Sequence Modeling

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Sequence modeling asks how information in an ordered stream—such as words, sensor readings, user actions, or DNA—can be used to predict what comes next or interpret the sequence as a whole. Common approaches include recurrent networks such as LSTMs, Transformer attention, state-space models such as Mamba, and Markov or hidden Markov models; hybrids and diffusion methods are also used for long or structured sequences. Applications range from language and time-series forecasting to recommendation, biological analysis, and action recognition, with evaluation often testing prediction quality, long-range recall, and generalization to new lengths or domains. A central tension is balancing expressive memory and reliable long-context behavior against computation, latency, and memory costs, while ensuring benchmarks measure genuine sequence understanding rather than leakage or repetition.

Latest papers

250 papers22 papers in the last four weeks, up 38% on the four weeks before. 0.1% of all new papers.

Mar 17, 2026

EMA Is Not All You Need: Mapping the Boundary Between Structure and Content in Recurrent Context

What exactly do efficient sequence models gain over simple temporal averaging? We use exponential moving average (EMA) traces, the simplest recurrent context (no gating, no content-based retrieval), as a controlled probe to map the boundary between what fixed-coefficient accumulation can and cannot represent. EMA traces encode temporal structure: a Hebbian architecture with multi-timescale traces achieves 96% of a supervised BiGRU on grammatical role assignment with zero labels, surpassing the supervised model on structure-dependent roles. EMA traces destroy token identity: a 130M-parameter language model using only EMA context reaches C4 perplexity 260 (8x GPT-2), and a predictor ablation (replacing the linear predictor with full softmax attention) yields identical loss, localizing the entire gap to the traces. The traces apply lossy, data-independent compression; by the data processing inequality, no downstream predictor can recover the discarded information. Fixed-coefficient accumulation, whether across time or depth, suffers irreversible information dilution that only learned, input-dependent selection can resolve.

Arth Singh

AIM Intelligence National Institute of Technology Agartala

Sequence Modeling Autoregressive Language Modeling

Mar 16, 2026

Mamba-3: Improved Sequence Modeling using State Space Principles

Scaling inference-time compute has emerged as an important driver of LLM performance, making inference efficiency a central focus of model design alongside model quality. While the current Transformer-based models deliver strong model quality, their quadratic compute and linear memory make inference expensive. This has spurred the development of sub-quadratic models with reduced linear compute and constant memory requirements. However, many recent linear models trade off model quality and capability for algorithmic efficiency, failing on tasks such as state tracking. Moreover, their theoretically linear inference remains hardware-inefficient in practice. Guided by an inference-first perspective, we introduce three core methodological improvements inspired by the state space model (SSM) viewpoint of linear models. We combine: (1) a more expressive recurrence derived from SSM discretization, (2) a complex-valued state update rule that enables richer state tracking, and (3) a multi-input, multi-output (MIMO) formulation for better model performance without increasing decode latency. Together with architectural refinements, our Mamba-3 model achieves significant gains across retrieval, state-tracking, and downstream language modeling tasks. At the 1.5B scale, Mamba-3 improves average downstream accuracy by 0.6 percentage points compared to the next best model (Gated DeltaNet), with Mamba-3's MIMO variant further improving accuracy by another 1.2 points for a total 1.8 point gain. Across state-size experiments, Mamba-3 achieves comparable perplexity to Mamba-2 despite using half of its predecessor's state size. Our evaluations demonstrate Mamba-3's ability to advance the performance-efficiency Pareto frontier.

Aakash Lahoti, Kevin Y. Li, Berlin Chen +5

Carnegie Mellon University · Princeton University · Together AI +1

State Space Language Models Sequence Modeling Efficient Language Model Inference State Space Models State Tracking

Mar 16, 2026

Embedding-Aware Feature Discovery: Bridging Latent Representations and Interpretable Features in Event Sequences

Industrial financial systems operate on temporal event sequences such as transactions, user actions, and system logs. While recent research emphasizes representation learning and large language models, production systems continue to rely heavily on handcrafted statistical features due to their interpretability, robustness under limited supervision, and strict latency constraints. This creates a persistent disconnect between learned embeddings and feature-based pipelines. We introduce Embedding-Aware Feature Discovery (EAFD), a unified framework that bridges this gap by coupling pretrained event-sequence embeddings with a self-reflective LLM-driven feature generation agent. EAFD iteratively discovers, evaluates, and refines features directly from raw event sequences using two complementary criteria: alignment, which explains information already encoded in embeddings, and complementarity, which identifies predictive signals missing from them. Across both open-source and industrial transaction benchmarks, EAFD consistently outperforms embedding-only and feature-based baselines, achieving relative gains of up to

+5.8\%

over state-of-the-art pretrained embeddings, resulting in new state-of-the-art performance across event-sequence datasets.

Artem Sakhno, Ivan Sergeev, Alexey Shestov +5

Sber AI Lab · ISP RAS Research Center for Trusted AI

Large Language Model-Based Feature Engineering Automated Feature Engineering Sequence Modeling Predictive Representation Learning

Mar 16, 2026

Training-Free Generation of Protein Sequences from Small Family Alignments via Stochastic Attention

Generating novel protein sequences that respect a family's statistical constraints typically requires training deep generative models on thousands to millions of examples. Yet most protein families are small: the median Pfam seed alignment contains only 22 sequences, a regime where learned models overfit or collapse. We propose stochastic attention (SA), a training-free sampler that treats the modern Hopfield energy over stored sequences as a Boltzmann distribution and draws samples via Langevin dynamics. The score function is the residual of a single softmax attention operation, eliminating the need for a trained score network, pretraining data, or graphics processing units (GPUs). Across eight Pfam families spanning 37 to 420 sequences and 23 to 262 residues, SA generates sequences with low composition divergence, novelty, and structural plausibility supported by ESMFold and AlphaFold2. Compared with profile hidden Markov models (HMMs), EvoDiff, and the multiple sequence alignment (MSA) Transformer, SA is the only tested method to simultaneously achieve low composition divergence, genuine novelty, and sequence identity within each family's nearest-neighbor identity range; the others drift outside this range or produce near-copies. The critical inverse temperature is predicted from principal component analysis (PCA) dimensionality alone, enabling fully automatic operation from a seed alignment. In two domains with deep mutational scanning data, SA-generated substitutions are enriched for experimentally tolerated mutations beyond a position-matched null, and an independent language model (ESM2-650M) scores them within the natural range. Stochastic attention thus opens training-free sequence generation to the long tail of protein families too small for deep learning.

Jeffrey D. Varner

R.F. Smith School of Chemical and Biomolecular Engineering · Cornell University, Ithaca, NY 14850

Hopfield Networks Molecular Generation Sequence Modeling

Mar 12, 2026

Probing Length Generalization in Mamba via Image Reconstruction

Mamba has attracted widespread interest as a general-purpose sequence model due to its low computational complexity and competitive performance relative to transformers. However, its performance can degrade when inference sequence lengths exceed those seen during training. We study this phenomenon using a controlled vision task in which Mamba reconstructs images from sequences of image patches. By analyzing reconstructions at different stages of sequence processing, we reveal that Mamba qualitatively adapts its behavior to the distribution of sequence lengths encountered during training, resulting in strategies that fail to generalize beyond this range. To support our analysis, we introduce a length-adaptive variant of Mamba that improves performance across training sequence lengths. Our results provide an intuitive perspective on length generalization in Mamba and suggest directions for improving the architecture.

Jan Rathjens, Robin Schiewer, Laurenz Wiskott +1

Institute for Neural Computation, Faculty of Computer Science, Ruhr University Bochum, Bochum, Germany · CITEC, Bielefeld University, Bielefeld, Germany · Department of Computer Science, Royal Holloway, University of London, Egham, UK

Mamba Length Generalization Sequence Modeling

Mar 12, 2026

EvoFlows: Evolutionary Edit-Based Flow-Matching for Protein Engineering

We introduce EvoFlows, a variable-length protein sequence-to-sequence modeling approach designed for protein engineering. Existing protein language models are poorly suited for optimization tasks: autoregressive models require full sequence generation, masked language and discrete diffusion models rely on pre-specified mutation locations, and no existing methods naturally support insertions and deletions relative to a template sequence. EvoFlows learns mutational trajectories between evolutionarily related protein sequences via edit flows, allowing it to perform a controllable number of mutations (insertions, deletions, and substitutions) on a template sequence, predicting not only which mutation to perform, but also where it should occur. Through extensive in silico evaluation on diverse protein families from UniRef and OAS, we show that EvoFlows generates variants that remain consistent with natural protein families while exploring farther from template sequences than leading baselines.

Nicolas Deutschmann, Constance Ferragu, Jonathan D. Ziegler +2

Cradle

Protein Design Sequence Modeling Flow-Based Generative Modeling Flow Matching

Mar 11, 2026

Single molecule localization microscopy challenge: a biologically inspired benchmark for long-sequence modeling

State space models (SSMs) have recently achieved strong performance on long sequence modeling tasks while offering improved memory and computational efficiency compared to transformer based architectures. However, their evaluation has been largely limited to synthetic benchmarks and application domains such as language and audio, leaving their behavior on sparse and stochastic temporal processes in biological imaging unexplored. In this work, we introduce the Single Molecule Localization Microscopy Challenge (SMLM-C), a benchmark dataset consisting of ten SMLM simulations spanning dSTORM and DNA-PAINT modalities with varying hyperparameter designed to evaluate state space models on biologically realistic spatiotemporal point process data with known ground truth. Using a controlled subset of these simulations, we evaluate state space models and find that performance degrades substantially as temporal discontinuity increases, revealing fundamental challenges in modeling heavy-tailed blinking dynamics. These results highlight the need for sequence models better suited to sparse, irregular temporal processes encountered in real world scientific imaging data.

Fatemeh Valeh, Monika Farsang, Radu Grosu +1

Department of Biophysics, Technische Universität Wien, Vienna, Austria · Department of Informatics, Technische Universität Wien, Vienna, Austria

Sequence Modeling State Space Models Irregular Time-Series Modeling Microscopy Image Analysis

Mar 11, 2026

Beyond Pairwise Attention: Higher-Order Modular Attention for Efficient Sequence Learning

Sequence modeling tasks can involve intrinsic higher-order dependencies, while standard self-attention assigns scores to token pairs and does not explicitly parameterize such interactions. We introduce Higher-Order Modular Attention (HOMA), which fuses pairwise attention with an explicit triadic attention pathway made tractable through overlapping blocks, local windows, and a low-rank projection. We compare HOMA with matched pairwise and purely triadic baselines on controlled PARITY and MATCH3 tasks, as well as TAPE benchmarks. HOMA is competitive with or outperforms the baselines, with its clearest advantages when the underlying dependencies extend beyond the explicitly modeled triadic order. These advantages are accompanied in several settings by faster convergence and improved parameter efficiency, with the learned nonlinear fusion providing an effective mechanism for combining the pairwise and triadic representations. Overall, our results provide empirical evidence that HOMA is an effective attention design when task structure extends beyond pairwise interactions.

Shirin Amiraslani, Xin Gao

Department of Mathematics and Statistics York University Toronto, ON M3J 1P3, Canada

Self-Attention Transformer Attention Efficient Attention Attention Mechanisms Sequence Modeling

Mar 10, 2026

Decoding the decoder: Contextual sequence-to-sequence modeling for intracortical speech decoding

Speech brain--computer interfaces require decoders that translate intracortical activity into linguistic output while remaining robust to limited data and day-to-day variability. While prior high-performing systems have largely relied on framewise phoneme decoding combined with downstream language models, it remains unclear what contextual sequence-to-sequence decoding contributes to sublexical neural readout, robustness, and interpretability. We evaluated a multitask Transformer-based sequence-to-sequence model for attempted speech decoding from area 6v intracortical recordings. The model jointly predicts phoneme sequences, word sequences, and auxiliary acoustic features. To address day-to-day nonstationarity, we introduced the Neural Hammer Scalpel (NHS) calibration module, which combines global alignment with feature-wise modulation. We further analyzed held-out-day generalization and attention patterns in the encoder and decoders. On the Willett et al. dataset, the proposed model achieved a state-of-the-art phoneme error rate of 14.3%. Word decoding reached 25.6% WER with direct decoding and 19.4% WER with candidate generation and rescoring. NHS substantially improved both phoneme and word decoding relative to linear or no day-specific transform, while held-out-day experiments showed increasing degradation on unseen days with temporal distance. Attention visualizations revealed recurring temporal chunking in encoder representations and distinct use of these segments by phoneme and word decoders. These results indicate that contextual sequence-to-sequence modeling can improve the fidelity of neural-to-phoneme readout from intracortical speech signals and suggest that attention-based analyses can generate useful hypotheses about how neural speech evidence is segmented and accumulated over time.

Michal Olak, Tommaso Boccato, Matteo Ferrante

Tether Evo

Sequence-to-Sequence Models Neural Decoding Sequence Modeling Transformer

Mar 9, 2026

Expressivity-Efficiency Tradeoffs for Hybrid Sequence Models

Hybrid sequence models--combining Transformer and state-space model layers--seek to gain the expressive versatility of attention as well as the computational efficiency of state-space model layers. Despite burgeoning interest in hybrid models, we lack a basic understanding of the settings where--and underlying mechanisms through which--they offer benefits over their constituent models. In this paper, we study this question, focusing on a broad family of core synthetic tasks. For this family of tasks, we prove the existence of fundamental limitations for non-hybrid models. Specifically, any Transformer or state-space model that solves the underlying task requires either a large number of parameters or a large working memory. On the other hand, for two prototypical tasks within this family--namely selective copying and associative recall--we construct hybrid models of small size and working memory that provably solve these tasks, thus achieving the best of both worlds. Our experimental evaluation empirically validates our theoretical findings. Importantly, going beyond the settings in our theoretical analysis, we empirically show that learned--rather than constructed--hybrids outperform non-hybrid models with up to 6x as many parameters. We additionally demonstrate that hybrid models exhibit stronger length generalization and out-of-distribution robustness than non-hybrids.

John Cooper, Ilias Diakonikolas, Mingchen Ma +1

Department of Computer Sciences, University of Wisconsin-Madison

Hybrid Transformer-State Space Model Architectures Sequence Modeling Transformer Expressivity

Mar 9, 2026

Structure from rank: Rank-order coding as a bridge from sequence to structure

Understanding how structured sequence information can be represented and generalized in neural systems is key to modeling the transition from acoustic input to emergent structure. In this study, we propose a rank-order based neural network inspired by the STG-LIFG-PMC pathway, modeling the bottom-up transition from acoustic input to abstract rank representation and the top-down generation from that representation to motor execution. Building on previous work in rank coding, we first demonstrate that this model efficiently compresses input while retaining the capacity to reconstruct full utterances from partial cues, revealing emergent structure-sensitive generation process that reflects context-general representations of sensorimotor states, which are later shaped into context-specific motor plans during speech planning. We then show that the network exhibits global-level novelty detection similar to the P3B novelty wave, replicating the global-sequence-sensitive mechanism. As a supplement, we also compare the model's behavior under local (index-level) and global (rank-level) perturbations, revealing robustness to superficial variation and sensitivity to abstract structural violation, key features associated with hierarchical generalization. These results suggest that rank-order coding not only serves as a compact encoding scheme but also captures hierarchical structure in acoustic sequences.

Xiaodan Chen, Alexandre Pitti, Mathias Quoy +1

ETIS, CY Cergy-Paris Université - ENSEA – CNRS, UMR 8051, 2 Av. Adolphe Chauvin, Pontoise, 95300, Ile de France, France · A*Star, 1 Fusionopolis Way, #20-10 Connexis North Tower, Singapore, 138632, Singapore · IPAL (International Research Laboratory on Artiﬁcial Intelligence), 1 Fusionopolis Way, #21-01 Connexis (South Tower), Singapore, 138632, Singapore

Speech Production Sequence Modeling Hierarchical Representation Learning

Mar 8, 2026

InfoMamba: An Attention-Free Hybrid Mamba-Transformer Model

Balancing fine-grained local modeling with long-range dependency capture under computational constraints remains a central challenge in sequence modeling. While Transformers provide strong token mixing, they suffer from quadratic complexity, whereas Mamba-style selective state-space models (SSMs) scale linearly but often struggle to capture high-rank and synchronous global interactions. We present a consistency boundary analysis that characterizes when diagonal short-memory SSMs can approximate causal attention and identifies structural gaps that remain. Motivated by this analysis, we propose InfoMamba, an attention-free hybrid architecture. InfoMamba replaces token-level self-attention with a concept bottleneck linear filtering layer that serves as a minimal-bandwidth global interface and integrates it with a selective recurrent stream through information-maximizing fusion (IMF). IMF dynamically injects global context into the SSM dynamics and encourages complementary information usage through a mutual-information-inspired objective. Extensive experiments on classification, dense prediction, and non-vision tasks show that InfoMamba consistently outperforms strong Transformer and SSM baselines, achieving competitive accuracy-efficiency trade-offs while maintaining near-linear scaling.

Youjin Wang, Jiaqiao Zhao, Rong Fu +5

Renmin University of China, Beijing, China · University of Macau, Macau SAR, China · Central South University, Changsha, China +1

Hybrid Mamba-Transformer Architectures Hybrid Transformer-State Space Model Architectures Sequence Modeling Selective SSMs Self-Attention

Mar 8, 2026

OrthoFormer: Instrumental Variable Estimation in Transformer Hidden States via Neural Control Functions

Transformer architectures excel at sequential modeling yet remain fundamentally limited by correlational learning - they capture spurious associations induced by latent confounders rather than invariant causal mechanisms. We identify this as an epistemological challenge: standard Transformers conflate static background factors (intrinsic identity, style, context) with dynamic causal flows (state evolution, mechanism), leading to catastrophic out-of-distribution failure. We propose OrthoFormer, a causally grounded architecture that embeds instrumental variable estimation directly into Transformer blocks via neural control functions. Our framework rests on four theoretical pillars: Structural Directionality (time-arrow enforcement), Representation Orthogonality (latent-noise separation), Causal Sparsity (Markov Blanket approximation), and End-to-End Consistency (gradient- detached stage separation). We prove that OrthoFormer achieves bias strictly less than OLS for any valid instrument lag, with residual bias decaying geometrically as O(\r{ho}k ). We characterize the bias-variance-exogeneity trilemma inherent in self-instrumenting and identify the neural forbidden regression - where removing gradient detachment improves prediction loss while destroying causal validity. Experiments confirm all theoretical predictions. OrthoFormer represents a paradigm shift from correlational to causal sequence modeling, with implications for robustness, interpretability, and reliable decision-making under distribution shift.

Charles Luo

Metro State University

Transformer Instrumental Variable Estimation Sequence Modeling Causal Representation Learning

Mar 5, 2026

Why Depth Matters in Parallelizable Sequence Models: A Lie Algebraic View

Scalable sequence models, such as Transformer variants and structured state-space models, often trade expressivity power for sequence-level parallelism, which enables efficient training. Here we examine the bounds on error and how error scales when models operate outside of their expressivity regimes using a Lie-algebraic control perspective. Our theory formulates a correspondence between the depth of a sequence model and the tower of Lie algebra extensions. Echoing recent theoretical studies, we characterize the Lie-algebraic class of constant-depth sequence models and their corresponding expressivity bounds. Furthermore, we analytically derive an approximation error bound and show that error diminishes exponentially as the depth increases, consistent with the strong empirical performance of these models. We validate our theoretical predictions using experiments on symbolic word and continuous-valued state-tracking problems.

Gyuryang Heo, Timothy Ngotiaoco, Kazuki Irie +2

Howard Hughes Medical Institute, Department of Neurobiology, Harvard Medical School, Boston, MA, USA · Kempner Institute for the Study of Natural and Artificial Intelligence, Harvard University, Cambridge, MA, USA · Department of Psychology and Center for Brain Science, Harvard University, Cambridge, MA, USA

Sequence Modeling Transformer Expressivity

Mar 5, 2026

IntSeqBERT: Learning Arithmetic Structure in OEIS via Modulo-Spectrum Embeddings

Integer sequences in the OEIS span values from single-digit constants to astronomical factorials and exponentials, making prediction challenging for standard tokenised models that cannot handle out-of-vocabulary values or exploit periodic arithmetic structure. We present IntSeqBERT, a dual-stream Transformer encoder for masked integer-sequence modelling on OEIS. Each sequence element is encoded along two complementary axes: a continuous log-scale magnitude embedding and sin/cos modulo embeddings for 100 residues (moduli

2

--

101

), fused via FiLM. Three prediction heads (magnitude regression, sign classification, and modulo prediction for 100 moduli) are trained jointly on 274,705 OEIS sequences. At the Large scale (91.5M parameters), IntSeqBERT achieves 95.85% magnitude accuracy and 50.38% Mean Modulo Accuracy (MMA) on the test set, outperforming a standard tokenised Transformer baseline by

+8.9

pt and

+4.5

pt, respectively. An ablation removing the modulo stream confirms it accounts for

+15.2

pt of the MMA gain and contributes an additional

+6.2

pt to magnitude accuracy. A probabilistic Chinese Remainder Theorem (CRT)-based Solver converts the model's predictions into concrete integers, yielding a 7.4-fold improvement in next-term prediction over the tokenised-Transformer baseline (Top-1: 19.09% vs. 2.59%). Modulo spectrum analysis reveals a strong negative correlation between Normalised Information Gain (NIG) and Euler's totient ratio

\varphi(m)/m

(

r = -0.851

,

p < 10^{-28}

), providing empirical evidence that composite moduli capture OEIS arithmetic structure more efficiently via CRT aggregation.

Kazuhisa Nakasho

Iwate Prefectural University, Takizawa, Iwate, Japan

Sequence Modeling Transformer

Mar 5, 2026

Timer-S1: A Billion-Scale Time Series Foundation Model with Serial Scaling

We introduce Timer-S1, a strong Mixture-of-Experts (MoE) time series foundation model with 8.3B total parameters, 0.75B activated parameters for each token, and a context length of 11.5K. To overcome the scalability bottleneck in existing pre-trained time series foundation models, we perform Serial Scaling in three dimensions: model architecture, dataset, and training pipeline. Timer-S1 integrates sparse TimeMoE blocks and generic TimeSTP blocks for Serial-Token Prediction (STP), a generic training objective that adheres to the serial nature of forecasting. The proposed paradigm introduces serial computations to improve long-term predictions while avoiding costly rolling-style inference and pronounced error accumulation in the standard next-token prediction. Pursuing a high-quality and unbiased training dataset, we curate TimeBench, a corpus with one trillion time points, and apply meticulous data augmentation to mitigate predictive bias. We further pioneer a post-training stage, including continued pre-training and long-context extension, to enhance short-term and long-context performance. Evaluated on the large-scale GIFT-Eval leaderboard, Timer-S1 achieves state-of-the-art forecasting performance, attaining the best MASE and CRPS scores as a pre-trained model. Timer-S1 is released to facilitate further research.

Yong Liu, Xingjian Su, Shiyu Wang +7

Tsinghua University · ByteDance

Time Series Forecasting Time-Series Foundation Models Long-Term Time Series Forecasting Sequence Modeling Mixture-of-Experts Models

Mar 4, 2026

The Volterra signature

Modern approaches for learning from non-Markovian time series, such as recurrent neural networks, neural controlled differential equations or transformers, typically rely on implicit memory mechanisms that can be difficult to interpret or to train over long horizons. We propose the Volterra signature

\mathrm{VSig}(x;K)

as a principled, explicit feature representation for history-dependent systems. By developing the input path

x

weighted by a temporal kernel

K

into the tensor algebra, we leverage the associated Volterra--Chen identity to derive rigorous learning-theoretic guarantees. Specifically, we prove an injectivity statement (identifiability under augmentation) that leads to a universal approximation theorem on the infinite dimensional path space, which in certain cases is achieved by linear functionals of

\mathrm{VSig}(x;K)

. Moreover, we demonstrate applicability of the kernel trick by showing that the inner product associated with Volterra signatures admits a closed characterization via a two-parameter integral equation, enabling numerical methods from PDEs for computation. For a large class of exponential-type kernels,

\mathrm{VSig}(x;K)

solves a linear state-space ODE in the tensor algebra. Combined with inherent invariance to time reparameterization, these results position the Volterra signature as a robust, computationally tractable feature map for data science. We demonstrate its efficacy in dynamic learning tasks on real and synthetic data, where it consistently improves classical path signature baselines.

Paul P. Hager, Fabian N. Harang, Luca Pelizzari +1

Path Signatures Time Series Representation Learning Sequence Modeling

Mar 4, 2026

Coupling Local Context and Global Semantic Prototypes via a Hierarchical Architecture for Rhetorical Roles Labeling

Rhetorical Role Labeling (RRL) identifies the functional role of each sentence in a document, a key task for discourse understanding in domains such as law and medicine. While hierarchical models capture local dependencies effectively, they are limited in modeling global, corpus-level features. To address this limitation, we propose two prototype-based methods that integrate local context with global representations. Prototype-Based Regularization (PBR) learns soft prototypes through a distance-based auxiliary loss to structure the latent space, while Prototype-Conditioned Modulation (PCM) constructs corpus-level prototypes and injects them during training and inference. Given the scarcity of RRL resources, we introduce SCOTUS-Law, the first dataset of U.S. Supreme Court opinions annotated with rhetorical roles at three levels of granularity: category, rhetorical function, and step. Experiments on legal, medical, and scientific benchmarks show consistent improvements over strong baselines, with 4 Macro-F1 gains on low-frequency roles. We further analyze the implications in the era of Large Language Models and complement our findings with expert evaluation.

Anas Belfathi, Nicolas Hernandez, Laura Monceaux +4

Nantes Université, École Centrale Nantes, CNRS, LS2N, UMR 6004, F-44000 Nantes, France · University of Lorraine, France

Prototype Learning Legal NLP Sequence Modeling

Mar 3, 2026

MaBERT:A Padding Safe Interleaved Transformer Mamba Hybrid Encoder for Efficient Extended Context Masked Language Modeling

Self attention encoders such as Bidirectional Encoder Representations from Transformers(BERT) scale quadratically with sequence length, making long context modeling expensive. Linear time state space models, such as Mamba, are efficient; however, they show limitations in modeling global interactions and can suffer from padding induced state contamination. We propose MaBERT, a hybrid encoder that interleaves Transformer layers for global dependency modeling with Mamba layers for linear time state updates. This design alternates global contextual integration with fast state accumulation, enabling efficient training and inference on long inputs. To stabilize variable length batching, we introduce paddingsafe masking, which blocks state propagation through padded positions, and mask aware attention pooling, which aggregates information only from valid tokens. On GLUE, MaBERT achieves the best mean score on five of the eight tasks, with strong performance on the CoLA and sentence pair inference tasks. When extending the context from 512 to 4,096 tokens, MaBERT reduces training time and inference latency by 2.36x and 2.43x, respectively, relative to the average of encoder baselines, demonstrating a practical long context efficient encoder.

Jinwoong Kim, Sangjin Park

Graduate School of Industrial Data Engineering, Hanyang University, Seoul, Republic of Korea

Hybrid Transformer-State Space Model Architectures Long-Context Language Modeling Hybrid Mamba-Transformer Architectures Sequence Modeling Long-Context Language Model Inference Masked Language Modeling+1

Mar 1, 2026

Efficient Extractive Summarization with MAMBA-Transformer Hybrids for Low-Resource Scenarios

Extractive summarization of long documents is bottlenecked by quadratic complexity, often forcing truncation and limiting deployment in resource-constrained settings. We introduce the first Mamba-Transformer hybrid for extractive summarization, combining the semantic strength of pre-trained transformers with the linear-time processing of state space models. Leveraging Mamba's ability to process full documents without truncation, our approach preserves context while maintaining strong summarization quality. The architecture includes: (1) a transformer encoder for sentence-level semantics, (2) a Mamba state space model to capture inter-sentence dependencies efficiently, and (3) a linear classifier for sentence relevance prediction. Across news, argumentative, and scientific domains under low-resource conditions, our method achieves: (1) large gains over BERTSUM and MATCHSUM, including +0.23 ROUGE-1 on ArXiv and statistically significant improvements on all datasets (p < 0.001); (2) consistent advantages across domains, strongest on the longest documents; (3) robust performance with limited training data; and (4) 24-27% faster inference on news summarization (CNN/DailyMail). We introduce the first hybrid Transformer-state space architecture for summarization, showing significant ROUGE improvements in low-resource scenarios.

Nisrine Ait Khayi

Independent Researcher · University of Memphis

Hybrid Transformer-State Space Model Architectures Text Summarization Hybrid Mamba-Transformer Architectures Long-Context Modeling Sequence Modeling State Space Models

Mar 1, 2026

Probabilistic Learning and Generation in Deep Sequence Models

Despite exceptional predictive performance of Deep sequence models (DSMs), the main concern of their deployment centers around the lack of uncertainty awareness. In contrast, probabilistic models quantify the uncertainty associated with unobserved variables with rules of probability. Notably, Bayesian methods leverage Bayes' rule to express our belief of unobserved variables in a principled way. Since exact Bayesian inference is computationally infeasible at scale, approximate inference is required in practice. Two major bottlenecks of Bayesian methods, especially when applied in deep neural networks, are prior specification and approximation quality. In Chapter 3 & 4, we investigate how the architectures of DSMs themselves can be informative for the design of priors or approximations in probabilistic models. We first develop an approximate Bayesian inference method tailored to the Transformer based on the similarity between attention and sparse Gaussian process. Next, we exploit the long-range memory preservation capability of HiPPOs (High-order Polynomial Projection Operators) to construct an interdomain inducing point for Gaussian process, which successfully memorizes the history in online learning. In addition to the progress of DSMs in predictive tasks, sequential generative models consisting of a sequence of latent variables are popularized in the domain of deep generative models. Inspired by the explicit self-supervised signals for these latent variables in diffusion models, in Chapter 5, we explore the possibility of improving other generative models with self-supervision for their sequential latent states, and investigate desired probabilistic structures over them. Overall, this thesis leverages inductive biases in DSMs to design probabilistic inference or structure, which bridges the gap between DSMs and probabilistic models, leading to mutually reinforced improvement.

Wenlong Chen

Imperial College London Department of Computing

Bayesian Inference Sequence Modeling Bayesian Neural Networks Latent Variable Models Gaussian Processes

Feb 28, 2026

Wave-Attractor-Tree: A Hierarchical Binary Tree Reduction Architecture for Efficient Sequence Modeling

Work introduces a hierarchical binary tree-based reduction that replaces standard self-attention. The core idea is to use a recursive Gated Linear Unit merge operation, achieving O(n) total merge operations O(log n) parallel depth O(n d^2) total work and O(n) space complexity. In these experiments, the model significantly outperforms standard Transformers in both convergence speed and accuracy on long-range structural dependencies, specifically where hierarchical inductive bias is critical.

Igor Berezkin

Independent Researcher

Long-Range Dependency Modeling Sequence Modeling Hierarchical Representation Learning

Feb 28, 2026

Efficient Long-Sequence Diffusion Modeling for Symbolic Music Generation

Symbolic music generation is a challenging task in multimedia generation, involving long sequences with hierarchical temporal structures, long-range dependencies, and fine-grained local details. Though recent diffusion-based models produce high quality generations, they tend to suffer from high training and inference costs with long symbolic sequences due to iterative denoising and sequence-length-related costs. To deal with such problem, we put forth a diffusing strategy named SMDIM to combine efficient global structure construction and light local refinement. SMDIM uses structured state space models to capture long range musical context at near linear cost, and selectively refines local musical details via a hybrid refinement scheme. Experiments performed on a wide range of symbolic music datasets which encompass various Western classical music, popular music and traditional folk music show that the SMDIM model outperforms the other state-of-the-art approaches on both the generation quality and the computational efficiency, and it has robust generalization to underexplored musical styles. These results show that SMDIM offers a principled solution for long-sequence symbolic music generation, including associated attributes that accompany the sequences. We provide a project webpage with audio examples and supplementary materials at https://3328702107.github.io/smdim-music/.

Jinhan Xu, Xing Tang, Houpeng Yang +7

School of Computer Science and Artificial Intelligence, Wuhan University of Technology, Wuhan, China 430070 · School of Computer Science, Hubei University of Technology, Wuhan, China 430068 · School of Information Engineering, Hubei University of Economics, Wuhan, China 430205; Hubei Key Laboratory of Digital Finance Innovation, Wuhan, China 430205

Symbolic Music Generation Diffusion Models Diffusion Model Acceleration Sequence Modeling

Feb 26, 2026

MEDNA-DFM: A Dual-View FiLM-MoE Model for Explainable DNA Methylation Prediction

Accurate computational identification of DNA methylation is essential for understanding epigenetic regulation. Although deep learning excels in this binary classification task, its "black-box" nature impedes biological insight. We address this by introducing a high-performance model MEDNA-DFM, alongside mechanism-inspired signal purification algorithms. Our investigation demonstrates that MEDNA-DFM effectively captures conserved methylation patterns, achieving robust distinction across diverse species. Validation on external independent datasets confirms that the model's generalization is driven by conserved intrinsic motifs (e.g., GC content) rather than phylogenetic proximity. Furthermore, applying our developed algorithms extracted motifs with significantly higher reliability than prior studies. Finally, empirical evidence from a Drosophila 6mA case study prompted us to propose a "sequence-structure synergy" hypothesis, suggesting that the GAGG core motif and an upstream A-tract element function cooperatively. We further validated this hypothesis via in silico mutagenesis, confirming that the ablation of either or both elements significantly degrades the model's recognition capabilities. This work provides a powerful tool for methylation prediction and demonstrates how explainable deep learning can drive both methodological innovation and the generation of biological hypotheses.

Yi He, Yina Cao, Jixiu Zhai +3

Cuiying Honors College, Lanzhou University, Lanzhou, Gansu, China · School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, China · Cuiying Honors College, Lanzhou University, Lanzhou, Gansu, China. +7

Genomics Sequence Modeling

Feb 25, 2026

Support Tokens, Stability Margins, and a New Foundation for Robust LLMs

Self-attention is usually described as a flexible, content-adaptive way to mix a token with information from its past. We reinterpret causal self-attention transformers, the backbone of modern foundation models, within a probabilistic framework, much as classical PCA is extended to probabilistic PCA. This reformulation reveals a key structural consequence of the underlying change of variables: a barrier constraint emerges on the parameters of self-attention. The resulting geometry exposes a degeneracy boundary where the attention-induced mapping becomes locally ill-conditioned, yielding a stability-margin interpretation analogous to the margin in support vector machines. This, in turn, naturally gives rise to the concept of support tokens. We further show that causal transformers define a consistent stochastic process over infinite token sequences, providing a rigorous probabilistic foundation for sequence modeling. Building on this view, we derive a Bayesian MAP training objective that requires only a minimal modification to standard LLM training: adding a smooth log-barrier penalty to the usual cross-entropy loss. Empirically, the resulting training objective improves robustness to input perturbations and sharpens the margin geometry of the learned representations without sacrificing out-of-sample accuracy.

Deepak Agarwal, Dhyey Dharmendrakumar Mavani, Suyash Gupta +2

LinkedIn, Mountain View, CA

Self-Attention Language Model Robustness Sequence Modeling Adversarial Robustness of Language Models

Feb 24, 2026

Deep Sequence Modeling with Quantum Dynamics: Language as a Wave Function

We introduce a sequence modeling framework in which the latent state is a complex-valued wave function evolving on a finite-dimensional Hilbert space under a learned, time-dependent Hamiltonian. Unlike standard recurrent architectures that rely on gating mechanisms to suppress competing hypotheses, our framework utilizes quantum interference: the Hamiltonian steers the phases of complex amplitudes so that conflicting interpretations cancel while compatible ones reinforce. The dynamics are strictly unitary, ensuring that the state norm is preserved exactly at every time step via a Cayley (Crank--Nicolson) discretization. Token probabilities are extracted using the Born rule, a quadratic measurement operator that couples magnitudes and relative phases. Our primary theoretical contribution is a separation theorem characterizing the representational advantage of this readout: we define a family of disambiguation tasks that a complex unitary model of dimension

N

solves exactly, but which requires a state dimension of

Ω(N^2)

for any real-valued orthogonal model equipped with a standard affine-softmax readout. This quadratic gap arises because the Born rule implicitly lifts the

N

-dimensional state into the space of rank-one Hermitian matrices, accessing pairwise phase correlations that are inaccessible to linear projections. Finally, we derive a continuity equation for the latent probability mass, yielding conserved pairwise currents that serve as a built-in diagnostic for tracing information flow between dimensions.

Ahmed Nebli, Hadi Saadatdoorabi, Kevin Yam

cAI Technology GmbH

Sequence Modeling Quantum-Inspired ML Language Modeling Quantum Machine Learning Quantum Neural Networks

Feb 24, 2026

HiPPO Zoo: Explicit Memory Mechanisms for Interpretable State Space Models

Representing the past in a compressed, efficient, and informative manner is a central problem for systems trained on sequential data. The HiPPO framework, originally proposed by Gu & Dao et al., provides a principled approach to sequential compression by projecting signals onto orthogonal polynomial (OP) bases via structured linear ordinary differential equations. Subsequent works have embedded these dynamics in state space models (SSMs), where HiPPO structure serves as an initialization. Nonlinear successors of these SSM methods such as Mamba are state-of-the-art for many tasks with long-range dependencies, but the mechanisms by which they represent and prioritize history remain largely implicit. In this work, we revisit the HiPPO framework with the goal of making these mechanisms explicit. We show how polynomial representations of history can be extended to support capabilities of modern SSMs such as adaptive memory allocation and associative memory, while retaining direct interpretability in the OP basis. We introduce a unified framework comprising five such extensions, which we collectively refer to as a "HiPPO zoo." Each extension exposes a specific modeling capability through an explicit, interpretable modification of the HiPPO framework. The resulting models adapt their memory online and train in streaming settings with efficient updates. We illustrate the behaviors and modeling advantages of these extensions through a range of synthetic sequence modeling tasks, demonstrating that capabilities typically associated with modern SSMs can be realized through explicit, interpretable polynomial memory structures.

Jack Goffinet, Casey Hanks, David E. Carlson

Department of Computer Science, Duke University, Durham NC, USA · Departments of Civil and Environmental Engineering; Biostatistics and Bioinformatics; and Electrical and Computer Engineering, Duke University, Durham NC, USA

Sequence Modeling State Space Models

Feb 24, 2026

Test-Time Training with KV Binding Is Secretly Linear Attention

Test-time training (TTT) with KV binding as sequence modeling layer is commonly interpreted as a form of online meta-learning that memorizes a key-value mapping at test time. However, our analysis reveals multiple phenomena that contradict this memorization-based interpretation. Motivated by these findings, we revisit the formulation of TTT and show that a broad class of TTT architectures can be expressed as a form of learned linear attention operator. Beyond explaining previously puzzling model behaviors, this perspective yields multiple practical benefits: it enables principled architectural simplifications, admits fully parallel formulations that preserve performance while improving efficiency, and provides a systematic reduction of diverse TTT variants to a standard linear attention form. Overall, our results reframe TTT not as test-time memorization, but as learned linear attention with enhanced representational capacity. Project page: https://research.nvidia.com/labs/sil/projects/tttla/.

Junchen Liu, Sven Elflein, Or Litany +2

NVIDIA, Toronto, Ontario, Canada · University of Toronto, Toronto, Ontario, Canada · Vector Institute, Toronto, Ontario, Canada +1

Test-Time Training Linear Attention Sequence Modeling

Feb 18, 2026

Online Prediction of Stochastic Sequences with High Probability Regret Bounds

We revisit the classical problem of universal prediction of stochastic sequences with a finite time horizon

T

known to the learner. The question we investigate is whether it is possible to derive vanishing regret bounds that hold with high probability, complementing existing bounds from the literature that hold in expectation. We propose such high-probability bounds which have a very similar form as the prior expectation bounds. For the case of universal prediction of a stochastic process over a countable alphabet, our bound states a convergence rate of

\mathcal{O}(T^{-1/2} δ^{-1/2})

with probability as least

1-δ

compared to prior known in-expectation bounds of the order

\mathcal{O}(T^{-1/2})

. We also propose an impossibility result which proves that it is not possible to improve the exponent of

δ

in a bound of the same form without making additional assumptions.

Matthias Frey, Jonathan H. Manton, Jingge Zhu

Department of Electrical and Electronic Engineering, The University of Melbourne

Sequence Prediction Sequence Modeling

Feb 16, 2026

Learning State-Tracking from Code Using Linear RNNs

Over the last years, state-tracking tasks, particularly permutation composition, have become a testbed to understand the limits of sequence models architectures like Transformers and RNNs (linear and non-linear). However, these are often sequence-to-sequence tasks: learning to map actions (permutations) to states, which is incompatible with the next-token prediction setting commonly used to train language models. We address this gap by converting permutation composition into code via REPL traces that interleave state-reveals through prints and variable transformations. We show that linear RNNs capable of state-tracking excel also in this setting, while Transformers still fail. Motivated by this representation, we investigate why tracking states in code is generally difficult: actions are not always fully observable. We frame this as tracking the state of a probabilistic finite-state automaton with deterministic state reveals and show that linear RNNs can be worse than non-linear RNNs at tracking states in this setup.

Julien Siems, Riccardo Grazzi, Korbinian Pöppel +3

University of Freiburg · Prior Labs · Microsoft Research +2

Recurrent Neural Networks State Tracking Linear RNNs Sequence Modeling