out-of-distribution turbulent flow settings. Our code is available at "https://github.com/Edward-Sun/TSM-PDE".

Recent studies in deep learning-based speech separation have proven the superiority of time-domain approaches to conventional time-frequency-based methods. Unlike the time-frequency domain approaches, the time-domain separation systems often receive input sequences consisting of a huge number of time steps, which introduces challenges for modeling extremely long sequences. Conventional recurrent neural networks (RNNs) are not effective for modeling such long sequences due to optimization difficulties, while one-dimensional convolutional neural networks (1-D CNNs) cannot perform utterance-level sequence modeling when its receptive field is smaller than the sequence length. In this paper, we propose dual-path recurrent neural network (DPRNN), a simple yet effective method for organizing RNN layers in a deep structure to model extremely long sequences. DPRNN splits the long sequential input into smaller chunks and applies intra- and inter-chunk operations iteratively, where the input length can be made proportional to the square root of the original sequence length in each operation. Experiments show that by replacing 1-D CNN with DPRNN and apply sample-level modeling in the time-domain audio separation network (TasNet), a new state-of-the-art performance on WSJ0-2mix is achieved with a 20 times smaller model than the previous best system.

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.

Foundation models, now powering most of the exciting applications in deep learning, are almost universally based on the Transformer architecture and its core attention module. Many subquadratic-time architectures such as linear attention, gated convolution and recurrent models, and structured state space models (SSMs) have been developed to address Transformers' computational inefficiency on long sequences, but they have not performed as well as attention on important modalities such as language. We identify that a key weakness of such models is their inability to perform content-based reasoning, and make several improvements. First, simply letting the SSM parameters be functions of the input addresses their weakness with discrete modalities, allowing the model to selectively propagate or forget information along the sequence length dimension depending on the current token. Second, even though this change prevents the use of efficient convolutions, we design a hardware-aware parallel algorithm in recurrent mode. We integrate these selective SSMs into a simplified end-to-end neural network architecture without attention or even MLP blocks (Mamba). Mamba enjoys fast inference (5times higher throughput than Transformers) and linear scaling in sequence length, and its performance improves on real data up to million-length sequences. As a general sequence model backbone, Mamba achieves state-of-the-art performance across several modalities such as language, audio, and genomics. On language modeling, our Mamba-3B model outperforms Transformers of the same size and matches Transformers twice its size, both in pretraining and downstream evaluation.

Linear State Space Models (SSMs) have demonstrated strong performance in a variety of sequence modeling tasks due to their efficient encoding of the recurrent structure. However, in more comprehensive tasks like language modeling and machine translation, self-attention-based models still outperform SSMs. Hybrid models employing both SSM and self-attention generally show promising performance, but current approaches apply attention modules statically and uniformly to all elements in the input sequences, leading to sub-optimal quality-efficiency trade-offs. In this work, we introduce Sparse Modular Activation (SMA), a general mechanism enabling neural networks to sparsely and dynamically activate sub-modules for sequence elements in a differentiable manner. Through allowing each element to skip non-activated sub-modules, SMA reduces computation and memory consumption at both training and inference stages of sequence modeling. As a specific instantiation of SMA, we design a novel neural architecture, SeqBoat, which employs SMA to sparsely activate a Gated Attention Unit (GAU) based on the state representations learned from an SSM. By constraining the GAU to only conduct local attention on the activated inputs, SeqBoat can achieve linear inference complexity with theoretically infinite attention span, and provide substantially better quality-efficiency trade-off than the chunking-based models. With experiments on a wide range of tasks, including language modeling, speech classification and long-range arena, SeqBoat brings new state-of-the-art results among hybrid models with linear complexity and reveals the amount of attention needed for each task through the learned sparse activation patterns.

Efficiently capturing the long-range patterns in sequential data sources salient to a given task -- such as classification and generative modeling -- poses a fundamental challenge. Popular approaches in the space tradeoff between the memory burden of brute-force enumeration and comparison, as in transformers, the computational burden of complicated sequential dependencies, as in recurrent neural networks, or the parameter burden of convolutional networks with many or large filters. We instead take inspiration from wavelet-based multiresolution analysis to define a new building block for sequence modeling, which we call a MultiresLayer. The key component of our model is the multiresolution convolution, capturing multiscale trends in the input sequence. Our MultiresConv can be implemented with shared filters across a dilated causal convolution tree. Thus it garners the computational advantages of convolutional networks and the principled theoretical motivation of wavelet decompositions. Our MultiresLayer is straightforward to implement, requires significantly fewer parameters, and maintains at most a O(Nlog N) memory footprint for a length N sequence. Yet, by stacking such layers, our model yields state-of-the-art performance on a number of sequence classification and autoregressive density estimation tasks using CIFAR-10, ListOps, and PTB-XL datasets.

Data of sequential nature arise in many application domains in forms of, e.g. textual data, DNA sequences, and software execution traces. Different research disciplines have developed methods to learn sequence models from such datasets: (i) in the machine learning field methods such as (hidden) Markov models and recurrent neural networks have been developed and successfully applied to a wide-range of tasks, (ii) in process mining process discovery techniques aim to generate human-interpretable descriptive models, and (iii) in the grammar inference field the focus is on finding descriptive models in the form of formal grammars. Despite their different focuses, these fields share a common goal - learning a model that accurately describes the behavior in the underlying data. Those sequence models are generative, i.e, they can predict what elements are likely to occur after a given unfinished sequence. So far, these fields have developed mainly in isolation from each other and no comparison exists. This paper presents an interdisciplinary experimental evaluation that compares sequence modeling techniques on the task of next-element prediction on four real-life sequence datasets. The results indicate that machine learning techniques that generally have no aim at interpretability in terms of accuracy outperform techniques from the process mining and grammar inference fields that aim to yield interpretable models.

In reasoning about sequential events it is natural to pose probabilistic queries such as "when will event A occur next" or "what is the probability of A occurring before B", with applications in areas such as user modeling, medicine, and finance. However, with machine learning shifting towards neural autoregressive models such as RNNs and transformers, probabilistic querying has been largely restricted to simple cases such as next-event prediction. This is in part due to the fact that future querying involves marginalization over large path spaces, which is not straightforward to do efficiently in such models. In this paper we introduce a general typology for predictive queries in neural autoregressive sequence models and show that such queries can be systematically represented by sets of elementary building blocks. We leverage this typology to develop new query estimation methods based on beam search, importance sampling, and hybrids. Across four large-scale sequence datasets from different application domains, as well as for the GPT-2 language model, we demonstrate the ability to make query answering tractable for arbitrary queries in exponentially-large predictive path-spaces, and find clear differences in cost-accuracy tradeoffs between search and sampling methods.

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

Transformer has achieved remarkable success in language, image, and speech processing. Recently, various efficient attention architectures have been proposed to improve transformer's efficiency while largely preserving its efficacy, especially in modeling long sequences. A widely-used benchmark to test these efficient methods' capability on long-range modeling is Long Range Arena (LRA). However, LRA only focuses on the standard bidirectional (or noncausal) self attention, and completely ignores cross attentions and unidirectional (or causal) attentions, which are equally important to downstream applications. Although designing cross and causal variants of an attention method is straightforward for vanilla attention, it is often challenging for efficient attentions with subquadratic time and memory complexity. In this paper, we propose Comprehensive Attention Benchmark (CAB) under a fine-grained attention taxonomy with four distinguishable attention patterns, namely, noncausal self, causal self, noncausal cross, and causal cross attentions. CAB collects seven real-world tasks from different research areas to evaluate efficient attentions under the four attention patterns. Among these tasks, CAB validates efficient attentions in eight backbone networks to show their generalization across neural architectures. We conduct exhaustive experiments to benchmark the performances of nine widely-used efficient attention architectures designed with different philosophies on CAB. Extensive experimental results also shed light on the fundamental problems of efficient attentions, such as efficiency length against vanilla attention, performance consistency across attention patterns, the benefit of attention mechanisms, and interpolation/extrapolation on long-context language modeling.

In the rapidly evolving landscape of deep learning, the quest for models that balance expressivity with computational efficiency has never been more critical. This paper introduces Orchid, a novel architecture that reimagines sequence modeling by incorporating a new data-dependent convolution mechanism. Orchid is designed to address the inherent limitations of traditional attention mechanisms, particularly their quadratic complexity, without compromising the ability to capture long-range dependencies and in-context learning. At the core of Orchid lies the data-dependent convolution layer, which dynamically adjusts its kernel conditioned on input data using a dedicated conditioning neural network. We design two simple conditioning networks that maintain shift equivariance in the adaptive convolution operation. The dynamic nature of data-dependent convolution kernel, coupled with gating operations, grants Orchid high expressivity while maintaining efficiency and quasilinear scalability for long sequences. We rigorously evaluate Orchid across multiple domains, including language modeling and image classification, to showcase its performance and generality. Our experiments demonstrate that Orchid architecture not only outperforms traditional attention-based architectures such as BERT and Vision Transformers with smaller model sizes, but also extends the feasible sequence length beyond the limitations of the dense attention layers. This achievement represents a significant step towards more efficient and scalable deep learning models for sequence modeling.

Image-based sequence recognition has been a long-standing research topic in computer vision. In this paper, we investigate the problem of scene text recognition, which is among the most important and challenging tasks in image-based sequence recognition. A novel neural network architecture, which integrates feature extraction, sequence modeling and transcription into a unified framework, is proposed. Compared with previous systems for scene text recognition, the proposed architecture possesses four distinctive properties: (1) It is end-to-end trainable, in contrast to most of the existing algorithms whose components are separately trained and tuned. (2) It naturally handles sequences in arbitrary lengths, involving no character segmentation or horizontal scale normalization. (3) It is not confined to any predefined lexicon and achieves remarkable performances in both lexicon-free and lexicon-based scene text recognition tasks. (4) It generates an effective yet much smaller model, which is more practical for real-world application scenarios. The experiments on standard benchmarks, including the IIIT-5K, Street View Text and ICDAR datasets, demonstrate the superiority of the proposed algorithm over the prior arts. Moreover, the proposed algorithm performs well in the task of image-based music score recognition, which evidently verifies the generality of it.

World models represent a promising approach for training reinforcement learning agents with significantly improved sample efficiency. While most world model methods primarily rely on sequences of discrete latent variables to model environment dynamics, this compression often neglects critical visual details essential for reinforcement learning. Recent diffusion-based world models condition generation on a fixed context length of frames to predict the next observation, using separate recurrent neural networks to model rewards and termination signals. Although this architecture effectively enhances visual fidelity, the fixed context length approach inherently limits memory capacity. In this paper, we introduce EDELINE, a unified world model architecture that integrates state space models with diffusion models. Our approach outperforms existing baselines across visually challenging Atari 100k tasks, memory-demanding Crafter benchmark, and 3D first-person ViZDoom environments, demonstrating superior performance in all these diverse challenges.

We present a neural transducer model with visual attention that learns to generate LaTeX markup of a real-world math formula given its image. Applying sequence modeling and transduction techniques that have been very successful across modalities such as natural language, image, handwriting, speech and audio; we construct an image-to-markup model that learns to produce syntactically and semantically correct LaTeX markup code over 150 words long and achieves a BLEU score of 89%; improving upon the previous state-of-art for the Im2Latex problem. We also demonstrate with heat-map visualization how attention helps in interpreting the model and can pinpoint (detect and localize) symbols on the image accurately despite having been trained without any bounding box data.

This paper introduces VALL-E 2, the latest advancement in neural codec language models that marks a milestone in zero-shot text-to-speech synthesis (TTS), achieving human parity for the first time. Based on its predecessor, VALL-E, the new iteration introduces two significant enhancements: Repetition Aware Sampling refines the original nucleus sampling process by accounting for token repetition in the decoding history. It not only stabilizes the decoding but also circumvents the infinite loop issue. Grouped Code Modeling organizes codec codes into groups to effectively shorten the sequence length, which not only boosts inference speed but also addresses the challenges of long sequence modeling. Our experiments on the LibriSpeech and VCTK datasets show that VALL-E 2 surpasses previous systems in speech robustness, naturalness, and speaker similarity. It is the first of its kind to reach human parity on these benchmarks. Moreover, VALL-E 2 consistently synthesizes high-quality speech, even for sentences that are traditionally challenging due to their complexity or repetitive phrases. The advantages of this work could contribute to valuable endeavors, such as generating speech for individuals with aphasia or people with amyotrophic lateral sclerosis. Demos of VALL-E 2 will be posted to https://aka.ms/valle2.

Recent advances in sequence modeling have significantly improved ASR systems, bringing them close to human-level recognition accuracy and enhancing robustness across diverse acoustic conditions and languages. In contrast, Forced Alignment has not experienced comparable progress, and traditional HMM-GMM frameworks remain widely adopted and highly competitive. To address this gap, we propose an end-to-end, fully differentiable neural architecture specifically designed for phoneme alignment. The model consists of an encoder that processes the input signal and a decoder that produces alignment decisions. The encoder is structured into two complementary branches: one dedicated to phoneme identity verification and the other to phoneme boundary detection. The decoder is implemented as a trainable module based on differentiable soft dynamic programming. The entire system is optimized end-to-end using a novel contrastive loss that encourages clear separation between steady-state phoneme regions and transition boundaries. The proposed approach outperforms the current state of the art in phoneme alignment on hand-annotated English benchmarks, achieves strong word-level generalization results, and demonstrates generalization on unseen languages.

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.

Toeplitz Neural Networks (TNNs) have exhibited outstanding performance in various sequence modeling tasks. They outperform commonly used Transformer-based models while benefiting from log-linear space-time complexities. On the other hand, State Space Models (SSMs) achieve lower performance than TNNs in language modeling but offer the advantage of constant inference complexity. In this paper, we aim to combine the strengths of TNNs and SSMs by converting TNNs to SSMs during inference, thereby enabling TNNs to achieve the same constant inference complexities as SSMs. To accomplish this, we formulate the conversion process as an optimization problem and provide a closed-form solution. We demonstrate how to transform the target equation into a Vandermonde linear system problem, which can be efficiently solved using the Discrete Fourier Transform (DFT). Notably, our method requires no training and maintains numerical stability. It can be also applied to any LongConv-based model. To assess its effectiveness, we conduct extensive experiments on language modeling tasks across various settings. Additionally, we compare our method to other gradient-descent solutions, highlighting the superior numerical stability of our approach. The source code is available at https://github.com/OpenNLPLab/ETSC-Exact-Toeplitz-to-SSM-Conversion.

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.

We propose Scalable Mechanistic Neural Network (S-MNN), an enhanced neural network framework designed for scientific machine learning applications involving long temporal sequences. By reformulating the original Mechanistic Neural Network (MNN) (Pervez et al., 2024), we reduce the computational time and space complexities from cubic and quadratic with respect to the sequence length, respectively, to linear. This significant improvement enables efficient modeling of long-term dynamics without sacrificing accuracy or interpretability. Extensive experiments demonstrate that S-MNN matches the original MNN in precision while substantially reducing computational resources. Consequently, S-MNN can drop-in replace the original MNN in applications, providing a practical and efficient tool for integrating mechanistic bottlenecks into neural network models of complex dynamical systems.

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.

Machine learning plays an increasing role in intelligent tutoring systems as both the amount of data available and specialization among students grow. Nowadays, these systems are frequently deployed on mobile applications. Users on such mobile education platforms are dynamic, frequently being added, accessing the application with varying levels of focus, and changing while using the service. The education material itself, on the other hand, is often static and is an exhaustible resource whose use in tasks such as problem recommendation must be optimized. The ability to update user models with respect to educational material in real-time is thus essential; however, existing approaches require time-consuming re-training of user features whenever new data is added. In this paper, we introduce a neural pedagogical agent for real-time user modeling in the task of predicting user response correctness, a central task for mobile education applications. Our model, inspired by work in natural language processing on sequence modeling and machine translation, updates user features in real-time via bidirectional recurrent neural networks with an attention mechanism over embedded question-response pairs. We experiment on the mobile education application SantaTOEIC, which has 559k users, 66M response data points as well as a set of 10k study problems each expert-annotated with topic tags and gathered since 2016. Our model outperforms existing approaches over several metrics in predicting user response correctness, notably out-performing other methods on new users without large question-response histories. Additionally, our attention mechanism and annotated tag set allow us to create an interpretable education platform, with a smart review system that addresses the aforementioned issue of varied user attention and problem exhaustion.

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.

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

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.

Vision-language-action (VLA) models rely on discrete action tokenizers to bridge continuous robot control and autoregressive sequence modeling, yet existing tokenizers often trade off between compression, latency, and downstream performance. We revisit this design through the lens of neural audio codecs-convolutional encoder-decoder architectures with residual vector quantization that serve as the standard front end for audio foundation models. Motivated by their success, we introduce the Neural Action Codec (NAC), which treats short robot action trajectories as multi-channel 1D signals and compresses them using a multi-scale RVQGAN architecture. We observe that audio-specific mel-spectrogram objectives are ill-suited for kinematic signals; however, by replacing them with simple time-domain and non-mel spectral reconstruction losses, audio-codec-style models can autoencode actions with high fidelity without substantial architectural changes. NAC provides a compact, ordered token space via offset codebooks, enabling standard autoregressive policies to operate over short, structured sequences. Meanwhile, a Vocos-style decoder with an ISTFT head and adversarial discriminators recovers smooth, detailed trajectories. Across LIBERO-10, RoboMimic, and a suite of real-world manipulation tasks, NAC achieves lower reconstruction error and higher success rates than binning, FAST, and prior VQ-based tokenizers at comparable or better compression rates. These results demonstrate that repurposed neural audio codecs offer a strong, practical backbone for learned action tokenization in modern VLAs.

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.

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.

Designing a unified neural network to efficiently and inherently process sequential data with arbitrary lengths is a central and challenging problem in sequence modeling. The design choices in Transformer, including quadratic complexity and weak length extrapolation, have limited their ability to scale to long sequences. In this work, we propose Gecko, a neural architecture that inherits the design of Mega and Megalodon (exponential moving average with gated attention), and further introduces multiple technical components to improve its capability to capture long range dependencies, including timestep decay normalization, sliding chunk attention mechanism, and adaptive working memory. In a controlled pretraining comparison with Llama2 and Megalodon in the scale of 7 billion parameters and 2 trillion training tokens, Gecko achieves better efficiency and long-context scalability. Gecko reaches a training loss of 1.68, significantly outperforming Llama2-7B (1.75) and Megalodon-7B (1.70), and landing close to Llama2-13B (1.67). Notably, without relying on any context-extension techniques, Gecko exhibits inherent long-context processing and retrieval capabilities, stably handling sequences of up to 4 million tokens and retrieving information from contexts up to 4times longer than its attention window. Code: https://github.com/XuezheMax/gecko-llm

In this paper, we present Neural Phrase-based Machine Translation (NPMT). Our method explicitly models the phrase structures in output sequences using Sleep-WAke Networks (SWAN), a recently proposed segmentation-based sequence modeling method. To mitigate the monotonic alignment requirement of SWAN, we introduce a new layer to perform (soft) local reordering of input sequences. Different from existing neural machine translation (NMT) approaches, NPMT does not use attention-based decoding mechanisms. Instead, it directly outputs phrases in a sequential order and can decode in linear time. Our experiments show that NPMT achieves superior performances on IWSLT 2014 German-English/English-German and IWSLT 2015 English-Vietnamese machine translation tasks compared with strong NMT baselines. We also observe that our method produces meaningful phrases in output languages.

Reinforcement learning agents based on Transformer architectures have achieved impressive performance on sequential decision-making tasks, but their reliance on dense matrix operations makes them ill-suited for energy-constrained, edge-oriented platforms. Spiking neural networks promise ultra-low-power, event-driven inference, yet no prior work has seamlessly merged spiking dynamics with return-conditioned sequence modeling. We present the Spiking Decision Transformer (SNN-DT), which embeds Leaky Integrate-and-Fire neurons into each self-attention block, trains end-to-end via surrogate gradients, and incorporates biologically inspired three-factor plasticity, phase-shifted spike-based positional encodings, and a lightweight dendritic routing module. Our implementation matches or exceeds standard Decision Transformer performance on classic control benchmarks (CartPole-v1, MountainCar-v0, Acrobot-v1, Pendulum-v1) while emitting fewer than ten spikes per decision, an energy proxy suggesting over four orders-of-magnitude reduction in per inference energy. By marrying sequence modeling with neuromorphic efficiency, SNN-DT opens a pathway toward real-time, low-power control on embedded and wearable devices.

We show that the MinMax algebra provides a form of recurrence that is expressively powerful, efficiently implementable, and most importantly it is not affected by vanishing or exploding gradient. We call MinMax Recurrent Neural Cascades (RNCs) the models obtained by cascading several layers of neurons that employ such recurrence. We show that MinMax RNCs enjoy many favourable theoretical properties. First, their formal expressivity includes all regular languages, arguably the maximal expressivity for a finite-memory system. Second, they can be evaluated in parallel with a runtime that is logarithmic in the input length given enough processors; and they can also be evaluated sequentially. Third, their state and activations are bounded uniformly for all input lengths. Fourth, at almost all points, their loss gradient exists and it is bounded. Fifth, they do not exhibit a vanishing state gradient: the gradient of a state w.r.t. a past state can have constant value one regardless of the time distance between the two states. Finally, we find empirical evidence that the favourable theoretical properties of MinMax RNCs are matched by their practical capabilities: they are able to perfectly solve a number of synthetic tasks, showing superior performance compared to the considered state-of-the-art recurrent neural networks; also, we train a MinMax RNC of 127M parameters on next-token prediction, and the obtained model shows competitive performance for its size, providing evidence of the potential of MinMax RNCs on real-world tasks.

Multivariate time-series data often exhibit complex temporal dependencies, irregular sampling, and heterogeneous dynamics across multiple time scales, making accurate sequence modeling particularly challenging. Traditional recurrent neural networks (RNNs), such as Long Short-Term Memory (LSTM) networks, operate in discrete time and may struggle to effectively capture continuous and irregular temporal behaviors. Liquid Neural Networks (LNNs) address some of these limitations through continuous-time dynamics, but standard LNN architectures typically rely on a single dynamical system, limiting their ability to model heterogeneous temporal patterns. To address these challenges, we propose a Multi-Rate Mixture-of-Experts (MR-MoE) framework built on top of Liquid Neural Networks. In the proposed architecture, multiple LNN-based experts operate at distinct time scales, enabling the model to explicitly separate fast-changing dynamics from slow-evolving temporal trends. A gating network further enables adaptive expert specialization based on input conditions. In addition, we incorporate both feature-level and temporal attention mechanisms to improve robustness, interpretability, and long-range dependency modeling. Feature-level attention suppresses noisy or irrelevant variables, while temporal attention selectively focuses on informative historical states. We evaluate the proposed framework on a complex multivariate time-series prediction task and compare it against strong baselines, including LSTM, monolithic LNN, and standard MoE models. Experimental results demonstrate that the proposed MR-MoE framework consistently achieves improved AUROC and AUPRC performance while maintaining favorable computational efficiency. These results highlight the effectiveness of combining continuous-time dynamics, multi-scale expert decomposition, and adaptive attention mechanisms for time-series modeling.

Deep learning employs multi-layer neural networks trained via the backpropagation algorithm. This approach has achieved success across many domains and relies on adaptive gradient methods such as the Adam optimizer. Sequence modeling evolved from recurrent neural networks to attention-based models, culminating in the Transformer architecture. Transformers have achieved state-of-the-art performance in natural language processing (for example, BERT and GPT-3) and have been applied in computer vision and computational biology. However, theoretical understanding of these models remains limited. In this paper, we examine the mathematical foundations of deep learning and Transformers and present a novel theoretical result. We review key concepts from linear algebra, probability, and optimization that underpin deep learning, and we analyze the multi-head self-attention mechanism and the backpropagation algorithm in detail. Our main contribution is a universal approximation theorem for Transformers: we prove that a single-layer Transformer, comprising one self-attention layer followed by a position-wise feed-forward network with ReLU activation, can approximate any continuous sequence-to-sequence mapping on a compact domain to arbitrary precision. We provide a formal statement and a complete proof. Finally, we present case studies that demonstrate the practical implications of this result. Our findings advance the theoretical understanding of Transformer models and help bridge the gap between theory and practice.

Sequence modeling has produced diverse architectures -- from classical recurrent neural networks to modern Transformers and state space models (SSMs) -- yet a unified theoretical understanding of expressivity and trainability trade-offs remains limited. We introduce a unified framework that represents a broad class of sequence maps via an input-dependent effective interaction operator W_{ij}(X), making explicit two recurring construction patterns: (i) the Unified Factorized Framework (Explicit) (attention-style mixing), in which W_{ij}(X) varies through scalar coefficients applied to shared value maps, and (ii) Structured Dynamics (Implicit) (state-space recurrences), in which W_{ij} is induced by a latent dynamical system. Using this framework, we derive three theoretical results. First, we establish the Interaction Rank Gap: models in the Unified Factorized Framework, such as single-head attention, are constrained to a low-dimensional operator span and cannot represent certain structured dynamical maps. Second, we prove an Equivalence (Head-Count) Theorem showing that, within our multi-head factorized class, representing a linear SSM whose lag operators span a k-dimensional subspace on length-n sequences requires and is achievable with H=k heads. Third, we prove a Gradient Highway Result, showing that attention layers admit inputs with distance-independent gradient paths, whereas stable linear dynamics exhibit distance-dependent gradient attenuation. Together, these results formalize a fundamental trade-off between algebraic expressivity (interaction/operator span) and long-range gradient propagation, providing theoretical grounding for modern sequence architecture design.

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.

Sequence modeling plays a vital role across various domains, with recurrent neural networks being historically the predominant method of performing these tasks. However, the emergence of transformers has altered this paradigm due to their superior performance. Built upon these advances, transformers have conjoined CNNs as two leading foundational models for learning visual representations. However, transformers are hindered by the O(N^2) complexity of their attention mechanisms, while CNNs lack global receptive fields and dynamic weight allocation. State Space Models (SSMs), specifically the \textbf{Mamba} model with selection mechanisms and hardware-aware architecture, have garnered immense interest lately in sequential modeling and visual representation learning, challenging the dominance of transformers by providing infinite context lengths and offering substantial efficiency maintaining linear complexity in the input sequence. Capitalizing on the advances in computer vision, medical imaging has heralded a new epoch with Mamba models. Intending to help researchers navigate the surge, this survey seeks to offer an encyclopedic review of Mamba models in medical imaging. Specifically, we start with a comprehensive theoretical review forming the basis of SSMs, including Mamba architecture and its alternatives for sequence modeling paradigms in this context. Next, we offer a structured classification of Mamba models in the medical field and introduce a diverse categorization scheme based on their application, imaging modalities, and targeted organs. Finally, we summarize key challenges, discuss different future research directions of the SSMs in the medical domain, and propose several directions to fulfill the demands of this field. In addition, we have compiled the studies discussed in this paper along with their open-source implementations on our GitHub repository.

Linear recurrent neural networks (LRNNs) provide a structured approach to sequence modeling that bridges classical linear dynamical systems and modern deep learning, offering both expressive power and theoretical guarantees on stability and trainability. In recent years, multiple LRNN-based architectures have been proposed, each introducing distinct parameterizations, discretization schemes, and implementation constraints. However, existing implementations are fragmented across different software frameworks, often rely on framework-specific optimizations, and in some cases require custom CUDA kernels or lack publicly available code altogether. As a result, using, comparing, or extending LRNNs requires substantial implementation effort. To address this, we introduce lrnnx, a unified software library that implements several modern LRNN architectures under a common interface. The library exposes multiple levels of control, allowing users to work directly with core components or higher-level model abstractions. lrnnx aims to improve accessibility, reproducibility, and extensibility of LRNN research and applications. We make our code available under a permissive MIT license.

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.

The design choices in the Transformer attention mechanism, including weak inductive bias and quadratic computational complexity, have limited its application for modeling long sequences. In this paper, we introduce Mega, a simple, theoretically grounded, single-head gated attention mechanism equipped with (exponential) moving average to incorporate inductive bias of position-aware local dependencies into the position-agnostic attention mechanism. We further propose a variant of Mega that offers linear time and space complexity yet yields only minimal quality loss, by efficiently splitting the whole sequence into multiple chunks with fixed length. Extensive experiments on a wide range of sequence modeling benchmarks, including the Long Range Arena, neural machine translation, auto-regressive language modeling, and image and speech classification, show that Mega achieves significant improvements over other sequence models, including variants of Transformers and recent state space models.

Handwritten Text Recognition (HTR) in free-layout pages is a challenging image understanding task that can provide a relevant boost to the digitization of handwritten documents and reuse of their content. The task becomes even more challenging when dealing with historical documents due to the variability of the writing style and degradation of the page quality. State-of-the-art HTR approaches typically couple recurrent structures for sequence modeling with Convolutional Neural Networks for visual feature extraction. Since convolutional kernels are defined on fixed grids and focus on all input pixels independently while moving over the input image, this strategy disregards the fact that handwritten characters can vary in shape, scale, and orientation even within the same document and that the ink pixels are more relevant than the background ones. To cope with these specific HTR difficulties, we propose to adopt deformable convolutions, which can deform depending on the input at hand and better adapt to the geometric variations of the text. We design two deformable architectures and conduct extensive experiments on both modern and historical datasets. Experimental results confirm the suitability of deformable convolutions for the HTR task.

The quadratic complexity and weak length extrapolation of Transformers limits their ability to scale to long sequences, and while sub-quadratic solutions like linear attention and state space models exist, they empirically underperform Transformers in pretraining efficiency and downstream task accuracy. We introduce Megalodon, a neural architecture for efficient sequence modeling with unlimited context length. Megalodon inherits the architecture of Mega (exponential moving average with gated attention), and further introduces multiple technical components to improve its capability and stability, including complex exponential moving average (CEMA), timestep normalization layer, normalized attention mechanism and pre-norm with two-hop residual configuration. In a controlled head-to-head comparison with Llama2, Megalodon achieves better efficiency than Transformer in the scale of 7 billion parameters and 2 trillion training tokens. Megalodon reaches a training loss of 1.70, landing mid-way between Llama2-7B (1.75) and 13B (1.67). Code: https://github.com/XuezheMax/megalodon

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.

State-space models (SSMs) offer a powerful framework for dynamical system analysis, wherein the temporal dynamics of the system are assumed to be captured through the evolution of the latent states, which govern the values of the observations. This paper provides a selective review of recent advancements in deep neural network-based approaches for SSMs, and presents a unified perspective for discrete time deep state space models and continuous time ones such as latent neural Ordinary Differential and Stochastic Differential Equations. It starts with an overview of the classical maximum likelihood based approach for learning SSMs, reviews variational autoencoder as a general learning pipeline for neural network-based approaches in the presence of latent variables, and discusses in detail representative deep learning models that fall under the SSM framework. Very recent developments, where SSMs are used as standalone architectural modules for improving efficiency in sequence modeling, are also examined. Finally, examples involving mixed frequency and irregularly-spaced time series data are presented to demonstrate the advantage of SSMs in these settings.

Recent neural network sequence models with softmax classifiers have achieved their best language modeling performance only with very large hidden states and large vocabularies. Even then they struggle to predict rare or unseen words even if the context makes the prediction unambiguous. We introduce the pointer sentinel mixture architecture for neural sequence models which has the ability to either reproduce a word from the recent context or produce a word from a standard softmax classifier. Our pointer sentinel-LSTM model achieves state of the art language modeling performance on the Penn Treebank (70.9 perplexity) while using far fewer parameters than a standard softmax LSTM. In order to evaluate how well language models can exploit longer contexts and deal with more realistic vocabularies and larger corpora we also introduce the freely available WikiText corpus.

This paper presents the Jazz Transformer, a generative model that utilizes a neural sequence model called the Transformer-XL for modeling lead sheets of Jazz music. Moreover, the model endeavors to incorporate structural events present in the Weimar Jazz Database (WJazzD) for inducing structures in the generated music. While we are able to reduce the training loss to a low value, our listening test suggests however a clear gap between the average ratings of the generated and real compositions. We therefore go one step further and conduct a series of computational analysis of the generated compositions from different perspectives. This includes analyzing the statistics of the pitch class, grooving, and chord progression, assessing the structureness of the music with the help of the fitness scape plot, and evaluating the model's understanding of Jazz music through a MIREX-like continuation prediction task. Our work presents in an analytical manner why machine-generated music to date still falls short of the artwork of humanity, and sets some goals for future work on automatic composition to further pursue.

Accurate detection of cardiac abnormalities from electrocardiogram recordings is regarded as essential for clinical diagnostics and decision support. Traditional deep learning models such as residual networks and transformer architectures have been applied successfully to this task, but their performance has been limited when long sequential signals are processed. Recently, state space models have been introduced as an efficient alternative. In this study, a hybrid framework named One Dimensional Convolutional Neural Network Electrocardiogram Mamba is introduced, in which convolutional feature extraction is combined with Mamba, a selective state space model designed for effective sequence modeling. The model is built upon Vision Mamba, a bidirectional variant through which the representation of temporal dependencies in electrocardiogram data is enhanced. Comprehensive experiments on the PhysioNet Computing in Cardiology Challenges of 2020 and 2021 were conducted, and superior performance compared with existing methods was achieved. Specifically, the proposed model achieved substantially higher AUPRC and AUROC scores than those reported by the best previously published algorithms on twelve lead electrocardiograms. These results demonstrate the potential of Mamba-based architectures to advance reliable ECG classification. This capability supports early diagnosis and personalized treatment, while enhancing accessibility in telemedicine and resource-constrained healthcare systems.

Traditional convolutional neural networks have a limited receptive field while transformer-based networks are mediocre in constructing long-term dependency from the perspective of computational complexity. Such the bottleneck poses a significant challenge when processing long video sequences in video analysis tasks. Very recently, the state space models (SSMs) with efficient hardware-aware designs, famous by Mamba, have exhibited impressive achievements in long sequence modeling, which facilitates the development of deep neural networks on many vision tasks. To better capture available cues in video frames, this paper presents a generic Video Vision Mamba-based framework for medical video object segmentation tasks, named Vivim. Our Vivim can effectively compress the long-term spatiotemporal representation into sequences at varying scales by our designed Temporal Mamba Block. Compared to existing video-level Transformer-based methods, our model maintains excellent segmentation results with better speed performance. Extensive experiments on the breast US dataset demonstrate the effectiveness and efficiency of our Vivim. The code for Vivim is available at: https://github.com/scott-yjyang/Vivim.

Human action recognition (HAR) plays a key role in various applications such as video analysis, surveillance, autonomous driving, robotics, and healthcare. Most HAR algorithms are developed from RGB images, which capture detailed visual information. However, these algorithms raise concerns in privacy-sensitive environments due to the recording of identifiable features. Event cameras offer a promising solution by capturing scene brightness changes sparsely at the pixel level, without capturing full images. Moreover, event cameras have high dynamic ranges that can effectively handle scenarios with complex lighting conditions, such as low light or high contrast environments. However, using event cameras introduces challenges in modeling the spatially sparse and high temporal resolution event data for HAR. To address these issues, we propose the SpikMamba framework, which combines the energy efficiency of spiking neural networks and the long sequence modeling capability of Mamba to efficiently capture global features from spatially sparse and high a temporal resolution event data. Additionally, to improve the locality of modeling, a spiking window-based linear attention mechanism is used. Extensive experiments show that SpikMamba achieves remarkable recognition performance, surpassing the previous state-of-the-art by 1.45%, 7.22%, 0.15%, and 3.92% on the PAF, HARDVS, DVS128, and E-FAction datasets, respectively. The code is available at https://github.com/Typistchen/SpikMamba.

We propose a novel text-to-speech (TTS) framework centered around a neural transducer. Our approach divides the whole TTS pipeline into semantic-level sequence-to-sequence (seq2seq) modeling and fine-grained acoustic modeling stages, utilizing discrete semantic tokens obtained from wav2vec2.0 embeddings. For a robust and efficient alignment modeling, we employ a neural transducer named token transducer for the semantic token prediction, benefiting from its hard monotonic alignment constraints. Subsequently, a non-autoregressive (NAR) speech generator efficiently synthesizes waveforms from these semantic tokens. Additionally, a reference speech controls temporal dynamics and acoustic conditions at each stage. This decoupled framework reduces the training complexity of TTS while allowing each stage to focus on semantic and acoustic modeling. Our experimental results on zero-shot adaptive TTS demonstrate that our model surpasses the baseline in terms of speech quality and speaker similarity, both objectively and subjectively. We also delve into the inference speed and prosody control capabilities of our approach, highlighting the potential of neural transducers in TTS frameworks.

We present a neural architecture that takes as input a 2D or 3D shape and outputs a program that generates the shape. The instructions in our program are based on constructive solid geometry principles, i.e., a set of boolean operations on shape primitives defined recursively. Bottom-up techniques for this shape parsing task rely on primitive detection and are inherently slow since the search space over possible primitive combinations is large. In contrast, our model uses a recurrent neural network that parses the input shape in a top-down manner, which is significantly faster and yields a compact and easy-to-interpret sequence of modeling instructions. Our model is also more effective as a shape detector compared to existing state-of-the-art detection techniques. We finally demonstrate that our network can be trained on novel datasets without ground-truth program annotations through policy gradient techniques.

Spiking neural networks (SNNs) are becoming a promising alternative to conventional artificial neural networks (ANNs) due to their rich neural dynamics and the implementation of energy-efficient neuromorphic chips. However, the non-differential binary communication mechanism makes SNN hard to converge to an ANN-level accuracy. When SNN encounters sequence learning, the situation becomes worse due to the difficulties in modeling long-range dependencies. To overcome these difficulties, researchers developed variants of LIF neurons and different surrogate gradients but still failed to obtain good results when the sequence became longer (e.g., >500). Unlike them, we obtain an optimal SNN in sequence learning by directly mapping parameters from a quantized CRNN. We design two sub-pipelines to support the end-to-end conversion of different structures in neural networks, which is called CNN-Morph (CNN rightarrow QCNN rightarrow BIFSNN) and RNN-Morph (RNN rightarrow QRNN rightarrow RBIFSNN). Using conversion pipelines and the s-analog encoding method, the conversion error of our framework is zero. Furthermore, we give the theoretical and experimental demonstration of the lossless CRNN-SNN conversion. Our results show the effectiveness of our method over short and long timescales tasks compared with the state-of-the-art learning- and conversion-based methods. We reach the highest accuracy of 99.16% (0.46 uparrow) on S-MNIST, 94.95% (3.95 uparrow) on PS-MNIST (sequence length of 784) respectively, and the lowest loss of 0.057 (0.013 downarrow) within 8 time-steps in collision avoidance dataset.

Modeling attention in neural multi-source sequence-to-sequence learning remains a relatively unexplored area, despite its usefulness in tasks that incorporate multiple source languages or modalities. We propose two novel approaches to combine the outputs of attention mechanisms over each source sequence, flat and hierarchical. We compare the proposed methods with existing techniques and present results of systematic evaluation of those methods on the WMT16 Multimodal Translation and Automatic Post-editing tasks. We show that the proposed methods achieve competitive results on both tasks.

Reconstructing nonlinear dynamical systems (DS) from data (DSR) is a fundamental challenge in science and engineering, but it inherently relies on sequential models. Recent breakthroughs for sequential models have produced algorithms that parallelize computation along sequence length T, achieving logarithmic time complexity, O(log T). Since sequence lengths have been practically limited due to the linear runtime complexity O(T) of classical backpropagation through time, this opens new avenues for DSR. This paper studies two prominent classes of parallel-in-time algorithms for this task, both of which leverage parallel associative scans as their core computational primitive. The first class comprises models with linear yet non-autonomous dynamics and a nonlinear readout, such as modern State Space Models (SSMs), while the second consists of general nonlinear models which can be parallelized using the DEER framework. We find that the linear training-time recurrence of the first class of models imposes limitations that often hinder learning of accurate nonlinear dynamics. To address this, we augment DEER with Generalized Teacher Forcing (GTF), a novel variant within the more general nonlinear framework that ensures stable and effective learning of nonlinear dynamics across arbitrary sequence lengths. Using GTF-DEER, we investigate the benefits of training on extremely long sequences (T>10^4) for DSR. Our results show that access to such long trajectories significantly improves DSR if the data features long time scales. This work establishes GTF-DEER as a robust tool for data-driven discovery and underscores the largely untapped potential of long-sequence learning in modeling complex DS.

The language model (LM) approach based on acoustic and linguistic prompts, such as VALL-E, has achieved remarkable progress in the field of zero-shot audio generation. However, existing methods still have some limitations: 1) repetitions, transpositions, and omissions in the output synthesized speech due to limited alignment constraints between audio and phoneme tokens; 2) challenges of fine-grained control over the synthesized speech with autoregressive (AR) language model; 3) infinite silence generation due to the nature of AR-based decoding, especially under the greedy strategy. To alleviate these issues, we propose ELLA-V, a simple but efficient LM-based zero-shot text-to-speech (TTS) framework, which enables fine-grained control over synthesized audio at the phoneme level. The key to ELLA-V is interleaving sequences of acoustic and phoneme tokens, where phoneme tokens appear ahead of the corresponding acoustic tokens. The experimental findings reveal that our model outperforms VALL-E in terms of accuracy and delivers more stable results using both greedy and sampling-based decoding strategies. The code of ELLA-V will be open-sourced after cleanups. Audio samples are available at https://ereboas.github.io/ELLAV/.

Named Entity Recognition (NER) is a fundamental NLP task, commonly formulated as classification over a sequence of tokens. Morphologically-Rich Languages (MRLs) pose a challenge to this basic formulation, as the boundaries of Named Entities do not necessarily coincide with token boundaries, rather, they respect morphological boundaries. To address NER in MRLs we then need to answer two fundamental questions, namely, what are the basic units to be labeled, and how can these units be detected and classified in realistic settings, i.e., where no gold morphology is available. We empirically investigate these questions on a novel NER benchmark, with parallel tokenlevel and morpheme-level NER annotations, which we develop for Modern Hebrew, a morphologically rich-and-ambiguous language. Our results show that explicitly modeling morphological boundaries leads to improved NER performance, and that a novel hybrid architecture, in which NER precedes and prunes morphological decomposition, greatly outperforms the standard pipeline, where morphological decomposition strictly precedes NER, setting a new performance bar for both Hebrew NER and Hebrew morphological decomposition tasks.

Recursive Neural Networks (RvNNs), which compose sequences according to their underlying hierarchical syntactic structure, have performed well in several natural language processing tasks compared to similar models without structural biases. However, traditional RvNNs are incapable of inducing the latent structure in a plain text sequence on their own. Several extensions have been proposed to overcome this limitation. Nevertheless, these extensions tend to rely on surrogate gradients or reinforcement learning at the cost of higher bias or variance. In this work, we propose Continuous Recursive Neural Network (CRvNN) as a backpropagation-friendly alternative to address the aforementioned limitations. This is done by incorporating a continuous relaxation to the induced structure. We demonstrate that CRvNN achieves strong performance in challenging synthetic tasks such as logical inference and ListOps. We also show that CRvNN performs comparably or better than prior latent structure models on real-world tasks such as sentiment analysis and natural language inference.

Named Entity Recognition (NER) models capable of Continual Learning (CL) are realistically valuable in areas where entity types continuously increase (e.g., personal assistants). Meanwhile the learning paradigm of NER advances to new patterns such as the span-based methods. However, its potential to CL has not been fully explored. In this paper, we propose SpanKL, a simple yet effective Span-based model with Knowledge distillation (KD) to preserve memories and multi-Label prediction to prevent conflicts in CL-NER. Unlike prior sequence labeling approaches, the inherently independent modeling in span and entity level with the designed coherent optimization on SpanKL promotes its learning at each incremental step and mitigates the forgetting. Experiments on synthetic CL datasets derived from OntoNotes and Few-NERD show that SpanKL significantly outperforms previous SoTA in many aspects, and obtains the smallest gap from CL to the upper bound revealing its high practiced value. The code is available at https://github.com/Qznan/SpanKL.

Neural Temporal Point Processes (TPPs) are the prevalent paradigm for modeling continuous-time event sequences, such as user activities on the web and financial transactions. In real-world applications, event data is typically received in a streaming manner, where the distribution of patterns may shift over time. Additionally, privacy and memory constraints are commonly observed in practical scenarios, further compounding the challenges. Therefore, the continuous monitoring of a TPP to learn the streaming event sequence is an important yet under-explored problem. Our work paper addresses this challenge by adopting Continual Learning (CL), which makes the model capable of continuously learning a sequence of tasks without catastrophic forgetting under realistic constraints. Correspondingly, we propose a simple yet effective framework, PromptTPPOur code is available at {\small \url{ https://github.com/yanyanSann/PromptTPP}}, by integrating the base TPP with a continuous-time retrieval prompt pool. The prompts, small learnable parameters, are stored in a memory space and jointly optimized with the base TPP, ensuring that the model learns event streams sequentially without buffering past examples or task-specific attributes. We present a novel and realistic experimental setup for modeling event streams, where PromptTPP consistently achieves state-of-the-art performance across three real user behavior datasets.

We propose a novel convolutional architecture, named genCNN, for word sequence prediction. Different from previous work on neural network-based language modeling and generation (e.g., RNN or LSTM), we choose not to greedily summarize the history of words as a fixed length vector. Instead, we use a convolutional neural network to predict the next word with the history of words of variable length. Also different from the existing feedforward networks for language modeling, our model can effectively fuse the local correlation and global correlation in the word sequence, with a convolution-gating strategy specifically designed for the task. We argue that our model can give adequate representation of the history, and therefore can naturally exploit both the short and long range dependencies. Our model is fast, easy to train, and readily parallelized. Our extensive experiments on text generation and n-best re-ranking in machine translation show that genCNN outperforms the state-of-the-arts with big margins.

Modeling dynamic graphs, such as those found in social networks, recommendation systems, and e-commerce platforms, is crucial for capturing evolving relationships and delivering relevant insights over time. Traditional approaches primarily rely on graph neural networks with temporal components or sequence generation models, which often focus narrowly on the historical context of target nodes. This limitation restricts the ability to adapt to new and emerging patterns in dynamic graphs. To address this challenge, we propose a novel framework, Retrieval-Augmented Generation for Dynamic Graph modeling (RAG4DyG), which enhances dynamic graph predictions by incorporating contextually and temporally relevant examples from broader graph structures. Our approach includes a time- and context-aware contrastive learning module to identify high-quality demonstrations and a graph fusion strategy to effectively integrate these examples with historical contexts. The proposed framework is designed to be effective in both transductive and inductive scenarios, ensuring adaptability to previously unseen nodes and evolving graph structures. Extensive experiments across multiple real-world datasets demonstrate the effectiveness of RAG4DyG in improving predictive accuracy and adaptability for dynamic graph modeling. The code and datasets are publicly available at https://github.com/YuxiaWu/RAG4DyG.

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.

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.

Long short-term memory (LSTM) is a kind of recurrent neural networks (RNN) for sequence and temporal dependency data modeling and its effectiveness has been extensively established. In this work, we propose a hybrid quantum-classical model of LSTM, which we dub QLSTM. We demonstrate that the proposed model successfully learns several kinds of temporal data. In particular, we show that for certain testing cases, this quantum version of LSTM converges faster, or equivalently, reaches a better accuracy, than its classical counterpart. Due to the variational nature of our approach, the requirements on qubit counts and circuit depth are eased, and our work thus paves the way toward implementing machine learning algorithms for sequence modeling on noisy intermediate-scale quantum (NISQ) devices.

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

We propose Algorithm Distillation (AD), a method for distilling reinforcement learning (RL) algorithms into neural networks by modeling their training histories with a causal sequence model. Algorithm Distillation treats learning to reinforcement learn as an across-episode sequential prediction problem. A dataset of learning histories is generated by a source RL algorithm, and then a causal transformer is trained by autoregressively predicting actions given their preceding learning histories as context. Unlike sequential policy prediction architectures that distill post-learning or expert sequences, AD is able to improve its policy entirely in-context without updating its network parameters. We demonstrate that AD can reinforcement learn in-context in a variety of environments with sparse rewards, combinatorial task structure, and pixel-based observations, and find that AD learns a more data-efficient RL algorithm than the one that generated the source data.

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.

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

State-space language models such as Mamba and gated linear attention (GLA) offer efficient alternatives to transformers due to their linear complexity and parallel training, but often lack the expressivity and robust state-tracking needed for complex reasoning. We address these limitations by reframing sequence modelling through a probabilistic lens, using Bayesian filters as a core primitive. While classical filters such as Kalman filters provide principled state estimation and uncertainty tracking, they are typically viewed as inherently sequential. We show that reparameterising the Kalman filter in information form enables its updates to be computed via an associative scan, allowing efficient parallel training. Building on this insight, we introduce the Kalman Linear Attention (KLA) layer, a neural sequence-modelling primitive that performs time-parallel probabilistic inference while maintaining explicit belief-state uncertainty. KLA offers strictly more expressive nonlinear updates and gating than GLA variants while retaining their computational advantages. On language modelling tasks, KLA matches or outperforms modern SSMs and GLAs across representative discrete token-manipulation and state-tracking benchmarks.

Sequence models lie at the heart of modern deep learning. However, rapid advancements have produced a diversity of seemingly unrelated architectures, such as Transformers and recurrent alternatives. In this paper, we introduce a unifying framework to understand and derive these sequence models, inspired by the empirical importance of associative recall, the capability to retrieve contextually relevant tokens. We formalize associative recall as a two-step process, memorization and retrieval, casting memorization as a regression problem. Layers that combine these two steps perform associative recall via ``test-time regression'' over its input tokens. Prominent layers, including linear attention, state-space models, fast-weight programmers, online learners, and softmax attention, arise as special cases defined by three design choices: the regression weights, the regressor function class, and the test-time optimization algorithm. Our approach clarifies how linear attention fails to capture inter-token correlations and offers a mathematical justification for the empirical effectiveness of query-key normalization in softmax attention. Further, it illuminates unexplored regions within the design space, which we use to derive novel higher-order generalizations of softmax attention. Beyond unification, our work bridges sequence modeling with classic regression methods, a field with extensive literature, paving the way for developing more powerful and theoretically principled architectures.

Transformers are powerful sequence models, but require time and memory that grows quadratically with the sequence length. In this paper we introduce sparse factorizations of the attention matrix which reduce this to O(n n). We also introduce a) a variation on architecture and initialization to train deeper networks, b) the recomputation of attention matrices to save memory, and c) fast attention kernels for training. We call networks with these changes Sparse Transformers, and show they can model sequences tens of thousands of timesteps long using hundreds of layers. We use the same architecture to model images, audio, and text from raw bytes, setting a new state of the art for density modeling of Enwik8, CIFAR-10, and ImageNet-64. We generate unconditional samples that demonstrate global coherence and great diversity, and show it is possible in principle to use self-attention to model sequences of length one million or more.

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.

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

We present the Compressive Transformer, an attentive sequence model which compresses past memories for long-range sequence learning. We find the Compressive Transformer obtains state-of-the-art language modelling results in the WikiText-103 and Enwik8 benchmarks, achieving 17.1 ppl and 0.97 bpc respectively. We also find it can model high-frequency speech effectively and can be used as a memory mechanism for RL, demonstrated on an object matching task. To promote the domain of long-range sequence learning, we propose a new open-vocabulary language modelling benchmark derived from books, PG-19.

Recurrent neural networks have been very successful at predicting sequences of words in tasks such as language modeling. However, all such models are based on the conventional classification framework, where the model is trained against one-hot targets, and each word is represented both as an input and as an output in isolation. This causes inefficiencies in learning both in terms of utilizing all of the information and in terms of the number of parameters needed to train. We introduce a novel theoretical framework that facilitates better learning in language modeling, and show that our framework leads to tying together the input embedding and the output projection matrices, greatly reducing the number of trainable variables. Our framework leads to state of the art performance on the Penn Treebank with a variety of network models.

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), 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.

For most deep learning practitioners, sequence modeling is synonymous with recurrent networks. Yet recent results indicate that convolutional architectures can outperform recurrent networks on tasks such as audio synthesis and machine translation. Given a new sequence modeling task or dataset, which architecture should one use? We conduct a systematic evaluation of generic convolutional and recurrent architectures for sequence modeling. The models are evaluated across a broad range of standard tasks that are commonly used to benchmark recurrent networks. Our results indicate that a simple convolutional architecture outperforms canonical recurrent networks such as LSTMs across a diverse range of tasks and datasets, while demonstrating longer effective memory. We conclude that the common association between sequence modeling and recurrent networks should be reconsidered, and convolutional networks should be regarded as a natural starting point for sequence modeling tasks. To assist related work, we have made code available at http://github.com/locuslab/TCN .

Neural sequence-to-sequence models are currently the dominant approach in several natural language processing tasks, but require large parallel corpora. We present a sequence-to-sequence-to-sequence autoencoder (SEQ^3), consisting of two chained encoder-decoder pairs, with words used as a sequence of discrete latent variables. We apply the proposed model to unsupervised abstractive sentence compression, where the first and last sequences are the input and reconstructed sentences, respectively, while the middle sequence is the compressed sentence. Constraining the length of the latent word sequences forces the model to distill important information from the input. A pretrained language model, acting as a prior over the latent sequences, encourages the compressed sentences to be human-readable. Continuous relaxations enable us to sample from categorical distributions, allowing gradient-based optimization, unlike alternatives that rely on reinforcement learning. The proposed model does not require parallel text-summary pairs, achieving promising results in unsupervised sentence compression on benchmark datasets.

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

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.

Neural sequence models are widely used to model time-series data. Equally ubiquitous is the usage of beam search (BS) as an approximate inference algorithm to decode output sequences from these models. BS explores the search space in a greedy left-right fashion retaining only the top-B candidates - resulting in sequences that differ only slightly from each other. Producing lists of nearly identical sequences is not only computationally wasteful but also typically fails to capture the inherent ambiguity of complex AI tasks. To overcome this problem, we propose Diverse Beam Search (DBS), an alternative to BS that decodes a list of diverse outputs by optimizing for a diversity-augmented objective. We observe that our method finds better top-1 solutions by controlling for the exploration and exploitation of the search space - implying that DBS is a better search algorithm. Moreover, these gains are achieved with minimal computational or memory over- head as compared to beam search. To demonstrate the broad applicability of our method, we present results on image captioning, machine translation and visual question generation using both standard quantitative metrics and qualitative human studies. Further, we study the role of diversity for image-grounded language generation tasks as the complexity of the image changes. We observe that our method consistently outperforms BS and previously proposed techniques for diverse decoding from neural sequence models.

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

In this work we explore recent advances in Recurrent Neural Networks for large scale Language Modeling, a task central to language understanding. We extend current models to deal with two key challenges present in this task: corpora and vocabulary sizes, and complex, long term structure of language. We perform an exhaustive study on techniques such as character Convolutional Neural Networks or Long-Short Term Memory, on the One Billion Word Benchmark. Our best single model significantly improves state-of-the-art perplexity from 51.3 down to 30.0 (whilst reducing the number of parameters by a factor of 20), while an ensemble of models sets a new record by improving perplexity from 41.0 down to 23.7. We also release these models for the NLP and ML community to study and improve upon.

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

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

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

Despite the extensive success of pretrained language models as encoders for building NLP systems, they haven't seen prominence as decoders for sequence generation tasks. We explore the question of whether these models can be adapted to be used as universal decoders. To be considered "universal," a decoder must have an implicit representation for any target sentence s, such that it can recover that sentence exactly when conditioned on its representation. For large transformer-based language models trained on vast amounts of English text, we investigate whether such representations can be easily discovered using standard optimization methods. We present and compare three representation injection techniques for transformer-based models and three accompanying methods which map sentences to and from this representation space. Experiments show that not only do representations exist for sentences from a variety of genres. More importantly, without needing complex optimization algorithms, our methods recover these sentences almost perfectly without fine-tuning the underlying language model at all.

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

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.

Encoder-decoder models have become an effective approach for sequence learning tasks like machine translation, image captioning and speech recognition, but have yet to show competitive results for handwritten text recognition. To this end, we propose an attention-based sequence-to-sequence model. It combines a convolutional neural network as a generic feature extractor with a recurrent neural network to encode both the visual information, as well as the temporal context between characters in the input image, and uses a separate recurrent neural network to decode the actual character sequence. We make experimental comparisons between various attention mechanisms and positional encodings, in order to find an appropriate alignment between the input and output sequence. The model can be trained end-to-end and the optional integration of a hybrid loss allows the encoder to retain an interpretable and usable output, if desired. We achieve competitive results on the IAM and ICFHR2016 READ data sets compared to the state-of-the-art without the use of a language model, and we significantly improve over any recent sequence-to-sequence approaches.

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.

A central goal of sequence modeling is designing a single principled model that can address sequence data across a range of modalities and tasks, particularly on long-range dependencies. Although conventional models including RNNs, CNNs, and Transformers have specialized variants for capturing long dependencies, they still struggle to scale to very long sequences of 10000 or more steps. A promising recent approach proposed modeling sequences by simulating the fundamental state space model (SSM) \( x'(t) = Ax(t) + Bu(t), y(t) = Cx(t) + Du(t) \), and showed that for appropriate choices of the state matrix \( A \), this system could handle long-range dependencies mathematically and empirically. However, this method has prohibitive computation and memory requirements, rendering it infeasible as a general sequence modeling solution. We propose the Structured State Space sequence model (S4) based on a new parameterization for the SSM, and show that it can be computed much more efficiently than prior approaches while preserving their theoretical strengths. Our technique involves conditioning \( A \) with a low-rank correction, allowing it to be diagonalized stably and reducing the SSM to the well-studied computation of a Cauchy kernel. S4 achieves strong empirical results across a diverse range of established benchmarks, including (i) 91\% accuracy on sequential CIFAR-10 with no data augmentation or auxiliary losses, on par with a larger 2-D ResNet, (ii) substantially closing the gap to Transformers on image and language modeling tasks, while performing generation 60times faster (iii) SoTA on every task from the Long Range Arena benchmark, including solving the challenging Path-X task of length 16k that all prior work fails on, while being as efficient as all competitors.

Transformers have impressive generalization capabilities on tasks with a fixed context length. However, they fail to generalize to sequences of arbitrary length, even for seemingly simple tasks such as duplicating a string. Moreover, simply training on longer sequences is inefficient due to the quadratic computation complexity of the global attention mechanism. In this work, we demonstrate that this failure mode is linked to positional encodings being out-of-distribution for longer sequences (even for relative encodings) and introduce a novel family of positional encodings that can overcome this problem. Concretely, our randomized positional encoding scheme simulates the positions of longer sequences and randomly selects an ordered subset to fit the sequence's length. Our large-scale empirical evaluation of 6000 models across 15 algorithmic reasoning tasks shows that our method allows Transformers to generalize to sequences of unseen length (increasing test accuracy by 12.0% on average).

We present two approaches that use unlabeled data to improve sequence learning with recurrent networks. The first approach is to predict what comes next in a sequence, which is a conventional language model in natural language processing. The second approach is to use a sequence autoencoder, which reads the input sequence into a vector and predicts the input sequence again. These two algorithms can be used as a "pretraining" step for a later supervised sequence learning algorithm. In other words, the parameters obtained from the unsupervised step can be used as a starting point for other supervised training models. In our experiments, we find that long short term memory recurrent networks after being pretrained with the two approaches are more stable and generalize better. With pretraining, we are able to train long short term memory recurrent networks up to a few hundred timesteps, thereby achieving strong performance in many text classification tasks, such as IMDB, DBpedia and 20 Newsgroups.

We study automatic question generation for sentences from text passages in reading comprehension. We introduce an attention-based sequence learning model for the task and investigate the effect of encoding sentence- vs. paragraph-level information. In contrast to all previous work, our model does not rely on hand-crafted rules or a sophisticated NLP pipeline; it is instead trainable end-to-end via sequence-to-sequence learning. Automatic evaluation results show that our system significantly outperforms the state-of-the-art rule-based system. In human evaluations, questions generated by our system are also rated as being more natural (i.e., grammaticality, fluency) and as more difficult to answer (in terms of syntactic and lexical divergence from the original text and reasoning needed to answer).

Transformers are the dominant architecture for sequence modeling, but there is growing interest in models that use a fixed-size latent state that does not depend on the sequence length, which we refer to as "generalized state space models" (GSSMs). In this paper we show that while GSSMs are promising in terms of inference-time efficiency, they are limited compared to transformer models on tasks that require copying from the input context. We start with a theoretical analysis of the simple task of string copying and prove that a two layer transformer can copy strings of exponential length while GSSMs are fundamentally limited by their fixed-size latent state. Empirically, we find that transformers outperform GSSMs in terms of efficiency and generalization on synthetic tasks that require copying the context. Finally, we evaluate pretrained large language models and find that transformer models dramatically outperform state space models at copying and retrieving information from context. Taken together, these results suggest a fundamental gap between transformers and GSSMs on tasks of practical interest.

People can learn a new concept and use it compositionally, understanding how to "blicket twice" after learning how to "blicket." In contrast, powerful sequence-to-sequence (seq2seq) neural networks fail such tests of compositionality, especially when composing new concepts together with existing concepts. In this paper, I show how memory-augmented neural networks can be trained to generalize compositionally through meta seq2seq learning. In this approach, models train on a series of seq2seq problems to acquire the compositional skills needed to solve new seq2seq problems. Meta se2seq learning solves several of the SCAN tests for compositional learning and can learn to apply implicit rules to variables.

Most unsupervised NLP models represent each word with a single point or single region in semantic space, while the existing multi-sense word embeddings cannot represent longer word sequences like phrases or sentences. We propose a novel embedding method for a text sequence (a phrase or a sentence) where each sequence is represented by a distinct set of multi-mode codebook embeddings to capture different semantic facets of its meaning. The codebook embeddings can be viewed as the cluster centers which summarize the distribution of possibly co-occurring words in a pre-trained word embedding space. We introduce an end-to-end trainable neural model that directly predicts the set of cluster centers from the input text sequence during test time. Our experiments show that the per-sentence codebook embeddings significantly improve the performances in unsupervised sentence similarity and extractive summarization benchmarks. In phrase similarity experiments, we discover that the multi-facet embeddings provide an interpretable semantic representation but do not outperform the single-facet baseline.

Recent advances in efficient sequence modeling have introduced selective state-space layers, a key component of the Mamba architecture, which have demonstrated remarkable success in a wide range of NLP and vision tasks. While Mamba's empirical performance has matched or surpassed SoTA transformers on such diverse benchmarks, the theoretical foundations underlying its powerful representational capabilities remain less explored. In this work, we investigate the expressivity of selective state-space layers using multivariate polynomials, and prove that they surpass linear transformers in expressiveness. Consequently, our findings reveal that Mamba offers superior representational power over linear attention-based models for long sequences, while not sacrificing their generalization. Our theoretical insights are validated by a comprehensive set of empirical experiments on various datasets.

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

Users engage with financial services companies through multiple channels, often interacting with mobile applications, web platforms, call centers, and physical locations to service their accounts. The resulting interactions are recorded at heterogeneous temporal resolutions across these domains. This multi-channel data can be combined and encoded to create a comprehensive representation of the customer's journey for accurate intent prediction. This demands sequential learning solutions. NMT transformers achieve state-of-the-art sequential representation learning by encoding context and decoding for the next best action to represent long-range dependencies. However, three major challenges exist while combining multi-domain sequences within an encoder-decoder transformers architecture for intent prediction applications: a) aligning sequences with different sampling rates b) learning temporal dynamics across multi-variate, multi-domain sequences c) combining dynamic and static sequences. We propose an encoder-decoder transformer model to address these challenges for contextual and sequential intent prediction in financial servicing applications. Our experiments show significant improvement over the existing tabular method.

This work presents an analysis of the effectiveness of using standard shallow feed-forward networks to mimic the behavior of the attention mechanism in the original Transformer model, a state-of-the-art architecture for sequence-to-sequence tasks. We substitute key elements of the attention mechanism in the Transformer with simple feed-forward networks, trained using the original components via knowledge distillation. Our experiments, conducted on the IWSLT2017 dataset, reveal the capacity of these "attentionless Transformers" to rival the performance of the original architecture. Through rigorous ablation studies, and experimenting with various replacement network types and sizes, we offer insights that support the viability of our approach. This not only sheds light on the adaptability of shallow feed-forward networks in emulating attention mechanisms but also underscores their potential to streamline complex architectures for sequence-to-sequence tasks.

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.

Recent large-scale neural autoregressive sequence models have shown impressive performances on a variety of natural language generation tasks. However, their generated sequences often exhibit degenerate properties such as non-termination, undesirable repetition, and premature termination, when generated with decoding algorithms such as greedy search, beam search, top-k sampling, and nucleus sampling. In this paper, we focus on the problem of non-terminating sequences resulting from an incomplete decoding algorithm. We first define an incomplete probable decoding algorithm which includes greedy search, top-k sampling, and nucleus sampling, beyond the incomplete decoding algorithm originally put forward by Welleck et al. (2020). We then propose a non-monotonic self-terminating language model, which significantly relaxes the constraint of monotonically increasing termination probability in the originally proposed self-terminating language model by Welleck et al. (2020), to address the issue of non-terminating sequences when using incomplete probable decoding algorithms. We prove that our proposed model prevents non-terminating sequences when using not only incomplete probable decoding algorithms but also beam search. We empirically validate our model on sequence completion tasks with various architectures.

We propose a new benchmark corpus to be used for measuring progress in statistical language modeling. With almost one billion words of training data, we hope this benchmark will be useful to quickly evaluate novel language modeling techniques, and to compare their contribution when combined with other advanced techniques. We show performance of several well-known types of language models, with the best results achieved with a recurrent neural network based language model. The baseline unpruned Kneser-Ney 5-gram model achieves perplexity 67.6; a combination of techniques leads to 35% reduction in perplexity, or 10% reduction in cross-entropy (bits), over that baseline. The benchmark is available as a code.google.com project; besides the scripts needed to rebuild the training/held-out data, it also makes available log-probability values for each word in each of ten held-out data sets, for each of the baseline n-gram models.

Language is typically modelled with discrete sequences. However, the most successful approaches to language modelling, namely neural networks, are continuous and smooth function approximators. In this work, we show that Transformer-based language models implicitly learn to represent sentences as continuous-time functions defined over a continuous input space. This phenomenon occurs in most state-of-the-art Large Language Models (LLMs), including Llama2, Llama3, Phi3, Gemma, Gemma2, and Mistral, and suggests that LLMs reason about language in ways that fundamentally differ from humans. Our work formally extends Transformers to capture the nuances of time and space continuity in both input and output space. Our results challenge the traditional interpretation of how LLMs understand language, with several linguistic and engineering implications.

We present a novel neural network for processing sequences. The ByteNet is a one-dimensional convolutional neural network that is composed of two parts, one to encode the source sequence and the other to decode the target sequence. The two network parts are connected by stacking the decoder on top of the encoder and preserving the temporal resolution of the sequences. To address the differing lengths of the source and the target, we introduce an efficient mechanism by which the decoder is dynamically unfolded over the representation of the encoder. The ByteNet uses dilation in the convolutional layers to increase its receptive field. The resulting network has two core properties: it runs in time that is linear in the length of the sequences and it sidesteps the need for excessive memorization. The ByteNet decoder attains state-of-the-art performance on character-level language modelling and outperforms the previous best results obtained with recurrent networks. The ByteNet also achieves state-of-the-art performance on character-to-character machine translation on the English-to-German WMT translation task, surpassing comparable neural translation models that are based on recurrent networks with attentional pooling and run in quadratic time. We find that the latent alignment structure contained in the representations reflects the expected alignment between the tokens.

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

The Transformer architecture, underpinned by the self-attention mechanism, has become the de facto standard for sequence modeling tasks. However, its core computational primitive scales quadratically with sequence length (O(N^2)), creating a significant bottleneck for processing long contexts. In this paper, we propose the Gated Associative Memory (GAM) network, a novel, fully parallel architecture for sequence modeling that exhibits linear complexity (O(N)) with respect to sequence length. The GAM block replaces the self-attention layer with two parallel pathways: a causal convolution to efficiently capture local, position-dependent context, and a parallel associative memory retrieval mechanism to model global, content-based patterns. These pathways are dynamically fused using a gating mechanism, allowing the model to flexibly combine local and global information for each token. We implement GAM from scratch and conduct a rigorous comparative analysis against a standard Transformer model and a modern linear-time baseline (Mamba) on the WikiText-2 benchmark, as well as against the Transformer on the TinyStories dataset. Our experiments demonstrate that GAM is consistently faster, outperforming both baselines on training speed, and achieves a superior or competitive final validation perplexity across all datasets, establishing it as a promising and efficient alternative for sequence modeling.

Neural sequence models can generate highly fluent sentences, but recent studies have also shown that they are also prone to hallucinate additional content not supported by the input. These variety of fluent but wrong outputs are particularly problematic, as it will not be possible for users to tell they are being presented incorrect content. To detect these errors, we propose a task to predict whether each token in the output sequence is hallucinated (not contained in the input) and collect new manually annotated evaluation sets for this task. We also introduce a method for learning to detect hallucinations using pretrained language models fine tuned on synthetic data that includes automatically inserted hallucinations Experiments on machine translation (MT) and abstractive summarization demonstrate that our proposed approach consistently outperforms strong baselines on all benchmark datasets. We further demonstrate how to use the token-level hallucination labels to define a fine-grained loss over the target sequence in low-resource MT and achieve significant improvements over strong baseline methods. We also apply our method to word-level quality estimation for MT and show its effectiveness in both supervised and unsupervised settings. Codes and data available at https://github.com/violet-zct/fairseq-detect-hallucination.