Autoregressive Language Modeling

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Autoregressive language models learn to predict each next token from the preceding context, a simple objective that supports both generation and tasks such as speech or protein modeling. Transformer attention remains a common approach, while recurrent and state-space models, sparse memory, and alternative tokenizations aim to reduce the cost of long contexts and large vocabularies. Current work also explores faster generation through multi-token prediction, latent lookahead, and combinations of causal and diffusion methods, evaluated on measures such as perplexity, retrieval, and downstream reasoning benchmarks. A central tension is how to gain speed and long-range capability without losing the quality, reliability, and generalization associated with left-to-right prediction.

Latest papers

133 papers15 papers in the last four weeks, up 25% on the four weeks before. 0.1% of all new papers.

May 1, 2026

Characterizing the Expressivity of Local Attention in Transformers

The transformer is the most popular neural architecture for language modeling. The cornerstone of the transformer is its global attention mechanism, which lets the model aggregate information from all preceding tokens before generating the next token. One common variant of attention is called local attention, which restricts each token to aggregating information from a bounded window of predecessors, reducing the quadratic cost of global attention to linear. Although this restriction is usually motivated by efficiency, it has also been found to improve model quality, a phenomenon that has so far lacked a satisfactory explanation. We provide a formal account of this phenomenon in terms of recognizer expressivity. It has been shown that fixed-precision transformers with global attention correspond to a fragment of linear temporal logic containing a single past operator. We additionally prove that adding local attention introduces a second temporal operator, strictly enlarging the class of recognizable regular languages. Moreover, global and local attention are expressively complementary: neither subsumes the other, and combining them yields the richest fragment. Experiments on formal language recognition and natural language modeling corroborate the theory, showing that hybrid global--local transformers outperform their global-only counterparts.

Jiaoda Li, Ryan Cotterell

Transformer Expressivity Transformer Autoregressive Language Modeling Local Attention Attention Mechanisms Neural Network Expressivity

Apr 30, 2026

Caracal: Causal Architecture via Spectral Mixing

The scalability of Large Language Models to long sequences is hindered by the quadratic cost of attention and the limitations of positional encodings. To address these, we introduce Caracal, a novel architecture that replaces attention with a parameter-efficient, O(L log(L)) Multi-Head Fourier (MHF) module. Our contributions are threefold: (1) We leverage the Fast Fourier Transform (FFT) for sequence mixing, inherently addressing both bottlenecks mentioned above. (2) We apply a frequency-domain causal masking technique that enforces autoregressive capabilities via asymmetric padding and truncation, overcoming a critical barrier for Fourier-based generative models. (3) Unlike efficient models relying on hardware-specific implementations (e.g., Mamba), we uses standard library operators. This ensures robust portability, eliminating common deployment barriers. Evaluations demonstrate that Caracal performs competitively with Transformer and SSM baselines, offering a scalable and simple pathway for efficient long-sequence modeling. Code is available in Appendix.

Bingzheng Gan, Tianyi Zhang, Yusu Li +4

Huawei Technologies Co., Ltd., China.

Long-Context Language Modeling Autoregressive Language Modeling LLM Inference Acceleration

Apr 27, 2026

Representational Curvature Modulates Behavioral Uncertainty in Large Language Models

In autoregressive large language models (LLMs), temporal straightening offers an account of how the next-token prediction objective shapes representations. Models learn to progressively straighten the representational trajectory of input sequences across layers, potentially facilitating next-token prediction via linear extrapolation. However, a direct link between this trajectory and token-level behavior has been missing. We provide such a link by relating contextual curvature-a geometric measure of how sharply the representational trajectory bends over recent context-to next-token entropy. Across two models (GPT-2 XL and Pythia-2.8B), contextual curvature is correlated with entropy, and this relationship emerges during training. Perturbation experiments reveal selective dependence: manipulating curvature through trajectory-aligned interventions reliably modulates entropy, while geometrically misaligned perturbations have no effect. Finally, regularizing representations to be straighter during training modestly reduces token-level entropy without degrading validation loss. These results identify trajectory curvature as a task-aligned representational feature that influences behavioral uncertainty in LLMs.

Jack King, Evelina Fedorenko, Eghbal A. Hosseini

Brain and Cognitive Sciences Massachusetts Institute of Technology Cambridge, MA 02139 · Google DeepMind

Neural Representation Geometry Autoregressive Language Modeling LLM Uncertainty Estimation Representation Geometry in Language Models

Apr 23, 2026

The Recurrent Transformer: Greater Effective Depth and Efficient Decoding

Transformers process tokens in parallel but are temporally shallow: at position

t

, each layer attends to key-value pairs computed based on the previous layer, yielding a depth capped by the number of layers. Recurrent models offer unbounded temporal depth but suffer from optimization instability and historically underutilize modern accelerators. We introduce the Recurrent Transformer, a simple architectural change where each layer attends to key-value pairs computed off its own activations, yielding layerwise recurrent memory while preserving standard autoregressive decoding cost. We show that the architecture can emulate both (i) a conventional Transformer and (ii) token-to-token recurrent updates under mild assumptions, while avoiding optimization instability. Naively, prefill/training appears bandwidth-bound with effective arithmetic intensity near

1

because keys and values are revealed sequentially; we give an exact tiling-based algorithm that preserves the mathematical computation while reducing HBM traffic from

Θ(N^2)

to

Θ(N\log N)

, increasing effective arithmetic intensity to

Θ(N/\log N)

for sequence length

N

. On 150M and 300M parameter C4 pretraining, Recurrent Transformers improve cross-entropy over a parameter-matched Transformer baseline and achieve the improvement with fewer layers (fixed parameters), suggesting that recurrence can trade depth for width, thus reducing KV cache memory footprint and inference latency.

Costin-Andrei Oncescu, Depen Morwani, Samy Jelassi +3

Harvard University

Autoregressive Language Modeling Self-Attention Attention Mechanisms Efficient Transformer Inference Recurrent Transformers Efficient Attention+1

Apr 21, 2026

StarTSE: Towards Streaming Target Speaker Extraction via Chunk-wise Interleaved Splicing of Autoregressive Language Model

While generative models have set new benchmarks for Target Speaker Extraction (TSE), their inherent reliance on global context precludes deployment in real-time applications. Direct adaptation to streaming scenarios often leads to catastrophic inference performance degradation due to the severe mismatch between training and streaming inference. To bridge this gap, we present the first autoregressive (AR) models tailored for streaming TSE. Our approach introduces a Chunk-wise Interleaved Splicing Paradigm that ensures highly efficient and stable streaming inference. To ensure the coherence between the extracted speech segments, we design a historical context refinement mechanism that mitigates boundary discontinuities by leveraging historical information. Experiments on Libri2Mix show that while AR generative baseline exhibits performance degradation at low latencies, our approach maintains 100% stability and superior intelligibility. Furthermore, our streaming results are comparable to or even surpass offline baselines. Additionally, our model achieves a Real-Time-Factor (RTF) of 0.248 on consumer-level GPUs. This work provides empirical evidence that AR generative backbones are viable for latency-sensitive applications through the Chunk-wise Interleaved Splicing Paradigm.

Shuhai Peng, Hui Lu, Jinjiang Liu +8

Shenzhen International Graduate School, Tsinghua University · The Chinese University of Hong Kong · SenseTime Research

Target Speaker Extraction Speech Processing Autoregressive Language Modeling Streaming Algorithms

Apr 17, 2026

Generic Triple-Latent Compression with Gated Associative Retrieval

We study generic triple-latent sequence models that maintain a running token state and compressed pair-memory pathway to capture higher-order token interactions without benchmark-specific parsing. The triple-latent family improves a small Transformer baseline on byte-level WikiText-2 and on a tokenizer-based MiniMind language-model benchmark, while a recall-focused gated key-value retrieval extension improves associative recall but remains seed-sensitive and much slower in the current reference implementation.

Liu Xiao

Memory-Augmented Language Models Autoregressive Language Modeling Associative Memory Sequence Modeling

Apr 16, 2026

Hallucination as Trajectory Commitment: Causal Evidence for Asymmetric Attractor Dynamics in Transformer Generation

We present causal evidence that hallucination in autoregressive language models is an early trajectory commitment governed by asymmetric attractor dynamics. Using same-prompt bifurcation, in which we repeatedly sample identical inputs to observe spontaneous divergence, we isolate trajectory dynamics from prompt-level confounds. On Qwen2.5-1.5B across 61 prompts spanning six categories, 27 prompts (44.3%) bifurcate with factual and hallucinated trajectories diverging at the first generated token (KL = 0 at step 0, KL > 1.0 at step 1). Activation patching across 28 layers reveals a pronounced causal asymmetry: injecting a hallucinated activation into a correct trajectory corrupts output in 87.5% of trials (layer 20), while the reverse recovers only 33.3% (layer 24); both exceed the 10.4% baseline (p = 0.025) and 12.5% random-patch control. Window patching shows correction requires sustained multi-step intervention, whereas corruption needs only a single perturbation. Probing the prompt encoding itself, step-0 residual states predict per-prompt hallucination rate at Pearson r = 0.776 at layer 15 (p < 0.001 against a 1000-permutation null); unsupervised clustering identifies five regime-like groups (eta^2 = 0.55) whose saddle-adjacent cluster concentrates 12 of the 13 bifurcating false-premise prompts, indicating that the basin structure is organized around regime commitments fixed at prompt encoding. These findings characterize hallucination as a locally stable attractor basin: entry is probabilistic and rapid, exit demands coordinated intervention across layers and steps, and the relevant basins are selected by clusterable regimes already discernible at step 0.

G. Aytug Akarlar

Chimera Research Initiative Istanbul, Türkiye · Chimera Research Initiative is an independent research effort exploring causal and neuro-symbolic approaches to AI systems.

Transformer Interpretability Hallucination in Language Models Autoregressive Language Modeling

Apr 13, 2026

Sample Complexity of Autoregressive Reasoning: Chain-of-Thought vs. End-to-End

Modern large language models generate text autoregressively, producing tokens one at a time. To study the learnability of such systems, Joshi et al. (COLT 2025) introduced a PAC-learning framework for next-token generators, the primitive underlying autoregressive models. In this framework, an unknown next-token generator maps a sequence of tokens to the next token and is iteratively applied for

T

steps, producing a chain of tokens whose final token constitutes the model's output. The learning task is to learn the input-output mapping induced by this autoregressive process. Depending on the available supervision, training examples may reveal only the final output (End-to-End supervision) or the entire generated chain (Chain-of-Thought supervision). This raises two natural questions: how the sample complexity depends on the generation length

T

, and how much Chain-of-Thought supervision can reduce this dependence. In this work we give a nearly complete answer to both questions by uncovering a taxonomy of how the sample complexity scales with

T

. For End-to-End learning, we show that the landscape is remarkably rich: subject to mild conditions, essentially any growth rate

r(T)

between constant and linear can arise as the sample complexity, and combined with the linear upper bound of Joshi et al., this yields an essentially complete characterization. In contrast, under Chain-of-Thought supervision we show that the sample complexity is independent of

T

, demonstrating that access to intermediate reasoning steps can eliminate the dependence on the generation length altogether. Our analysis introduces new combinatorial tools, and as corollaries we resolve several open questions posed by Joshi et al. regarding the dependence of learnability on the generation length and the role of Chain-of-Thought supervision.

Steve Hanneke, Idan Mehalel, Shay Moran

Purdue University · The Hebrew University · Technion and Google Research

CoT Supervision Sample Complexity Autoregressive Language Modeling

Apr 13, 2026

MIXAR: Scaling Autoregressive Pixel-based Language Models to Multiple Languages and Scripts

Pixel-based language models are gaining momentum as alternatives to traditional token-based approaches, promising to circumvent tokenization challenges; however, existing models remain English-centric and are hard to train as generators. This paper introduces MIXAR, the first generative multilingual pixel-based language model, pretrained on eight high-resource languages spanning Latin and CJK scripts and scaled up to 0.5B parameters. Although pretrained on high-resource languages only, MIXAR generalizes to unseen low-resource languages better than a tokenizer-based model pretrained on the same corpus, with its largest gains on the scripts most distant from the pretraining mix, taking a step toward more equitable language technology. To make free generation work in pixel space, MIXAR replaces the notoriously unstable adversarial training stage of prior pixel-based models with a GRPO-based reinforcement-learning stage that rewards the model on its own free-running generations: it proves more stable and multiplies free-generation accuracy by up to 2.3x on multilingual benchmarks. Finally, MIXAR performs on par with comparable tokenizer-based models on discriminative benchmarks, improves consistently with scale, and withstands orthographic attacks more gracefully than tokenizer-based models. Code and models are available at https://github.com/april-tools/mixar.

Chen Hu, Yintao Tai, Antonio Vergari +2

School of Informatics, University of Edinburgh

Multilingual Language Models Autoregressive Language Modeling Multilingual Language Model Evaluation Language Model Robustness

Apr 13, 2026

Winner-Take-All Spiking Transformer for Language Modeling

Spiking Transformers, which combine the scalability of Transformers with the sparse, energy-efficient property of Spiking Neural Networks (SNNs), have achieved impressive results in neuromorphic and vision tasks and attracted increasing attention. However, existing directly trained spiking transformers primarily focus on vision tasks. For language modeling with spiking transformer, convergence relies heavily on softmax-based spiking self-attention, which incurs high energy costs and poses challenges for neuromorphic deployment. To address this issue, we introduce Winner-Take-All (WTA) mechanisms into spiking transformers and propose two novel softmax-free, spike-driven self-attention modules: WTA Spiking Self-Attention (WSSA) and Causal WTA Spiking Self-Attention (CWSSA). Based on them, we design WTA-based Encoder-only Spiking Transformer (WE-Spikingformer) for masked language modeling and WTA-based Decoder-only Spiking Transformer (WD-Spikingformer) for causal language modeling, systematically exploring softmax-free, spiking-driven Transformer architectures trained end-to-end for natural language processing tasks. Extensive experiments on 16 datasets spanning natural language understanding, question-answering tasks, and commonsense reasoning tasks validate the effectiveness of our approach and highlight the promise of spiking transformers for general language modeling and energy-efficient artificial intelligence.

Chenlin Zhou, Sihang Guo, Jiaqi Wang +6

School of Electronic and Computer Engineering, Shenzhen Graduate School, Peking University · Pengcheng Laboratory · Harbin Institute of Technology +1

Spiking Transformers Spiking Language Models Transformer Attention Autoregressive Language Modeling Decoder-Only Language Models Masked Language Modeling

Apr 9, 2026

Hidden Biases in Conditioning Autoregressive Models

Large language and music models are increasingly used for constrained generation: rhyming lines, fixed meter, inpainting or infilling, positional endings, and other global form requirements. These systems often perform strikingly well, but the induced procedures are usually not exact conditioning of the underlying autoregressive model. This creates a hidden inferential bias, distinct from the better-known notion of bias inherited from the training set: samples are distorted relative to the true constrained distribution, with no generic guarantee of complete coverage of the admissible solution space or of correct conditional probabilities over valid completions. We formalize several exact inference tasks for autoregressive models and prove corresponding hardness results. For succinctly represented autoregressive models whose next-token probabilities are computable in polynomial time, exact sentence-level maximum a posteriori (MAP) decoding is NP-hard. This hardness persists under unary and metrical constraints. On the sampling side, exact conditioned normalization is #P-hard even for regular constraints such as fixed-length terminal events. Unlike finite-state Markov models, general autoregressive models do not admit a bounded-state dynamic program for these tasks. These results formalize a standard claim in the neural decoding literature: local autoregressive sampling is easy, whereas exact decoding and exact conditioning under global form constraints are computationally intractable in general.

Francois Pachet, Pierre Roy

LIP6, Sorbonne Université · Soundtrap

Constrained Generative Modeling Constrained Decoding Autoregressive Language Modeling Autoregressive Modeling

Apr 8, 2026

Optimal Decay Spectra for Linear Recurrences

Linear recurrent models offer linear-time sequence processing but often suffer from suboptimal long-range memory. We trace this to the decay spectrum: for

N

channels, random initialization collapses the minimum spectral gap to

O(N^{-2})

, yielding sub-exponential error

\exp(-Ω(N/\log N))

; linear spacing avoids collapse but degrades to

\exp(-O(N/\sqrt{T}))

, practically algebraic over long contexts. We introduce Position-Adaptive Spectral Tapering (PoST), an architecture-agnostic framework combining two mechanisms: (1) Spectral Reparameterization, which structurally enforces geometrically spaced log-decay rates, proven minimax optimal at rate

O(\exp(-cN/\log T))

; and (2) Position-Adaptive Scaling, the provably unique mechanism that eliminates the scale mismatch of static spectra (where only

N\log t/\log T

of

N

channels are effective at position

t

) by stretching the spectrum to the actual dependency range, sharpening the rate to

O(\exp(-cN/\log t))

. This scaling natively induces fractional invariance: the impulse response becomes scale-free, with channels interpolating between relative and absolute temporal coordinates. PoST integrates into any diagonal linear recurrence without overhead. We instantiate it across Mamba-2, RWKV-7, Gated DeltaNet, Gated Linear Attention, and RetNet. Pre-training at 180M-440M scales shows consistent zero-shot language modeling improvements, significant long-context retrieval gains for Mamba-2 (MQAR and NIAH), and competitive or improved performance across other architectures. Code: https://github.com/SiLifen/PoST.

Yang Cao

Linear RNNs Long-Range Dependency Modeling Long-Context Language Modeling Autoregressive Language Modeling

Apr 8, 2026

MARS: Enabling Autoregressive Models Multi-Token Generation

Autoregressive (AR) language models generate text one token at a time, even when consecutive tokens are highly predictable given earlier context. We introduce MARS (Mask AutoRegreSsion), a lightweight fine-tuning method that teaches an instruction-tuned AR model to predict multiple tokens per forward pass. MARS adds no architectural modifications, no extra parameters, and produces a single model that can still be called exactly like the original AR model with no performance degradation. Unlike speculative decoding, which maintains a separate draft model alongside the target, or multi-head approaches such as Medusa, which attach additional prediction heads, MARS requires only continued training on existing instruction data. When generating one token per forward pass, MARS matches or exceeds the AR baseline on six standard benchmarks. When allowed to accept multiple tokens per step, it maintains baseline-level accuracy while achieving 1.5-1.7x throughput. We further develop a block-level KV caching strategy for batch inference, achieving up to 1.71x wall-clock speedup over AR with KV cache on Qwen2.5-7B. Finally, MARS supports real-time speed adjustment via confidence thresholding: under high request load, the serving system can increase throughput on the fly without swapping models or restarting, providing a practical latency-quality knob for deployment.

Ziqi Jin, Lei Wang, Ziwei Luo +1

Nanyang Technological University · Singapore Management University · Uppsala University

Multi-Token Prediction LLM Inference Acceleration Autoregressive Language Modeling Autoregressive Transformer LLM Fine-Tuning

Apr 7, 2026

Task Ecologies and the Evolution of World-Tracking Representations in Large Language Models

We study language models as evolving model organisms and ask when autoregressive next-token learning selects for world-tracking representations. For any encoding of latent world states, the Bayes-optimal next-token cross-entropy decomposes into the irreducible conditional entropy plus a Jensen--Shannon excess term. That excess vanishes if and only if the encoding preserves the training ecology's equivalence classes. This yields a precise notion of ecological veridicality for language models and identifies the minimum-complexity zero-excess solution as the quotient partition by training equivalence. We then determine when this fixed-encoding analysis applies to transformer families: frozen dense and frozen Mixture-of-Experts transformers satisfy it, in-context learning does not enlarge the model's separation set, and per-task adaptation breaks the premise. The framework predicts two characteristic failure modes: simplicity pressure preferentially removes low-gain distinctions, and training-optimal models can still incur positive excess on deployment ecologies that refine the training ecology. A conditional dynamic extension shows how inter-model selection and post-training can recover such gap distinctions under explicit heredity, variation, and selection assumptions. Exact finite-ecology checks and controlled microgpt experiments validate the static decomposition, split-merge threshold, off-ecology failure pattern, and two-ecology rescue mechanism in a regime where the relevant quantities are directly observable. The goal is not to model frontier systems at scale, but to use small language models as laboratory organisms for theory about representational selection.

Giulio Valentino Dalla Riva

Baffelan OÜ

Autoregressive Language Modeling Latent World Models

Apr 6, 2026

Exemplar Retrieval Without Overhypothesis Induction: Limits of Distributional Sequence Learning in Early Word Learning

Background: Children do not simply learn that balls are round and blocks are square. They learn that shape is the kind of feature that tends to define object categories -- a second-order generalisation known as an overhypothesis [1, 2]. What kind of learning mechanism is sufficient for this inductive leap? Methods: We trained autoregressive transformer language models (3.4M-25.6M parameters) on synthetic corpora in which shape is the stable feature dimension across categories, with eight conditions controlling for alternative explanations. Results: Across 120 pre-registered runs evaluated on a 1,040-item wug test battery, every model achieved perfect first-order exemplar retrieval (100%) while second-order generalisation to novel nouns remained at chance (50-52%), a result confirmed by equivalence testing. A feature-swap diagnostic revealed that models rely on frame-to-feature template matching rather than structured noun-to-domain-to-feature abstraction. Conclusions: These results reveal a clear limitation of autoregressive distributional sequence learning under developmental-scale training conditions.

Jon-Paul Cacioli

Independent Researcher

Child Language Acquisition Autoregressive Language Modeling

Apr 6, 2026

Phase-Associative Memory: Sequence Modeling in Complex Hilbert Space

Experiments probing natural language processing by both humans and LLMs suggest that the meaning of a semantic expression is indeterminate prior to the act of interpretation rather than being specifiable simply as the sum of its parts (i.e. compositionality). This observer-dependent act dynamically actualizes meaning under genuine contextuality more consistent with quantum logical mechanisms than with classical Boolean approaches that assume separability, motivating an approach to language modeling that utilizes a Hilbert space formalism. In this work, we introduce Phase-Associative Memory (PAM) -- a complex-valued sequence model whose state S_t \in \mathbb{C}^{d \times d} accumulates outer products of complex token embeddings retrieved through the conjugate inner product

\mathrm{Re}\langle K \mid Q\rangle / \sqrt{d}

-- and evaluate it against a structurally matched real-valued ablation. Both architectures train stably across a 5M--100M parameter sweep on WikiText-103 under identical conditions; PAM sits at higher absolute loss at every measured scale but improves more rapidly with parameter count, with power-law exponents of

-0.15

vs.\

-0.12

in loss and

-0.65

vs.\

-0.49

in perplexity that narrow the gap between the two architectures monotonically. Further investigation of complex-valued sequence modeling at larger scales could reveal that the loss plateau characteristic of real-valued state-of-the-art language models (e.g. transformers) is reachable with PAM-style architectures with an order of magnitude fewer parameters than the current frontier (

\sim

1T), implying that similar capabilities are achievable at sizes runnable on consumer-grade hardware.

Gowrav Vishwakarma, Christopher J. Agostino

Xavoc Technocrats Pvt. Ltd., https: // xavoc. com , India · NPC Worldwide, Bloomington, Indiana 47403, USA

Autoregressive Language Modeling Complex-Valued Neural Networks Associative Memory Quantum-Inspired ML Memory-Augmented Language Models

Apr 5, 2026

CAWN: Continuous Acoustic Wave Networks for Autoregressive Language Modeling

Modern Large Language Models (LLMs) rely on Transformer self-attention, which scales quadratically with sequence length. Recent linear-time alternatives, like State Space Models (SSMs), often suffer from signal degradation over extended contexts. We introduce the Continuous Acoustic Wave Network (CAWN), a fully continuous sequence-mixing architecture. Instead of discrete matrix-based attention, CAWN projects hidden states into multi-headed complex-domain phasors, achieving sequence mixing through a causal,

O(L)

Phase Accumulation mechanism. To prevent signal degradation over ultra-long contexts, we introduce a dual-gated Selective Phase Resonance mechanism incorporating Frequency-Dependent Retention, Hard-Threshold Gating via Straight-Through Estimation, and a Temporal Syntax Cache to capture short-term local dependencies. We also replace standard dense linear projections with Depth-wise Harmonic Convolutions for optimal spatial frequency mixing, augmented by Block Attention Residuals for depth-wise state routing. Scaled to a 150M-parameter model, CAWN utilizes custom Triton kernels for hardware-efficient, true-complex phase accumulation in float32. Trained via a continuous streaming loop on a 100-Billion-token corpus, the prototype is evaluated at a 5-Billion-token milestone. Empirical evaluations via a Targeted Semantic Retrieval protocol demonstrate robust vocabulary acquisition and extended explicitly learned contextual denoising. By leveraging

O(1)

state-passing via chunked prefill, the model retrieves targeted information across 2,000,000 tokens while strictly plateauing at 8.72 GB of Peak VRAM, empirically overcoming the

O(L^2)

context memory wall.

Dejan Čugalj, Aleksandar Jevremovic

Singidunum University

Long-Context Language Modeling Sequence Modeling Autoregressive Language Modeling Complex-Valued Neural Networks

Apr 4, 2026

Differences in Text Generated by Diffusion and Autoregressive Language Models

Diffusion language models (DLMs) are promising alternatives to autoregressive language models (ARMs), yet the intrinsic differences in their generated text remain underexplored. We first find empirically that off-the-shelf DLMs exhibit lower

n

-gram entropy, higher semantic coherence, and higher semantic diversity. To understand the cause, we conduct controlled experiments that decouple the effects of training objectives and decoding algorithms. Results suggest that the DLM training objective contributes to the increases in semantic coherence and semantic diversity, but has a minor influence on entropy. These differences are primarily driven by the bidirectional context; other components in the training objective, such as input masking, label masking, and the weighting function, have a much weaker influence. Further, our experiments demonstrate that the reduction in entropy stems from DLMs' decoding algorithms, particularly confidence-based remasking strategies. We provide a theoretical understanding for this entropy reduction phenomenon. Together, our work uncovers key mechanisms underlying the differences between DLMs and ARMs in text generation, and informs future design of training objectives and decoding algorithms in DLMs.

Zeyang Zhang, Chengwei Liang, Xingyan Chen +4

Shanghai Qi Zhi Institute · Institute for Interdisciplinary Information Sciences, Tsinghua University · Xiongan AI Institute

Text Generation Diffusion Language Models Diffusion Language Model Decoding Language Model Generation Evaluation Autoregressive Language Modeling

Apr 2, 2026

Invertible Query-Key Coupling Composes with Attention Mechanisms

Scaled dot-product attention forms its queries and keys as independent linear projections, so the two never interact before the dot product that scores them. We study coupled query-key dynamics, a pre-scoring transformation that evolves each token's query and key jointly through a shared invertible coupling before standard scoring. We realize it as an alternating affine map in the style of real non-volume-preserving flows: the coupling is the identity at initialization, adds a small fraction of parameters per head, and leaves the softmax and surrounding architecture unchanged. We place coupling on top of existing attention methods rather than replacing them, and ask whether that composition helps. On WikiText-103, adding coupling to Differential Attention improves on it at both 150M and 455M parameters. At 455M the gain is significant at sequence length 512 (p=0.003, six seeds), survives a Bonferroni correction and replicates on a held-out test split; it also holds across rotary-embedding training lengths 512, 1024, and 2048. The same additive direction appears when coupling is added to query-key normalization (significant at 150M) and Multi-Token Attention (directional). Matched controls attribute the gain to the joint pre-scoring coupling rather than to added capacity, and show that removing the invertibility guarantee preserves the 455M gain yet is far worse than the base method at 150M, so invertibility is what makes the coupling reliable across scales. On its own, coupling lowers perplexity at 60M and 150M (one-sided Welch tests, p<0.05) but the gain narrows with scale and is not significant at 455M. We relate the construction to the expressivity of coupling flows, use an associative-recall study to map where coupling helps and where it degrades sharp retrieval, and conclude that coupling is most useful in composition with a scoring-stage method rather than as a standalone change.

Barak Gahtan, Alex M. Bronstein

Technion – Israel Institute of Technology · ISTA – Institute of Science and Technology Austria

Invertible Neural Networks Self-Attention Autoregressive Language Modeling Transformer Attention Attention Mechanisms

Apr 1, 2026

Associative-State Universal Transformers: Sparse Retrieval Meets Structured Recurrence

We study whether a structured recurrent state can serve as a compact associative backbone for language modeling while still supporting exact retrieval. We introduce UniMatrix, a Universal Transformer style family that reuses a shared recurrent block across depth and augments it with hybrid state updates, a ROSA-style residual path, and token-conditioned embedding modulation. We evaluate these models on byte-level WikiText-2, synthetic associative recall, throughput profiling on Apple MPS, and a corrected benchmark for triple-token interactions. At small scale, UniMatrix-Core and UniMatrix-ROSA slightly outperform a parameter-matched Transformer on WikiText-2 while using many fewer parameters, reaching 5.084 and 5.083 bits-per-byte versus 5.124. The main negative result is equally important: on associative recall, the original UniMatrix family remains near chance while the Transformer reaches 25.4 percent, showing that compressed recurrent state alone is not enough for exact lookup. A retrieval-oriented follow-up, UniMatrix-Assoc, helps only marginally. By contrast, UniMatrix-SparsePointer, which adds sparse slot routing and direct pointer-logit fusion, reaches 75.6 percent on the original pilot recipe and 99.2 percent on a no-dropout follow-up while using 53.8 percent fewer parameters than the Transformer baseline. Ablations show that the gain comes from sufficient slot capacity and exact pointer-level output routing. Overall, structured recurrent state is promising and parameter-efficient, but strong long-range behavior still requires explicit sparse retrieval and better kernels.

Liu Xiao

Liu Xiao

Recurrent Transformers Autoregressive Language Modeling Associative Memory Learned Sparse Retrieval

Mar 30, 2026

Variational Neurons in Transformers for Language Modeling

Transformers for language modeling usually rely on deterministic internal computation, with uncertainty expressed mainly at the output layer. We introduce variational neurons into Transformer feed-forward computation so that uncertainty becomes part of the internal computation itself. Concretely, we replace deterministic feed-forward units with local variational units based on EVE while preserving the overall Transformer backbone. We evaluate this design in compact next-token language-modeling settings. We compare deterministic and variational variants with both predictive and probabilistic criteria. Alongside negative log-likelihood, perplexity and accuracy, we analyze calibration, conditional variance, mutual information and latent-usage statistics. The resulting picture is clear. Variational neurons integrate stably into Transformers, preserve strong predictive performance and produce informative uncertainty signals. The experiments also show that task quality, useful depth and internal stability are distinct properties. These results establish variational Transformers as a practical form of uncertainty-aware language modeling. They show that Transformers can predict with an explicit internal structure of uncertainty, which supports stronger probabilistic evaluation and a more informative analysis of model behavior.

Yves Ruffenach

Conservatoire National des Arts et Métiers Strasbourg, France

LLM Uncertainty Estimation Transformer Transformer FFNs Autoregressive Language Modeling

Mar 23, 2026

Autoregressive vs. Masked Diffusion Language Models: A Controlled Comparison

We present a controlled empirical comparison between autoregressive (AR) and masked diffusion (MDLM) language models. Both models are trained on identical data (50M tokens from TinyStories), identical compute budget (20,000 steps, batch size 32, sequence length 512), and identical hardware (NVIDIA H100 80GB), isolating the generation paradigm as the sole variable. We report three findings. First, both paradigms achieve comparable training throughput (~50K tokens/second), with MDLM requiring only 4.7% more wall-clock time. Second, AR converges faster and begins overfitting by step 14,000, while MDLM converges more slowly and is still improving at step 20,000, suggesting different compute-optimal training regimes. Third, quantitative diversity analysis over 1,000 generated samples reveals a structural diversity-fluency trade-off: AR produces fluent but repetitive outputs (99.8% begin with the same word), while MDLM generates more diverse narratives (93.4% unique 5-word openings, higher Distinct-n, lower Self-BLEU), at the cost of occasional grammatical inconsistencies. All code, trained checkpoints, and data pipelines are released for reproducibility.

Caio Vicentino

Independent Researcher

Diffusion Language Models Autoregressive Language Modeling Diffusion Language Model Benchmarking LLM Training Diffusion Language Model Training Language Model Generation Evaluation

Mar 18, 2026

Dynamic sparsity in tree-structured feed-forward layers at scale

At typical context lengths, the feed-forward MLP block accounts for a large share of a transformer's compute budget, motivating sparse alternatives to dense MLP blocks. We study sparse, tree-structured feed-forward layers as drop-in replacements for MLP blocks in deep transformer architectures, enabling conditional computation via hard hierarchical routing without a separate router network. We demonstrate for the first time that this form of tree-structured conditional sparsity can be applied for autoregressive language modeling and downstream question answering, including zero- and few-shot settings, and its scalability beyond 1B parameters. Despite activating fewer than 5% of the feed-forward block's units per token, our models match dense baselines under controlled training and fine-tuning protocols. We further analyze training dynamics and identify an emergent auto-pruning effect: the interaction of hard routing with asymmetric nonlinearities progressively deactivates unused paths, yielding partial conversion of dynamic routing into static structural sparsity. We show that simple architectural choices can modulate this behavior and recover balanced trees without auxiliary losses. Overall, our work demonstrates that tree-structured feed-forward layers provide a scalable and controllable mechanism for sparsifying large transformer models.

Reza Sedghi, Robin Schiewer, Anand Subramoney +1

CITEC, Bielefeld University, Germany · Department of Computer Science, Royal Holloway, University of London, UK

Transformer FFNs Structured Sparsity Feedforward Neural Networks Conditional Computation Neural Network Pruning Autoregressive Language Modeling

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

A Family of LLMs Liberated from Static Vocabularies

Tokenization is a central component of natural language processing in current large language models (LLMs), enabling models to convert raw text into processable units. Although learned tokenizers are widely adopted, they exhibit notable limitations, including their large, fixed vocabulary sizes and poor adaptability to new domains or languages. We present a family of models with up to 70 billion parameters based on the hierarchical autoregressive transformer (HAT) architecture. In HAT, an encoder transformer aggregates bytes into word embeddings and then feeds them to the backbone, a classical autoregressive transformer. The outputs of the backbone are then cross-attended by the decoder and converted back into bytes. We show that we can reuse available pre-trained models by converting the Llama 3.1 8B and 70B models into the HAT architecture: Llama-3.1-8B-TFree-HAT and Llama-3.1-70B-TFree-HAT are byte-level models whose encoder and decoder are trained from scratch, but where we adapt the pre-trained Llama backbone, i.e., the transformer blocks with the embedding matrix and head removed, to handle word embeddings instead of the original tokens. We also provide a 7B HAT model, Llama-TFree-HAT-Pretrained, trained entirely from scratch on nearly 4 trillion words. The HAT architecture improves text compression by reducing the number of required sequence positions and enhances robustness to intra-word variations, e.g., spelling differences. Through pre-training, as well as subsequent supervised fine-tuning and direct preference optimization in English and German, we show strong proficiency in both languages, improving on the original Llama 3.1 in most benchmarks. We release our models (including 200 pre-training checkpoints) on Hugging Face.

Aleph Alpha, :, Adnen Abdessaied +35

Aleph Alpha Research

Language Modeling Byte-Level Language Model Tokenization in Language Models Autoregressive Language Modeling Transformer Language Model Pretraining

Mar 15, 2026

M $^2$ RNN: Non-Linear RNNs with Matrix-Valued States for Scalable Language Modeling

Transformers are highly parallel but are limited to computations in the TC

^0

complexity class, excluding tasks such as entity tracking and code execution that provably require greater expressive power. Motivated by this limitation, we revisit non-linear Recurrent Neural Networks (RNNs) for language modeling and introduce Matrix-to-Matrix RNN (M

^2

RNN): an architecture with matrix-valued hidden states and expressive non-linear state transitions. We demonstrate that the language modeling performance of non-linear RNNs is limited by their state size, and show how the state size expansion mechanism enables efficient use of tensor cores. Empirically, M

^2

RNN achieves perfect state tracking generalization at sequence lengths not seen during training. These benefits also translate to large-scale language modeling. In hybrid settings that interleave recurrent layers with attention, Hybrid M

^2

RNN outperforms equivalent Gated DeltaNet hybrids by

0.4

-

0.5

perplexity points on a 7B MoE model, while using

3\times

smaller state sizes for the recurrent layers. Notably, replacing even a single recurrent layer with M

^2

RNN in an existing hybrid architecture yields accuracy gains comparable to Hybrid M

^2

RNN with minimal impact on training throughput. Further, the Hybrid Gated DeltaNet models with a single M

^2

RNN layer also achieve superior long-context generalization, outperforming state-of-the-art hybrid linear attention architectures by up to

8

points on LongBench. Together, these results establish non-linear RNN layers as a compelling building block for efficient and scalable language models.

Mayank Mishra, Shawn Tan, Ion Stoica +2

UC Berkeley · Learning Machine · MIT-IBM Watson Lab +2

Recurrent Neural Networks Language Modeling Autoregressive Language Modeling Long-Context Language Modeling

Mar 12, 2026

LPC-SM: Local Predictive Coding and Sparse Memory for Long-Context Language Modeling

Most current long-context language models still rely on attention to handle both local interaction and long-range state, which leaves relatively little room to test alternative decompositions of sequence modeling. We propose LPC-SM, a hybrid autoregressive architecture that separates local attention, persistent memory, predictive correction, and run-time control within the same block, and we use Orthogonal Novelty Transport (ONT) to govern slow-memory writes. We evaluate a 158M-parameter model in three stages spanning base language modeling, mathematical continuation, and 4096-token continuation. Removing mHC raises the Stage-A final LM loss from 12.630 to 15.127, while adaptive sparse control improves the Stage-B final LM loss from 12.137 to 10.787 relative to a matched fixed-ratio continuation. The full route remains stable at sequence length 4096, where Stage C ends with final LM loss 11.582 and improves the delayed-identifier diagnostic from 14.396 to 12.031 in key cross-entropy. Taken together, these results show that long-context autoregressive modeling can be organized around a broader division of labor than attention alone.

Keqin Xie

Independent Researcher, Suzhou, China

Long-Context Language Modeling Autoregressive Language Modeling Long-Range Dependency Modeling Memory-Augmented Language Models Persistent Memory for Language Models Predictive Coding

Mar 12, 2026

Expert Threshold Routing for Autoregressive Language Modeling with Dynamic Computation Allocation and Load Balancing

Token-choice Mixture-of-Experts (TC-MoE) routes each token to a fixed number of experts, limiting dynamic computation allocation and requiring auxiliary losses to maintain load balance. We propose Expert Threshold (ET) routing, where each expert maintains an exponential moving average (EMA) threshold estimated from the global token distribution. At both training and inference, each token is independently routed to an expert if its score exceeds the expert's threshold, enabling dynamic computation allocation while achieving load balance without auxiliary losses. This fully causal mechanism eliminates dependence on other tokens in the batch, making it well-suited for autoregressive language modeling. In pretraining experiments scaling to 2.4B parameters on FineWeb-Edu, ET achieves 0.067 lower cross-entropy loss than TC-MoE, equivalent to reaching the same performance with 1.6

\times

fewer tokens.

Hanchi Sun, Yixin Liu, Yonghui Wu +1

Computer Science and Engineering, Lehigh University, Bethlehem, PA, USA · MD-HOBI-BIOMED INFORMATICS, University of Florida, Gainesville, FL, USA

Expert Routing Mixture-of-Experts Models Sparse Mixture-of-Experts Expert Load Balancing Autoregressive Language Modeling

Mar 10, 2026

N-gram-like Language Models Predict Naturalistic Reading Time Best

Recent work has found that contemporary language models such as transformers can become so good at next-word prediction that the probabilities they calculate become worse for predicting naturalistic reading time. In this paper, we propose that this can be explained by reading time being shaped by simple n-gram statistics rather than the more complex statistics learned by state-of-the-art transformer language models. We demonstrate that the neural language models whose predictions are most correlated with n-gram probability are also those that calculate probabilities that are the most correlated with eye-tracking-based metrics of reading time on naturalistic text.

James A. Michaelov, Roger P. Levy

Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology · MIT Libraries CREOS, Massachusetts Institute of Technology

Language Modeling Autoregressive Language Modeling

Mar 9, 2026

Benchmarking Language Modeling for Lossless Compression of Full-Fidelity Audio

Autoregressive "language" models (LMs) trained on raw waveforms can be repurposed for lossless audio compression, but prior work is limited to 8-bit audio, leaving open whether such approaches work for practical settings (16/24-bit) and can compete with existing codecs. We benchmark LM-based compression on full-fidelity audio across diverse domains (music, speech, bioacoustics), sampling rates (16kHz-48kHz), and bit depths (8, 16, 24-bit). Standard sample-level tokenization becomes intractable at higher bit depths due to vocabulary size (65K for 16-bit; 16.7M for 24-bit). We propose Trilobyte, a byte-level tokenization schema for full resolution audio, improving vocabulary scaling from

O(2^{b})

to

O(1)

and enabling the first tractable 24-bit LM-based lossless compression. While LMs consistently outperform FLAC and yield state-of-the-art compression at 8-bit and 16-bit, we observe that compression gains become more modest as bit depth increases beyond 8-bit.

Phillip Long, Zachary Novack, Chris Donahue

University of California, San Diego, Computer Science and Engineering Department · Carnegie Mellon University, School of Computer Science

Lossless Data Compression Byte-Level Language Model Audio Token Compression Autoregressive Language Modeling