Autoregressive Language Modeling

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9 papers in the last four weeks, up 50% on the four weeks before. 0.1% of all new papers.

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Jun 25, 2026cs.CL

Developmental approach reveals the statistical learning of Neural Language Models: Transformers generalize from the most abstract statistical patterns

In this study, we use a developmental approach to investigate the statistical learning and mental representation of neural language models (NLM). A series of Generative Transformer models are trained on a synthetic grammar. The model states are saved at multiple stages in the course of training. Through analyzing how the internal representations of these models change in the developmental path, we found that NLMs acquire the most abstract global statistical knowledge at the beginning of learning and later acquire the relatively local statistical dependencies. This learning path contains many over-generalizations from the very beginning and these over-generalizations are gradually constrained in the later stage of learning. Based on this observation, we propose a new framework to explain the statistical learning and language cognition of NLMs.

Wang Bojun, Holly Jenkins, Elizabeth Wonnacott

Department of Education, University of Oxford

Autoregressive Language Modeling Computational Psycholinguistics

Jun 25, 2026cs.LG

Structure Before Collapse: Transient semantic geometry in next-token prediction

Neural Collapse predicts that balanced one-hot classification pushes model representations to be equally far from each other; a symmetric configuration that depends only on the output label and ignores any semantic similarity in the inputs. This creates a puzzle: next-token prediction language models are trained predominantly (as context length increases) with one-hot labels: the same context is very unlikely to appear twice in training with different labels. However, they clearly learn latent structural features. That is, despite the one-hot training regime, a language model's contextual embeddings represent the fact that the next word in ''Mary broke the ___'' is likely to be filled by tokens in the latent classes of a) medium-sized, b) rigid, c) inanimate nouns. How does gradient descent find such categorical semantic structure when co-occurrence statistics collapse to one-hot sparsity, eliminating any shared next-tokens among different contexts? To investigate this tension we identify three synthetic controlled settings where inputs have latent semantic factors but are mapped to distinct one-hot labels. We find that semantic geometry emerges early in training, and that representations cluster by shared attributes despite receiving no explicit supervision to do so. This structure is transient: with sufficient capacity and time, the model eventually reaches the predicted symmetric state where all representations are equally separated. We study this phase transition through Gram matrix analysis and propose a preliminary modification to the commonly used unconstrained features model to capture the emergent semantic geometry.

Yize Zhao, Isabel Papadimitriou, Christos Thrampoulidis

Department of Electrical and Computer Engineering, The University of British Columbia · Department of Linguistics, The University of British Columbia

Autoregressive Language Modeling Next-Token Prediction Neural Collapse Representation Geometry in Language Models

Jun 22, 2026cs.LG

Tapered Language Models

Modern language models, including transformer, recurrent, and memory-based variants, share a common chassis: a stack of identical layers in which parameters are allocated uniformly across depth. This is a default inherited from the original transformer and largely unchanged since, yet a growing body of evidence suggests that layers contribute non-uniformly to the final output, with later layers refining the residual stream rather than transforming it. We ask whether parameter capacity should reflect this asymmetry. Our controlled experiment shows that, under a fixed budget, allocating more capacity to earlier layers and less to later layers improves perplexity over a uniform-width baseline, while the reverse allocation hurts. Building on this result, we introduce Tapered Language Models (TLMs), an architectural principle in which a parameter-bearing component is monotonically tapered across depth under a fixed total budget. MLPs are the natural site for this instantiation: they dominate parameter count across all modern LM families and expose width as a single, clean axis of variation. Across three model scales and four architectures (Transformer, Gated Attention, Hope-attention, and Titans), tapering MLP width via a smooth cosine schedule consistently improves perplexity and downstream benchmark performance over uniform baselines, at no additional parameter or compute cost. These findings establish depth-aware capacity allocation as a simple, architecture-agnostic axis of language model design, a free lever hidden in plain sight.

Reza Bayat, Ali Behrouz, Aaron Courville

1Mila · 2Cornell University · 3Université de Montréal +1

Autoregressive Language Modeling

Jun 17, 2026cs.LG

Attention as Frustrated Synchronization

A network of oscillators that synchronizes perfectly computes nothing further, so an attention architecture built from synchronization must locate its computation in structured departures from agreement. We introduce the Frustrated Synchronization Network (FSN), whose token states are phases on a torus and whose entire value pathway is one learned complex coupling kernel over harmonics and a one-step delay. Each component of the kernel is a frustration in the sense of the synchronization literature. The complex phases are static Kuramoto-Sakaguchi frustration angles, the signed harmonics are repulsive Daido components, and the delay term, which couples each token to the successors of the tokens it attends to, is algebraically identical to Kuramoto-Sakaguchi coupling whose frustration angle is the data's own transition, so next-token prediction is implemented as synchronization frustrated by the data. At matched one-million-parameter and training budgets on character-level text and code, the FSN's validation loss is below a tuned RoPE-SwiGLU transformer's at every epoch measured, and the comparison survives training the baseline to convergence: every thirty-epoch enwik8 seed finishes below the transformer's converged fifty-epoch loss of 1.611, and the FSN's completed fifty-epoch runs converge to 1.5953 +/- 0.0014. A variant with every feed-forward block replaced by mean-field coupling to learned collective modes, leaving no multilayer perceptron in the stack, tracks the transformer. On natural text the unfrustrated base layer falls behind the converged transformer at every copy depth, worst on long-range copy events; the kernel reverses the deficit at every depth of four and beyond. Headline comparisons are at the one-million-parameter scale; a scale ladder is complete through four million parameters with the advantage persisting, and remaining arms are marked as in progress.

Joshua Nunley

Cognitive Science Program Luddy School of Informatics, Computing, and Engineering Indiana University Bloomington

Oscillatory Neural Networks Autoregressive Language Modeling Attention Mechanisms

Jun 16, 2026cs.LG

Why SWAVE May Not Be All You Need:A Concept-Evolution Retrospective on Complex-Valued Recurrent Language Models

SWave is a complex-valued recurrent language model (169.26M parameters, D=384, L=16, T=2048) trained on FineWeb-Edu using 2xH100 NVL. It was designed around three founding premises: that representing language as complex waves rather than real-valued numbers enables richer information encoding; that a Cayley-parameterised unitary transition provides a mathematical guarantee against state decay or explosion; and that a hidden state which rotates rather than shrinks preserves signal integrity over arbitrarily long contexts. The core of SWave evolved substantially across three development phases. The Resonance Head was found to structurally admit imaginary-channel collapse as a global loss minimum (a failure mode we term cos-domination collapse) and was superseded by an untied head with independent real and imaginary embedding tables from the Phase-Associative Memory (PAM) architecture. This resolved the degenerate minimum and enabled stable 200,000-step training (best-step PPL 22.0 at step 89,861). ComplexNorm and the Wave Propagation Scan proved load-bearing throughout all three phases and were retained to the final architecture. ProtectGatedScan was reframed as a structural prior rather than a learned behaviour. The four multi-scale retention concepts showed no measurable improvement under controlled evaluation and were found non-load-bearing. The ComplexGatedUnit was superseded by a real-valued squared-ReLU channel mixer with fewer parameters. The auxiliary training objectives showed no benefit once structural constraints were resolved. The investigation yields a formal characterisation of cos-domination collapse, a parallel scan with a log-space backward pass for numerical stability, six transferable engineering principles for complex-valued recurrent training, and a plan-to-code traceability methodology for catching structural divergences that conventional test suites miss.

Ramprasath Ganesaraja, Swathika N, Sahil Dilip Panse

EdgeVerve Systems Limited

Recurrent Neural Networks Complex-Valued Neural Networks Autoregressive Language Modeling

Jun 15, 2026cs.LG

Demystifying Training-Time Augmentation for Data-Constrained Language Model Pretraining

As AI labs approach a data ceiling where compute capacity outpaces the rate of new high-quality text generation, language model pretraining is shifting toward a data-constrained, compute-abundant regime that demands productive multi-epoch training on fixed corpora. Standard autoregressive (AR) pretraining overfits severely in this setting, reaching its optimum early and then continuously deteriorating. We investigate training-time data augmentation as a regularizer to mitigate this overfitting and enable productive training for hundreds of epochs on the same data. We introduce three orthogonal categories of augmentation for AR pretraining: token-level noise (masking, random replacement), sequence permutations (right-to-left prediction, Fill-in-the-Middle), and target offset prediction (

x_{t+i}

for

i > 1

). Through systematic ablations, we find that individual augmentations delay overfitting and lower validation loss relative to the baseline, with random token replacement achieving the best minimum loss among individual methods. Combining augmentation categories further lowers the minimum validation loss. Our experiments demonstrate that data augmentations mitigate AR pretraining's data inefficiency and offer a promising solution to the data-constrained regime~\footnote{All code and data are available at https://github.com/ michaelchen-lab/ data-augmentations-for-pretraining.

Michael K. Chen, Xikun Zhang, Fan Bai +2

1UC San Diego · 2RMIT University · 3Bloomberg AI

Language Model Pretraining Data Augmentation Autoregressive Language Modeling

Jun 14, 2026cs.LG

Circuit Tracing in Autoregressive Protein Language Models

Protein language models (pLMs) can generate novel protein sequences with properties beyond those observed in nature, yet the mechanisms underlying protein generation remain poorly understood. Existing mechanistic interpretability methods based on sparse autoencoders and transcoders primarily focus on protein representation learning models and do not capture the computation required for autoregressive generation. Here, we introduce ProGenMech, a mechanistic interpretability framework for generative protein language models that extends cross-layer transcoders (CLTs) to ProGen3, a sparse Mixture-of-Experts model trained for both causal generation and span infilling. Unlike per-layer approaches, CLTs reconstruct each layer using sparse latent variables from all preceding layers, enabling faithful recovery of inter-layer generative computation. We further develop a zero-shot circuit discovery framework to identify sparse latent circuits responsible for protein generation and fitness prediction. In causal generation and zero-shot fitness estimation tasks, ProGenMech outperforms local transcoder baselines in recovering ProGen3's probability distribution and functional scoring behavior, while matching the original model's generative distribution in span infilling tasks. Moreover, the recovered circuits reveal biologically meaningful motifs and functional regions associated with conserved sequence patterns and protein fitness landscapes, establishing a foundation for interpretable and steerable protein generation.

Darin Tsui, William Deinzer, Daniel Saeedi +1

School of Electrical and Computer Engineering, Georgia Institute of Technology, Atltanta, GA.

Circuit Discovery Protein Fitness Prediction Protein Language Models Autoregressive Language Modeling Mechanistic Interpretability Molecular Generation

Jun 12, 2026cs.CL

Simplifying the Modeling of Arbitrary Conditionals in Natural Language

Causal Transformers model sequences through an autoregressive factorization of the joint distribution, which enables efficient left-to-right decoding and conditional likelihood computation. However, they cannot tractably sample from or evaluate arbitrary conditionals -- e.g., a block of text conditioned on past and future tokens. Recent work aims to solve this problem through novel architectures, but they often lead to sub-optimal modeling of such conditionals and degraded generations. We propose Arbitrary Conditionals GPT (AC-GPT) which introduces a simple modification to standard causal Transformers to enable evaluating and sampling from arbitrary conditionals -- including past, future, and mixed contexts -- within a single forward pass. Unlike prior approaches, our method preserves the standard left-to-right ordering and next-token prediction objective essential for both strong performance and efficient training on natural language. Crucially, this compatibility allows existing LLMs to be fine-tuned for arbitrary conditioning. Our empirical results indicate that our method outperforms baselines on modeling arbitrary conditionals, without degrading standard left-to-right performance.

Yinhan Lu, Eric Elmoznino, Léo Gagnon +3

Mila — Quebec AI Institute · McGill University · Université de Montréal

Transformer Autoregressive Language Modeling Language Modeling Conditional Generative Modeling

Jun 9, 2026cs.LG

K-Forcing: Joint Next-K-Token Decoding via Push-Forward Language Modeling

Autoregressive (AR) language modeling is the dominant paradigm for text generation, yet its sequential token-by-token decoding makes inference memory-bound and inefficient. Existing acceleration approaches, such as speculative decoding and diffusion language models, can yield speedups under certain conditions but do not directly address high-load batch serving--the scenario most critical for industrial-scale deployment. We introduce K-Forcing, a push-forward language modeling paradigm for joint next-k-token decoding. K-Forcing distills an existing AR model into a conditional push-forward mapping--one that transforms independent uniform noise variables into a joint sample of multiple future tokens in a single forward pass. This design preserves fixed-length outputs, reuses the AR teacher backbone, and remains compatible with standard AR serving infrastructure. We train this mapping via progressive self-forcing distillation, which gradually expands the prediction window while enabling the student to closely match the sequence distribution of the AR teacher. We evaluate K-Forcing on LM1B and OpenWebText using a standard causal Transformer backbone. When aggressively configured to generate k = 4 tokens per forward pass, K-Forcing delivers approximately 2.4-3.5x speedup across different batch sizes, while incurring modest quality degradation relative to its AR teacher. As inference increasingly dominates the lifetime compute cost of modern LLMs, K-Forcing offers a promising route toward accelerating AR generation under real-world high-load deployment.

Zhiwei Tang, Yuanyu He, Yizheng Han +4

1DAMO Academy, Alibaba Group · 2Hupan Lab · 3Zhejiang University +1

LLM Serving Language Model Decoding Autoregressive Language Modeling LLM Inference Acceleration Language Model Distillation

Jun 9, 2026cs.LG

Parallel Causal Associative Fields: Gated Sparse Memory for Long-Context Language Modeling

Transformers achieve strong language modeling performance by providing direct token-to-token communication paths, but causal self-attention scales quadratically with context length. Recurrent and state-space models reduce this cost, yet compress history into sequentially updated fixed-size states. This paper studies a third primitive: a parallel content-addressed memory over causal successor records. The proposed Parallel Causal Associative Field (PCAF) writes local records from a context window into hash buckets, retrieves a bounded candidate set for the current query, forms a sparse cache distribution over successor tokens, and mixes that cache with a parametric local language model through a learned gate. The resulting model maintains sparse long-context access while avoiding a single fixed recurrent state bottleneck. We evaluate PCAF under full autoregressive pretraining on WikiText-103 and PG-19 using a distributed Google Cloud TPU v4-32 pod. At 303M parameters and context length T = 2048, PCAF-semantic reaches 36.31 perplexity on WikiText-103 and 52.45 perplexity on PG-19, compared with 47.49 and 53.84 for a matched dense Transformer. PCAF-semantic simultaneously processes 0.61-0.62M tokens/s across the TPU pod, versus 0.43M tokens/s for dense and local attention baselines. Supporting 41M-parameter multi-seed sweeps and single-GPU component ablations show that the associative cache, retrieval capacity, and learned gate materially affect the speed-quality trade-off.

Muhammad Ahmed

Independent Researcher

Memory-Augmented Language Models Long-Context Language Model Inference Long-Context Language Modeling Autoregressive Language Modeling Associative Memory

May 31, 2026cs.LG

CART: Context-Anchored Recurrent Transformer -- A Parameter-Efficient Architecture with Learned Stability

We present CART (Context-Anchored Recurrent Transformer), a parameter-efficient language model that reuses a single shared core block R times across depth. Unlike prior looped transformers that recompute key-value tensors at every iteration, CART computes K and V once from a multi-layer prelude and has the recurrent core cross-attend to those frozen tensors via multi-head latent attention. A learned Linear Time-Invariant (LTI) gate keeps the recurrence stable: its spectral radius settles in a narrow band (rho in [0.79, 0.83]) across all 36 fully-trained configurations. We evaluate CART on single consumer GPUs in two stages: a 64-configuration screen at 3,000 steps, then 36 configurations (P=6, R in {6,8,10}, three seeds) trained for 30,500 steps (~1B tokens). Two patterns hold across widths d in {256,512,768,1024}: prelude depth P dominates loop count R, and the Stage-1 ranking of R reverses at full training (R=6 becomes best at d>=512). At the binding d=1024 parameter-parity test, CART does not beat a parameter-matched dense baseline, losing by 1-2% at stored-parameter parity and by ~10% at effective-parameter parity. Diagnostic ablations split the effective-parameter gap into ~5% from weight sharing and a residual ~5% from the heterogeneous prelude/anchor/core/coda framing; the recurrent-core machinery (hyper-connections, LTI gate, loop-index embedding) is individually vestigial. Variable-R inference degrades on both sides of the trained R, a negative result for test-time depth scaling under this recipe.

Chad A. Capps

Independent Researcher

Recurrent Neural Networks Autoregressive Language Modeling Recurrent Transformers

May 29, 2026cs.LG

Trading Complexity for Expressivity Through Structured Generalized Linear Token Mixing

Token mixing layers play a key role in how language models can learn and generate long-range dependencies. Their efficiency relies on the necessary trade-off between decoding speed and the memory requirements, along with the cache size. Considering causal generation, this paper explores new trade-offs thanks to a unified framework which separates two crucial features: (i) the direct influence of inputs on outputs in one generation step; (ii) the recurrent propagation of information through past outputs. This framework encompasses major architectures such as attention and state-space models, but also generalizes the recurrence equations by allowing each state to depend on multiple past states rather than only the immediate predecessor. By introducing structure, we design new recurrence patterns that provably achieve the desired complexity, while providing theoretical insights on their expressivity -- trading runtime for expressivity in a principled way. Empirical validation is performed on synthetic tasks, along with language modeling. Together, these results provide a unified toolkit for the understanding and design of efficient and expressive token mixers across model families.

Erwan Fagnou, Paul Caillon, Blaise Delattre +1

Miles Team, LAMSADE, Université Paris Dauphine-PSL, Paris, France · Department of Computer Science, School of Computing, Institute of Science Tokyo, Tokyo, Japan · ESPCI PSL, Paris, France

Transformer Expressivity Autoregressive Language Modeling Efficient Language Model Inference

May 29, 2026cs.CL

Cognitive Fatigue in Autoregressive Transformers: Formalization and Measurement

Autoregressive language models frequently degrade during long-horizon generation, producing repetitive text, losing instruction adherence, and exhibiting unstable entropy. Despite the prevalence of these failures, practitioners lack online diagnostics to detect them in real-time as they occur. We formalize this degradation as cognitive fatigue, a measurable generation-time state characterized by decay in attention to the original prompt, representational drift, and entropy miscalibration. We introduce the Fatigue Index (FI), a lightweight, model-agnostic diagnostic that aggregates these three signals under explicit axioms (monotonicity, boundedness, interpretability) enabling reliable runtime monitoring. Across nine models (1B-13B parameters), FI trajectories exhibit structured temporal dynamics, predict task degradation (AUROC = 0.95) and repetition (Spearman rho = 0.94), and reveal non-monotonic scaling behavior: instruction-tuned models below 3B exhibit faster collapse than base models, with this trend reversing at 7B. Stress analyses further show that FI onset accelerates under longer contexts, middle-positioned evidence, and reduced numerical precision. These results establish cognitive fatigue as a coherent and measurable phenomenon, and position FI as a principled tool for runtime reliability monitoring in production LLM systems.

Riju Marwah, Ritvik Garimella, Vishal Pallagani +3

Guru Gobind Singh Indraprastha University, India · Artificial Intelligence Institute, University of South Carolina, USA · Indian Institute of Technology, Kanpur, India +1

Autoregressive Language Modeling

May 28, 2026eess.AS

MELD: Mel-Spectrogram-Based Speech Language Modeling with Discrete Latent Variables

Recent speech language models rely on encoders that are optimized separately from autoregressive models. Since these encoders are unaware of the downstream objectives, the extracted representations may not be optimal for downstream tasks. To address this limitation, we introduce a discrete latent variable model on mel spectrograms that jointly optimizes the encoder and the speech language model. Joint optimization not only brings improvements over codec-based and other mel-spectrogram-based baselines on zero-shot Text-to-Speech (TTS) and Speech-to-Text (STT) tasks, but also effectively alleviates common issues in autoregressive mel spectrogram modeling, such as prolonged silence generation and word omissions.

Sung-Lin Yeh, Wei Zhou, Gil Keren +6

University of Edinburgh · *Work done at Meta · 2Google DeepMind +1

Audio Representation Learning Autoregressive Language Modeling Automatic Speech Recognition Speech Language Models Text-to-Speech Discrete Speech Representation Learning

May 28, 2026cs.AI

EvoMD-LLM: Learning the Language of Species Evolution in Reactive Molecular Dynamics

While large language models (LLMs) excel at static scientific reasoning, they struggle to model the temporal structure of dynamic physical processes. We present EvoMD-LLM (Evolutionary Molecular Dynamics Large Language Model), a framework that reformulates species-level molecular dynamics as a symbolic temporal language modeling problem. Reactive MD trajectories are discretized into sequences of molecular events, where each token represents a chemical species augmented with its persistence duration, enabling standard autoregressive LLMs to learn compositional evolution over time through efficient fine-tuning. A key component of EvoMD-LLM is temporal scaffolding, which treats event duration as an explicit linguistic token and serves as a structured inductive bias, significantly reducing invalid or hallucinated molecular outputs compared to conventional sequence modeling approaches. We evaluate EvoMD-LLM on multiple temporal prediction tasks, achieving up to 66.14% accuracy and consistently outperforming sequential neural networks and language-based baselines. Beyond quantitative improvements, we qualitatively observe that the model is capable of generating interpretations for its own predictions by incorporating relevant chemical knowledge, even though it was not explicitly supervised with paired trajectory-explanation data. These results demonstrate that symbolic temporal language modeling provides an effective framework for grounding LLMs in dynamic physical simulations.

Zhichen Tang, Zhengzheng Dang, Yulin Chen +3

Global College, Shanghai Jiao Tong University, Shanghai, China · Global Institute of Future Technology, Shanghai Jiao Tong University, Shanghai, China

Autoregressive Language Modeling Language Modeling Molecular Dynamics Simulation Sequence Modeling

May 26, 2026cs.LG

Kan Extension Transformers: A Categorical Unification of Attention, Diffusion, and Predict-Detach Self-Conditioning

We propose Kan Extension Transformers (KETs) as a unifying categorical framework for a diverse group of Transformer implementations. The core claim is that a Transformer layer can be viewed as a weighted structured extension operator: standard attention is the singleton-neighborhood case, Geometric Transformer style incidence mixing is a sparse edge-restricted case, and KET is the higher-order simplicial case. This lens also clarifies a bridge to diffusion-style completion. When the extension operator acts on detached predictive carriers instead of teacher-forced hidden states, it becomes a valid self-conditioning mechanism that exposes noncausal structure without leaking gold future tokens. We include a comprehensive experimental validation of 12 different Transformer implementations varying across strict-causal and predict-detach regimes on Penn Treebank, WikiText-2, and WikiText-103. In the strict-causal setting, quadratic KET is the strongest model among the compared causal architectures on WikiText-2 and WikiText-103. Across all datasets, however, the largest gains come from the predict-detach regime rather than from changing the neighborhood family alone.

Sridhar Mahadevan

Adobe Research San Jose, CA · Academic affiliation: Research Professor, University of Massachusetts, Amherst

Transformer Autoregressive Language Modeling Transformer Attention

May 26, 2026cs.LG

Latent Recurrent Transformer: Architecture Exploration, Training Strategies, and Scaling Behavior

We study Latent Recurrent Transformer (LRT), a lightweight augmentation of autoregressive transformers that reuses a high-level source-layer hidden state from the previous token as recurrent memory for the next token. Because this state is already computed during ordinary decoding, LRT introduces a cross-token, cross-layer latent pathway while preserving the standard attention mechanism, KV-cache interface, and one model forward per generated token. To pretrain this recurrence without sequentially unrolling the full sequence, we introduce interleaved parallel training: one full-sequence initialization forward constructs a shared buffer, followed by sequential refinement of disjoint position subsets with parallel computation within each subset. This provides every token with recurrent-memory-aware supervision at approximately 2x ideal token compute. Across 1.3B- and 2.1B-parameter nanochat-style backbones and a wide range of training budgets, LRT improves both BPB and CORE under matched effective compute. Additionally, LRT outperforms two-forward PonderLM-2 and matches a three-loop Transformer in BPB, while retaining one-forward-per-token decoding with 9% latency overhead over the standard Transformer.

Zeyi Huang, Xuehai He, LiLiang Ren +8

Microsoft · University of Washington · University of Wisconsin-Madison

Language Model Pretraining Transformer Inference Autoregressive Language Modeling Recurrent Transformers

May 24, 2026cs.IT

Polynomial Context-Truncation Sensitivity in Autoregressive Language Models: Sequential Wyner-Ziv Bounds for KV Cache Compression

We study the rate-distortion limits of online KV cache compression in autoregressive language models, formulating it as sequential Wyner-Ziv source coding on the filtration induced by the model, with the next-step query as decoder side information. Empirically, across four models spanning two families and

0.5

-

3

B parameters, we find that the next-token distribution's sensitivity to context truncation decays \emph{polynomially} rather than \emph{geometrically}: a power law improves on an exponential fit by an order of magnitude in extrapolation, the fitted exponent is recovered independently from a sink-plus-recent KL measurement, and the decay is verified to be free of positional-encoding artifacts by a position-preserving ablation. Under a corresponding \emph{polynomial truncation-sensitivity} assumption, our main result characterizes the per-token memory requirement of \emph{suffix-only} cache policies: a sliding-window scheme attains distortion

\varepsilon

with window

w = O(\varepsilon^{-1/α})

, and -- under an additional two-sided Bayes-risk condition -- a converse shows

w = Ω(\varepsilon^{-1/α})

is necessary within this policy class, so the scaling is

Θ(\varepsilon^{-1/α})

for suffix-only policies. Whether recurrent or propagating cache summaries can beat this scaling is left open. An explicit block-Markov scheme achieves the upper bound; its rate-of-convergence exponent matches the converse under additional forward-decay and regularity hypotheses (not implied by truncation sensitivity alone), and differs by a factor of two otherwise. Empirically, the polynomial law predicts the degradation curves of concrete cache policies: recency-based eviction (sliding, sink-plus-recent) suppresses distortion by roughly two orders of magnitude over random retention at equal budget, with a power-law decay in the budget.

Munsik Kim

Independent Researcher.

KV Caching Rate-Distortion Theory Autoregressive Language Modeling Rate-Distortion Optimization KV-Cache Compression

May 22, 2026cs.LG

TUBE: Tangent Upper Bound on Evidence for Discrete Diffusion Language Models

Log-likelihood is a standard metric for evaluating generative models. Unfortunately, in contrast to autoregressive models (ARMs), discrete diffusion models generally do not admit exact computation of this quantity. Existing evaluations, therefore, rely on the evidence lower bound (ELBO), leaving unclear how much higher the true value may be. We address this by introducing the Tangent Upper Bound on Evidence (TUBE), a variational upper bound on log-likelihood that admits an unbiased Monte Carlo estimator. Our TUBE extends across latent-variable models, including masked diffusion models (MDMs), any-order ARMs (AO-ARMs), and block variants of both. Applied to block MDMs and block AO-ARMs, TUBE reveals our key empirical finding that these models lie strictly below the exact ARM baseline, showing that ARMs still dominate in likelihood.

Arseny Ivanov, Sergei Kholkin, Vladislav Gromadskii +3

AXXX, Russia · Applied AI Institute, Moscow, Russia · MIRAI, Russia

Masked Diffusion Models Autoregressive Language Modeling Generative Modeling Diffusion Language Models Variational Inference Diffusion Models

May 22, 2026cs.CL

When Is Next-Token Prediction Useful? Marginalization, Ergodicity, Mixture Identifiability, Local Sufficiency, RAG, Tools, and Programming

Language models trained on observed sequences are often described as learning the conditional distribution of the next token given previous tokens. This description is only conditionally correct. A model trained on realized token trajectories does not observe full conditional laws; it receives sampled continuations. Moreover, real language generation is conditioned not only on previous words but also on non-textual circumstances: facts, events, intentions, goals, beliefs, social context, and task-specific constraints. This paper distinguishes three objects that are often conflated: the full conditional language process conditioned on latent circumstances, the marginal text-only process obtained by integrating those circumstances out, and the model-induced distribution learned from finite observed corpora. The paper argues that interpreting model training as estimating the marginal text-only law requires strong assumptions of stationarity, representativeness, and ergodicity, assumptions that are standard in statistical estimation but problematic when applied to heterogeneous language corpora. Even if these assumptions hold, the marginal text-only law is useful only when the observed prefix is an approximately sufficient statistic for the latent circumstances relevant to continuation. In information-theoretic terms, usefulness requires that the residual conditional mutual information between the next token and the omitted circumstances, given the observed text, be small. The paper then extends this argument to heterogeneous training corpora. Finally, the paper interprets Retrieval Augmented Generation (RAG) and tool use as conditional sufficiency devices.

Francesco Corielli

Autoregressive Language Modeling Next-Token Prediction Conditional Distribution Estimation Sequence Modeling

May 17, 2026cs.CL

MiniGPT: Rebuilding GPT from First Principles

This paper presents MiniGPT, a compact from-scratch implementation of GPT-style autoregressive language modeling in PyTorch. The aim is to rebuild the core GPT pipeline from first principles after studying the design of nanoGPT by Andrej Karpathy, while keeping the model and training code independently written in a single notebook. MiniGPT implements token and positional embeddings, causal multi-head self-attention, pre-LayerNorm Transformer blocks, residual connections, feed-forward MLP layers, next-token cross-entropy training (teacher forcing), validation tracking, checkpoint selection, and autoregressive text generation. This paper evaluates the implementation on Tiny Shakespeare dataset using character-level tokenization. A baseline 0.83M-parameter model reaches a validation loss of 1.7236 after 3000 training iterations. A stronger 10.77M-parameter configuration, using a larger context length and improved training settings, reaches a best validation loss of 1.4780 and generates text with recognizable Shakespeare-style dialogue structure. MiniGPT does not introduce a new language-model architecture. Instead, it documents a clear and reproducible implementation path from raw text to trained character-level generation, including design choices, training behavior, generation quality, and practical limitations.

Jibin Joseph

Department of Computer Science The University of Texas at Austin Austin, TX 78712

Language Model Pretraining Decoder-Only Language Models Autoregressive Language Modeling Language Modeling

May 15, 2026cs.SD

Modeling Music as a Time-Frequency Image: A 2D Tokenizer for Music Generation

Autoregressive music generation depends strongly on the audio tokenizer. Existing high-fidelity codecs often use residual multi-codebook quantization, which preserves reconstruction quality but complicates language modeling after sequence flattening, as the residual hierarchy imposes strong sequential dependencies and can amplify error accumulation. We propose BandTok, a generation-oriented 2D Mel-spectrogram tokenizer that represents each frame with Mel-frequency band tokens from a single shared codebook. This design yields a physically interpretable time-frequency token grid with a more independent token structure, making it better suited for autoregressive modeling. BandTok improves reconstruction with a multi-scale PatchGAN objective and EMA codebook updates. We further introduce an autoregressive language model with 2D Rotary Position Embedding (2D RoPE) to preserve temporal and frequency-band structure during generation. Experiments show that BandTok improves over residual-codebook tokenizers and achieves strong results in a data-limited setting. The source code and generation demos for this work are publicly available.

Yuqing Cheng, Xingyu Ma, Guochen Yu +1

Department of Music AI and Information Technology, Central Conservatory of Music, Beijing, China · Zhipu AI, Beijing, China

Neural Audio Codecs Autoregressive Language Modeling Audio Tokenization Music Generation

May 13, 2026cs.AI

Conditional Attribute Estimation with Autoregressive Sequence Models

Generative models are often trained with a next-token prediction objective, yet many downstream applications require the ability to estimate or control sequence-level properties. Next-token prediction can lead to overfitting of local patterns during training, underfitting of global structure, and requires significant downstream modifications or expensive sampling to guide or predict the global attributes of generated samples at inference time. Here, we introduce Conditional Attribute Transformers, a novel method for jointly estimating the next-token probability and the value of an attribute conditional on each potential next token selection. This framework enables three critical capabilities within a single forward pass, without modification of the input sequence: (1) per-token credit assignment across an entire sequence, by identifying how each token in a sequence is associated with an attribute's value; (2) counterfactual analysis, by quantifying attribute differences conditional on alternative next token choices; (3) steerable generation, by decoding sequences based on a combination of next-token and attribute likelihoods. Our approach achieves state of the art performance on sparse reward tasks, improves next-token prediction at sufficient model sizes, estimates attribute probabilities orders of magnitude faster than sampling, and can guide decoding of autoregressive sequence models on a range of language tasks.

Erica Stutz, Giacomo Marino, Daniella Meeker +2

Department of Biomedical Informatics and Data Science Yale University New Haven, CT 06510 · Department of Biostatistics Yale University New Haven, CT 06510 · Department of Biomedical Informatics and Data Science, Department of Pediatrics Yale University New Haven, CT 06510

Counterfactual Reasoning in Language Models Controllable Text Generation Autoregressive Language Modeling Next-Token Prediction Autoregressive Generation Conditional Generative Modeling

May 13, 2026cs.LG

A Hierarchical Language Model with Predictable Scaling Laws and Provable Benefits of Reasoning

We introduce a family of synthetic languages with hierarchical structure -- generated by a broadcast process on trees -- for which the role of context length and reasoning in autoregressive generation can be analyzed precisely. At the heart of our analytic approach is an \emph{exact

k

-gram ansatz} in place of transformers with context length

k

, a substitution we then validate empirically. Using this ansatz we derive explicit asymptotic predictions for distributional statistics of the sequences produced by a trained model, instantiated in two settings. For the \emph{Ising broadcast process} (a soft-constrained language), we prove that the variance of the generated sum scales log-linearly in the context depth and its kurtosis converges to that of a Gaussian -- both deviating from the true language for any sublinear context. For the \emph{coloring broadcast process} (a hard-constrained language) in the freezing regime, bounded-context autoregression produces sequences that, with high probability, are inconsistent with \emph{any} valid coloring of the underlying tree. Together these results imply an

Ω(n)

lower bound on the context length required to faithfully sample length-

n

sequences. In contrast, we prove that an autoregressive \emph{reasoning} model with only

Θ(\log n)

working memory can sample exactly from the true language -- an exponential improvement. We confirm both the lower-bound predictions and the reasoning-based upper bound empirically with transformers trained on the synthetic language; the trained models track our asymptotic predictions quantitatively across a wide range of context sizes.

Jason Gaitonde, Frederic Koehler, Elchanan Mossel +2

Duke University · University of Chicago · Massachusetts Institute of Technology +1

Long-Context Language Modeling Language Model Scaling Laws Autoregressive Language Modeling Language Modeling

May 13, 2026cs.LG

The Expressivity Boundary of Probabilistic Circuits: A Comparison with Large Language Models

Probabilistic Circuits (PCs) are deep generative models that support exact and efficient probabilistic inference. Yet in autoregressive language modeling, PCs still lag behind Transformer-based large language models (LLMs), suggesting an important expressivity gap. In this work, we compare PCs and LLMs under a unified autoregressive formulation. First, an output bottleneck: PCs parameterize predictions as convex combinations in probability space, which struggles to represent the sharp distributions typical of language; adopting a logit-space parameterization substantially narrows this gap. Second, a context-encoding bottleneck: we prove that structured-decomposable PCs can match Transformer separation rank on vtree-aligned partitions, but show, both theoretically and empirically, that this capacity is limited to partitions aligned with the fixed routing structure, leading to severe degradation when the data exhibits heterogeneous dependency topologies. We further prove that decomposable PCs are strictly more expressive than structured-decomposable ones, though effectively optimizing them remains an open challenge.

Zhiyu Zhao, Xuejie Liu, Muhan Zhang +1

School of Computing, National University of Singapore · School of Intelligence Science and Technology, Peking University · Institute for Artificial Intelligence, Peking University

Probabilistic Circuits Autoregressive Language Modeling

May 13, 2026cs.LG

The Efficiency Gap in Byte Modeling

Modern language models have historically relied on two dominant design choices: subword tokenization and autoregressive (AR) ordering. These design decisions bake in priors that dictate a model's learning. Recently, two alternative paradigms have challenged this: byte-level modeling, which bypasses static statistically-derived token vocabularies, and masked diffusion modeling (MDM), which conducts parallel, non-sequential generation. Their intersection represents a fully end-to-end modality-agnostic generative prototype; however, removing these structural priors incurs a significant computational cost. In this work, we investigate this cost through a compute-matched scaling study. Our results reveal that the performance penalty of byte modeling is not uniform; across scale, the scaling overhead of byte modeling is worse for MDM than for AR. We hypothesize that this disparity stems from context fragility: while AR's stable causal history allows models to naturally rediscover subword patterns, the MDM objective destroys the local contiguity required to efficiently resolve semantics from raw bytes. Our findings from controlled permutation experiments suggest that future modality-agnostic designs must incorporate alternative structural biases to maintain viable scaling trajectories in the byte regime.

Celine Lee, Jing Nathan Yan, Chen Liang +9

1Google DeepMind · 2Work done while at Google DeepMind · Department of Computer Science, Cornell University.

Language Model Scaling Laws Autoregressive Language Modeling Language Modeling Diffusion Language Models

May 12, 2026cs.CL

A Causal Language Modeling Detour Improves Encoder Continued Pretraining

When adapting an encoder to a new domain, the standard approach is to continue training with Masked Language Modeling (MLM). We show that temporarily switching to Causal Language Modeling (CLM) followed by a short MLM decay improves downstream performance. On biomedical texts with ModernBERT, this CLM detour outperforms MLM baselines trained on identical data and compute across 8 French and 11 English biomedical tasks, by +1.2-2.8pp and +0.3-0.8pp respectively, depending on model size. We investigate the reasons for these gains. We find that CLM's dense supervision impacts low transformer layers (0-7) far more than MLM does. Freezing low layers during CLM eliminates the downstream benefit; freezing mid layers preserves it. The representational changes persist through the MLM decay phase, even when it matches the CLM phase in length, and they scale with model capacity. We release ModernCamemBERT-bio and ModernBERT-bio as state-of-the-art biomedical encoders in Base and Large sizes.

Rian Touchent, Eric de la Clergerie

Sorbonne Université / INRIA Paris · ALMAnaCH Team · INRIA Paris

Language Model Pretraining Masked Language Modeling Autoregressive Language Modeling Language Modeling Continued Pretraining

May 12, 2026cs.CL

BitLM: Unlocking Multi-Token Language Generation with Bitwise Continuous Diffusion

Autoregressive language models generate text one token at a time, yet natural language is inherently structured in multi-token units, including phrases, n-grams, and collocations that carry meaning jointly. This one-token bottleneck limits both the expressiveness of the model during pre-training and its throughput at inference time. Existing remedies such as speculative decoding or diffusion-based language models either leave the underlying bottleneck intact or sacrifice the causal structure essential to language modeling. We propose BitLM, a language model that represents each token as a fixed-length binary code and employs a lightweight diffusion head to denoise multiple tokens in parallel within each block. Crucially, BitLM preserves left-to-right causal attention across blocks while making joint lexical decisions within each block, combining the reliability of autoregressive modeling with the parallelism of iterative refinement. By replacing the large-vocabulary softmax with bitwise denoising, BitLM reframes token generation as iterative commitment in a compact binary space, enabling more efficient pre-training and substantially faster inference without altering the causal foundation that makes language models effective. Our results demonstrate that the one-token-at-a-time paradigm is not a fundamental requirement but an interface choice, and that changing it can yield a stronger and faster language model. We hope BitLM points toward a promising direction for next-generation language model architectures.

Shaobin Zhuang, Yuang Ai, Jiaming Han +7

Shanghai Jiao Tong University · MMLab, The Chinese University of Hong Kong · Institute of Automation, Chinese Academy of Sciences +1

Multi-Token Prediction Autoregressive Language Modeling LLM Inference Acceleration Diffusion Language Model Decoding Diffusion Language Models

May 11, 2026cs.CL

A Single-Layer Model Can Do Language Modeling

Modern language models scale depth by stacking layers, each holding its own state - a per-layer KV cache in transformers, a per-layer matrix in Mamba, Gated DeltaNet (GDN), RWKV, and xLSTM. Biological systems lean heavily on recurrence rather than on stacking. We ask how far that shape can go on language modeling. We propose Grounded Prediction Networks (GPN): one state vector revisited at every step through a single recurrent block - one FFN, one shared matrix memory. At 130M parameters, a 1-layer GPN+M reaches FineWeb-Edu perplexity 18.06, within 13% of a 12-layer Transformer++ (16.05) and 18% of a 10-layer GDN (15.34); a 2-layer variant closes the gap to 6%/11%. We do not match the deep baselines. Because the working context is a single vector, we can directly inspect its geometry: a persistent default-token direction, a content-bearing horizon of tens of tokens, and memory heads that split spontaneously into fast and slow retention pools.

Zanmin Wang

Language Model Pretraining Recurrent Neural Networks Autoregressive Language Modeling Next-Token Prediction Language Modeling

May 11, 2026cs.LG

Self-Attention as a Covariance Readout: A Unified View of In-Context Learning and Repetition

Large language models (LLMs) exhibit two striking and ostensibly unrelated behaviours: in-context learning (ICL) and repetitive generation. In both, the model behaves as though it had summarised the context into a population-level statistic and discarded token-level detail. We ask whether this ``summarisation and forgetting'' can be derived from the attention mechanism itself, and answer in the affirmative. Under stationary, ergodic and elliptical inputs, the softmax attention output converges almost surely to

Θ_VΣΘ_K^{\top}Θ_Q x_t

, where

Σ

is the input covariance; the long-context limit is therefore a linear readout of the input's second-order statistics. Two consequences follow. (i) For in-context linear regression, a single softmax head can implement one step of population gradient descent. Stacking such heads with residual connections iterates this update and implements multiple gradient descent steps. (ii) Propagated across an

L

-layer transformer, this readout drives the terminal hidden state at the parametric

1/t

rate to a deterministic function of the current token alone, so that autoregressive generation collapses asymptotically to a first-order Markov chain whose attracting orbits furnish a structural account of repetition and mode collapse. The two phenomena thus emerge as facets of a single covariance-readout principle.

Haoren Xu, Guanhua Fang

Fudan University

Softmax Attention Self-Attention Autoregressive Language Modeling In-Context Learning Mode Collapse Text Generation