Sequence Modeling

Generative sequence modeling faces a fundamental tension between the expressivity of Transformers and the efficiency of linear sequence models. Existing efficient architectures are theoretically bounded by shallow, single-step linear updates, while powerful iterative methods like Test-Time Training (TTT) break hardware parallelism due to two dimensions of serial dependency: token-level state reliance and step-level iteration loops. We propose PRISM (Parallel Residual Iterative Sequence Model) to resolve this tension. PRISM explicitly approximates the expressive gate-residual-direction iteration pattern of TTT in a parallelizable form. We employ a Write-Forget Decoupling strategy that isolates non-linearity within the injection operator. To bypass the serial dependency of explicit solvers, PRISM utilizes a two-stage proxy architecture: a short-convolution anchors the initial residual using local history energy, while a learned predictor estimates the refinement updates directly from the input. This design distills structural patterns associated with iterative correction into a parallelizable feedforward operator. Theoretically, we prove that this formulation achieves Rank-$L$ accumulation, structurally expanding the update scheme beyond the single-step Rank-$1$ bottleneck. Empirically, it achieves comparable performance to explicit optimization methods while achieving 174x higher throughput. Codes are available in https://github.com/gpr-prism/prism/.

We propose a variational quantum implementation of self-attention (QSA)-the core operation in transformers and large language models-which predicts future elements of a sequence by forming overlap-weighted combinations of past data. At variance with previous approaches, our QSA realizes the required nonlinearity through interference of state overlaps and a degree-$k$ polynomial kernel, and estimates a loss based on Rényi-$1/2$ entropic functionals via two observables' expectation values, avoiding the decoding of amplitude-encoded predictions into classical probabilities. QSA also accommodates a constrained, trainable data-embedding tying state overlaps to data-level similarities. Its dominant end-to-end training complexity scales as $O\left(μ^{-1}k^2Td\right)$, versus $O\left(T d^{k+1}\right)$ of the fairest classical comparison, with $μ$ a training signal; we show numerically that this allows a complexity advantage in the regime where sequence length $T$ dominates the embedding size $d$. In simulations, our QSA-based quantum transformer learns sequence prediction on classical data and on many-body transverse-field Ising trajectories-establishing trainable attention as a practical primitive for quantum dynamical modeling.

While NLP typically treats documents as independent and unordered samples, in longitudinal studies, this assumption rarely holds: documents are nested within authors and ordered in time, forming person-indexed, time-ordered $\textit{behavioral sequences}$. Here, we demonstrate the need for and propose a longitudinal modeling and evaluation paradigm that consequently updates four parts of the NLP pipeline: (1) evaluation splits aligned to generalization over people ($\textit{cross-sectional}$) and/or time ($\textit{prospective}$); (2) accuracy metrics separating between-person differences from within-person dynamics; (3) sequence inputs to incorporate history by default; and (4) model internals that support different $\textit{coarseness}$ of latent state over histories (pooled summaries, explicit dynamics, or interaction-based models). We demonstrate the issues ensued by traditional pipeline and our proposed improvements on a dataset of 17k daily diary transcripts paired with PTSD symptom severity from 238 participants, finding that traditional document-level evaluation can yield substantially different and sometimes reversed conclusions compared to our ecologically valid modeling and evaluation. We tie our results to a broader discussion motivating a shift from word-sequence evaluation toward $\textit{behavior-sequence}$ paradigms for NLP.

Structured State Space Models (SSMs), which are at the heart of the recently popular Mamba architecture, are powerful tools for sequence modeling. However, their theoretical foundation relies on a complex, multistage process of continuous-time modeling and subsequent discretization, which can obscure intuition. We introduce a direct, first-principles framework for constructing discrete-time SSMs that is both flexible and modular. Our approach is based on a novel lag operator, which geometrically derives the discrete-time recurrence by measuring how the system's basis functions undergo what we call a domain expansion from one timestep to the next. The resulting state matrices are computed via a single inner product involving this operator, enabling a modular design space for creating novel SSMs by flexibly combining different basis functions and time-warping schemes. To validate our framework, we demonstrate that a specific instance exactly recovers the recurrence of the influential HiPPO model. Numerical simulations confirm our derivation, providing new theoretical tools for designing flexible and robust sequence models.

Motivation: Pre-trained protein language models (PLMs) such as ESM-2 have become the default representation for biological sequence tasks, but they are computationally heavy and require GPUs both for embedding and for fine-tuning. Whether they are actually necessary for sequence classification, as opposed to structure prediction, is rarely tested against strong, principled, lightweight alternatives. This question has direct practical stakes for large-scale genomic surveillance, where embedding millions of sequences on commodity hardware is a recurring bottleneck.\ Results: We introduce Murmur2Vec, an alignment-free, training-free embedding that aggregates $k$-mer counts into a small hash table via the deterministic MurmurHash function, and we cast it as a randomized sketch of the classical $k$-mer spectrum kernel. We provide a complete theoretical treatment: closed-form bias/variance of the inner product, an unbiased signed variant with a Johnson--Lindenstrauss-type concentration bound, an excess-risk bound for downstream linear classifiers that makes the bias--variance trade-off in the hash-table size explicit, and an implicit-regularization mechanism by which collisions damage frequent non-discriminative $k$-mers more than rare lineage-defining ones. Across four classification tasks, SARS-CoV-2 spike lineage (22 classes), HIV-1 Env subtype (8 classes), and two protein-family benchmarks (8 and 6 classes), Murmur2Vec matches a LoRA-fine-tuned 650M-parameter ESM-2 model on the two tasks for which LoRA fine-tuning was run to convergence (SARS-CoV-2 and HIV-1) and ties frozen ESM-2 on the two protein-family tasks, and it outperforms the fine-tuned model on the hardest task (SARS-CoV-2 lineage: $0.854$ vs.\ $0.807$ accuracy; macro-F1 $0.684$ vs.\ $0.401$).

This paper presents Naga, a deep State Space Model (SSM) encoding approach inspired by structural concepts from Vedic mathematics. The proposed method introduces a bidirectional representation for time series by jointly processing forward and time-reversed input sequences. These representations are then combined through an element-wise (Hadamard) interaction, resulting in a Vedic-inspired encoding that enhances the model's ability to capture temporal dependencies across distant time steps. We evaluate Naga on multiple long-term time series forecasting (LTSF) benchmarks, including ETTh1, ETTh2, ETTm1, ETTm2, Weather, Traffic, and ILI. The experimental results show that Naga outperforms 28 current state of the art models and demonstrates improved efficiency compared to existing deep SSM-based approaches. The findings suggest that incorporating structured, Vedic-inspired decomposition can provide an interpretable and computationally efficient alternative for long-range sequence modeling.

The remarkable success of modern AI has been closely tied to scaling laws, yet the finite supply of high-quality data makes data efficiency--learning more from less--an increasingly important frontier. A model's inductive bias is a critical lever for data efficiency, but foundational sequence models such as State Space Models (SSMs) often rely on fixed, task-agnostic biases. When this fixed prior is misaligned with the underlying structure of a task, the model may require additional samples to overcome its own bias before learning the relevant signal. In this work, we introduce a principled framework for understanding and aligning the inductive bias of linear time-invariant SSMs. We first formalize this bias through an SSM-induced kernel and show theoretically and empirically that its spectrum is governed by the model's frequency response. This characterization motivates Task-Dependent Initialization (TDI), a fast power-spectrum matching method that aligns the initial SSM bias with the task's spectral characteristics before downstream training. Across controlled synthetic experiments, trainable one-layer SSMs, and deep SSMs on diverse real-world benchmarks, TDI can improve data-efficient generalization primarily when task-relevant spectral structure is present and the default SSM bias is spectrally mismatched. Our results provide both a theoretical lens and a practical tool for task-adaptive inductive bias, suggesting a path toward more data-efficient sequence modeling.

Natural Language Processing (NLP) has transformed various fields beyond linguistics by applying techniques originally developed for human language to the analysis of biological sequences. This review explores the application of NLP methods to biological sequence data, focusing on genomics, transcriptomics, and proteomics. We examine how various NLP methods, from classic approaches like word2vec to advanced models employing transformers and hyena operators, are being adapted to analyze DNA, RNA, protein sequences, and entire genomes. The review also examines tokenization strategies and model architectures, evaluating their strengths, limitations, and suitability for different biological tasks. We further cover recent advances in NLP applications for biological data, such as structure prediction, gene expression, and evolutionary analysis, highlighting the potential of these methods for extracting meaningful insights from large-scale genomic data. As language models continue to advance, their integration into bioinformatics holds immense promise for advancing our understanding of biological processes in all domains of life.

Understanding causal event relationships and achieving fine-grained temporal grounding in videos remain challenging for vision-language models (VLMs). We propose TEMPURA (Temporal Event Masked Prediction and Understanding for Reasoning in Action), a two-stage training framework that enhances the video temporal understanding of VLMs. Inspired by infilling techniques in language modeling, TEMPURA first performs masked event prediction, learning to reconstruct missing events and generate step-by-step causal explanations from dense event annotations. It then learns video segmentation and dense captioning, decomposing videos into non-overlapping events with detailed, timestamp-aligned descriptions. We train TEMPURA on VER, our large-scale dataset of 500K videos annotated with temporally aligned event descriptions and structured reasoning steps. Experiments on video temporal grounding and highlight detection benchmarks show that TEMPURA substantially improves strong base VLMs across model families and scales, confirming that combining event-level reasoning with fine-grained temporal segmentation is an effective recipe for video temporal understanding.

Chord progressions encapsulate important information about music, pertaining to its structure and conveyed emotions. They serve as the backbone of musical composition, and in many cases, they are the sole information required for a musician to play along and follow the music. Despite their importance, chord progressions as a data domain remain underexplored; existing datasets lack the scale, structural annotation, and metadata diversity required for rigorous evaluation of music understanding models. In this work, we present Chordonomicon, the largest dataset of its kind, containing over 666,000 song-level symbolic chord progressions, annotated with structural parts (verse, chorus, bridge, etc.), genre, and release date, created by scraping various sources of user-generated progressions and associated metadata, showing strong similarity to well-established prior datasets. Beyond the dataset itself, we propose a reproducible benchmark suite for next chord prediction, evaluating three sequence modeling architectures (RNN, GRU, LSTM) across multiple context window sizes and data scales under strict exact-match evaluation. Our experiments reveal that structural part annotations consistently improve prediction performance. Chordonomicon is released as an open benchmark, providing split methodology, baselines, and evaluation protocols to enable fair and reproducible comparison for future work on chord prediction, classification, generation, and beyond.