Single-Token Output Distributions

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3 papers in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

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Latest papers 29

Sep 30, 2026cs.LG

Distribution Matching Distillation for Continuous Diffusion Language Models

Continuous diffusion language models generate all tokens in parallel, yet high-quality generation can still require hundreds of network evaluations (NFEs). We study how distributional distillation can reduce this cost by exploiting the student's probabilistic token outputs. Our unified formulation connects the student's output parameterization to the resulting gradient estimators and yields two methods with the same student architecture and reverse-KL matching objective: Simplex-DMD uses continuous token relaxations and pathwise gradients, while Reinforce-DMD uses categorical sampling and REINFORCE with a learned density ratio. We develop both methods for multi-step generation and investigate the training and sampling choices associated with each parameterization. On OpenWebText, for sequences of 1,024 tokens, Simplex-DMD achieves a generative perplexity of 45.6 at a unigram entropy of 5.44 nats in just 4 NFEs, a 49% reduction relative to the strongest evaluated diffusion baseline at matched entropy and sampling budget. Reinforce-DMD improves the frontier at larger budgets, reaching a generative perplexity of 14.9 at an entropy of 5.00 nats with 256 NFEs, a 20% reduction under the same comparison protocol.

Paul Le Van Kiem, Dario Shariatian, Umut Simsekli +1

Inria, PSL Research University · Cohere · CMAP, Ecole Polytechnique

Diffusion Language Models Diffusion Models Dataset Distillation Distribution Matching Distillation Single-Token Output Distributions Simplex

Sep 30, 2026cs.AI

Referential Uncertainty in Human--AI Collaboration

Effective human-AI collaboration requires partners to establish references through interaction, which becomes fragile when descriptions are ambiguous, similar referents compete, or partners see different things. We study referential uncertainty - uncertainty over which candidate object a description refers to - in a collaborative puzzle task where a human Helper instructs an AI Worker to place pieces. The Worker must identify and communicate its uncertainty, and the Helper must recognize and act on it. We show that a separately elicited belief distribution over candidate pieces is better calibrated (ECE 0.15) and better discriminates correct from incorrect placements (AUROC 0.65) than raw action-token probabilities, which are severely overconfident (0.97 mean confidence, ECE 0.44). Across three frontier vision-language models (GPT-4.1, GPT-5, GPT-5.5), this elicited uncertainty rises predictably with instruction vagueness, but not with competing referents in context, even when those increase errors. The models seldom externalize it, asking for clarification on only 3.5-16.7% of turns. In a controlled human study (N=210), participants given only the Worker's default message accept 78% of wrong placements and cannot tell right from wrong (AUC 0.50). Precise descriptions and, especially, well-targeted hedges cut wrong-move acceptance to 36% while largely preserving correct-move acceptance, compensating for missing shared awareness such as not seeing the Worker's action. But this benefit depends on targeting: a deployable hedge derived from the model's own belief entropy inherits that signal's weakness and can do more harm than good. Externalized uncertainty helps a human partner only when it is accurately targeted.

Christian Poelitz, Finale Doshi-Velez, Siân Lindley

Microsoft Research, Cambridge, UK · Harvard University, Cambridge, MA, USA

Human-Ai Collaboration Human-Robot Collaboration Uncertainty Collaboration Artificial Intelligence Alignment Single-Token Output Distributions

Sep 29, 2026cs.AI

Probability is Not Enough: Exploring and Counting Divergent Tokens for Reasoning Uncertainty Quantification in LLMs

As the chain-of-thought reasoning capabilities of large language models improve, evaluating and calibrating their reasoning confidence is becoming increasingly important for quantifying the uncertainty of their answers. Current methods for estimating the confidence of large language models are generally based on probabilities of selected key tokens, but the underlying mechanism remains unclear. Our pilot study finds that replacing selected token probabilities with coarse substitutes can also improve calibration, motivating us to further explore effective signals of model confidence. We introduce Divergent Token Confidence (DTC), a framework that estimates confidence by counting tokens at which two models strongly disagree during decoding. DTC identifies these divergent tokens using the Jensen-Shannon divergence between next-token distributions evaluated along the same reasoning trajectory. We find that their count is almost negatively associated with answer accuracy, thereby serving as a simple yet effective signal for uncertainty quantification. DTC supports both white-box and black-box evaluation using auxiliary models, without explicit training and affecting the generation process. Experiments across multiple model families and six mathematical benchmarks demonstrate improved calibration over probability-based and verbalized baselines. Under white-box evaluation, the count-only estimator achieves an average expected calibration error of 13.0%, compared with 32.7%-42.4% for standard full-sequence confidence methods. In black-box settings, it also improves calibration over the original verbalized scores. For example, mean expected calibration error falls from 32.1%-40.2% to 13.7%-16.3% on DeepSeek-V3.2. These findings provide new insights for improving reasoning uncertainty quantification in large language models. The code is released at https://github.com/szu-tera/DTC.git.

Feiyang Li, Shengjing Liu, Qi Zhan +7

College of Computer Science and Software Engineering, Shenzhen University · Tsinghua University · Behavioral and Spatial AI Lab, Peking University & Tongji University

Large Language Model Uncertainty Confidence Calibration LLM Reasoning Strategies Single-Token Output Distributions Uncertainty Quantification Probability

Sep 29, 2026cs.AI

XU-RS: Explaining Credal Width in Random-Set Language Models

Uncertainty estimates tell us how unsure a model is, but not why. Without knowing which parts of an input influences a model's uncertainty, we cannot tell whether that uncertainty score depends on input features that are relevant for the task. We study this problem in randomset classifiers built using pretrained language models. These classifiers assign probability to individual answers and to groups of answers, producing lower and upper probabilities for each answer; The difference between these probabilities, called credal width, is used to represent epistemic uncertainty about an answer arising from limited training data. We propose XU-RS, a framework that attributes an answer's credal width to the input tokens (words or word pieces) supplied to a language model. XU-RS uses Expected Gradients (a standard feature attribution method) to estimate how input tokens contribute to credal width. The proposed framework is evaluated on a MedQA dataset using SmolLM3-3B and Llama-2-7B models, demonstrating that setting the embedding of a token ranked highly by XU-RS to zero (zero-masking) causes larger changes in credal width than zero-masking randomly selected tokens. In addition, we show that normalisation can cause other answer groups to influence an answer's width, reveal how token attribution can mask numerical errors, and provide diagnostic checks to verify whether a token ranked highly by XU-RS meaningfully explains model uncertainty.

David Achara, Maryam Sultana, Alexander D. Rast +1

Institute for AI, Data Analysis and Systems (AIDAS) Oxford Brookes University

Large Language Model Uncertainty Uncertainty Score Single-Token Output Distributions

Sep 15, 2026cs.LG

Divergence Timing and Cumulative Disagreement under KV-Cache Eviction

KV-cache eviction perturbs the conditional token distributions governing autoregressive generation. We investigate how first-divergence timing and subsequent token mismatch determine cumulative disagreement. We derive an exact decomposition under a specified stepwise maximal coupling: the expected mismatch fraction equals a first-mismatch contribution plus post-divergence exposure multiplied by its mismatch rate. An explicit construction over unrestricted autoregressive kernel pairs realizes the sharp interval of risks compatible with a finite divergence-aligned observation window. Residual-branch conditional Monte Carlo provides unbiased joint estimates of occurrence, occupation, and window/tail contributions, with per-replicate variance dominance for total token loss. Complete trajectories from Meta-Llama-3.1-8B-Instruct and Qwen2.5-7B-Instruct show that SnapKV at 50% retention enters divergence later and less often than SnapKV-512 or recent-token retention with the same 50% prompt-cache budget, while post-divergence total variation (TV) remains high. In an exploratory analysis of 288 documents, post-divergence exposure accounts for 85-90% of four aggregate mismatch gaps. On 288 independent documents at 90% retention, prespecified comparisons show higher branch-aligned TV in the late than in the early window in both models.

Xinyue Luo, Fei Yu

Wealth AI Lab, Ant Group

Divergence Single-Token Output Distributions Disagreement Mismatch Autoregressive Model

Sep 14, 2026stat.ML

Predictive Likelihood Ratios for Language Model Watermark Detection

Keyed watermark detection tests dependence between observed tokens and pseudorandom variables reconstructed from a secret key. Building on the pivotal framework of Li et al. (2025), we construct predictive likelihood ratios that average over uncertain probability deficits and residual-tail distributions. The aim is robust detection power across alternative specifications without requiring a single signal-strength tuning. A mixture prior combines tail shape and effective width; hierarchical extensions allow within-document variation in deficit or width. The test maximizes prior-averaged power at a fixed size, but is not generally uniformly most powerful or minimax. Under the exact conditional pivot null, normalized predictive alternatives selected before each observation yield a Bayes factor that is also a test martingale: Type I error control is unaffected by alternative misspecification and remains valid under optional stopping. This guarantee does not cover violations of the conditional null, and the interpolated implementation has no certified anytime guarantee. Gumbel marginal likelihoods are evaluated by fixed quadrature. Across the evaluated tail-shape and tail-width alternatives and three horizons, the union-tail mixture has maximum observed Type II error regret .0080, compared with .0962 for the equal-tail mixture, relative to the best tested rule. On temperature-matched outputs from two open models, it improves AUC over the equal-tail baseline in all eight non-saturated model-temperature cells, although the leading reference score generally has higher AUC. Supplementary experiments show retained power under independent null-like replacement and smaller changes from hierarchical dependence modeling. The evidence supports robustness across the evaluated alternatives, not uniform power guarantees or resistance to arbitrary text edits.

Li Ma

Department of Statistics and Data Science Institute, University of Chicago

Large Language Model Watermarks Two-Sample Testing Tamper Localization Machine-Generated Text Detection Single-Token Output Distributions Long-Tailed Distribution

Sep 7, 2026cs.AI

Train What You Deploy:Token-Faithful Post-Training of a Production Coding

Existing post-training pipelines for coding and terminal agents suffer severe token and control fidelity errors: simplified training environments mismatch production deployments, and offline token reconstruction from agent logs distorts original prompts and conflates policy calls with background model operations. We present a fidelity-aware training coupling framework that retains trainer-side sampling over original prompts, eliminates spurious model calls via a negotiated training protocol, and restricts loss computation to verifiable token spans with closed-failure guarantees. We further propose Certified Divergence Proximal Policy Optimization (C-DPPO), which establishes tight two-sided TV certification bounds, adaptive-K rules, budget-aware sequence guarantees, and error-robust policy masking atop standard DPPO. Evaluated on matched Baize5B and Baize10B models with identical training and test protocols on TMax-100, C-DPPO yields a consistent +3.0-point performance gain over standard DPPO across model scales. Certificate audits validate the reliability and full operational coverage of our certified training pipeline.

Cheng Li, Jiexiong Liu, Yixuan Chen +1

KunlunMeta

Post-Training Single-Token Output Distributions Proximal Policy Optimization Transport Token Budget Allocation

Aug 10, 2026cs.AI

Privileged Likelihood Is Not Automatically Value: Three Checks for Token Credit in On-Policy Self-Distillation

Outcome verifiers score completed reasoning traces but do not assign credit to intermediate tokens. Privileged self-distillation attempts to fill this gap by rescoring a model's own rollout with training-only information. A token likelihood change, however, is not automatically outcome credit. We separate three questions: whether the score tracks better actions, whether feedback construction changes what is compared, and what behavior the training loss reinforces. We establish these distinctions formally. When a rollout is scored using hindsight feedback written about that same rollout, its content determines both the tokens and the scoring context, creating direct self-dependence. Using feedback from another rollout of the same problem removes this dependence but does not guarantee a useful score. In matched experiments with a 20B model on AIME 2025, the implemented additive score is near chance (AUC=0.505) and slightly favors incorrect traces after length adjustment. In the paired comparison, the outcome-only control records 64.2%, versus 24.2%--33.9% for five token-score variants. The results motivate validating score meaning, feedback construction, and training behavior separately before calling a likelihood signal credit.

Xuan-Phi Nguyen, Shrey Pandit, Yiran Zhao +3

Salesforce AI Research

Credit Assignment Single-Token Output Distributions Hindsight Value

Aug 7, 2026cs.LG

Stochastic Autoregressive Learning

Motivated by LLMs, which generate outputs by iteratively sampling from next-token distributions, we introduce a PAC-learning model for binary stochastic autoregressive learning. This generalizes the deterministic autoregressive learning framework of Joshi et al., COLT 2025. In our model, one fixed generator assigns a Bernoulli next-token distribution to every prompt string. Starting from an input prompt, a token is sampled and appended to the prompt; the same generator is then applied again to this expanded prompt; this procedure is repeated for

M

steps. Three forms of supervision are considered: base one-step samples, chain-of-thought (CoT) samples that reveal full random trajectories of length

M

, and end-to-end (e2e) samples that reveal only the final token of length

M

trajectories. For a generator class, we study the minimum number of samples

m_{base}(\varepsilon),m_{CoT}(\varepsilon), m_{e2e}(\varepsilon)

, resp., required to learn the one-step probabilities in the base model, and the final-token probability in the CoT and e2e models, under squared loss error~

\varepsilon

. We show that stochastic autoregressive learning fundamentally differs from the deterministic theory. At scale

\varepsilon

, there is no universal comparison between the three learning tasks: both

m_{CoT}/m_{base}

and

m_{e2e}/m_{CoT}

can be made simultaneously arbitrarily larger than

M/\varepsilon

, the natural analogue for the existing deterministic results. Nevertheless, after altering scales, for every class, CoT learning at scale

\varepsilon

is upper-bounded by base learning at scale

\varepsilon/M^2

, whereas e2e learning at scale

\varepsilon

is upper-bounded, up to logarithmic factors, by

(M/\varepsilon) m_{CoT}(Θ(\varepsilon))

. These dependencies and scales are essentially tight. We complement these bounds by studying dimension

d

logistic functions in our model.

Ilan Doron-Arad, Idan Mehalel, Elchanan Mossel

1MIT · 2The Hebrew University

Autoregressive Model Single-Token Output Distributions

Jul 25, 2026cs.LG

Guarantees on Dynamical System Distinguishability for LLM Token Generation

Recent work has shown that classifying large language models (LLMs)' responses can be distinguished by modeling token embeddings as trajectories of a black-box dynamical system (DS) and comparing prediction residuals of two DSs. Despite the empirical success of this dynamical approach, a theoretical understanding of why it works, how well it scales as a function of the token sequence, and when it transfers across embedding models remains lacking. We address these questions by formalizing the classification task as a binary hypothesis test between two stochastic linear DSs. We show that the total variation distance between the stationary marginal distributions of the two DSs can be arbitrarily small even when the dynamics differ substantially, which provides a fundamental accuracy floor for any classifier that ignores token dynamics. We then show that the misclassification probability of DS-based classification decays exponentially in the sequence length

L

, with the decay governed by a dynamical discriminability quantity

δ^2

that captures the spectral distance between the two DSs. We also characterize cross-embedding generalization by introducing an approximate intertwining condition between embedding models and establishing a lower bound on the transferable discriminability in terms of the intertwining map's smallest singular value. Together, these results explain the empirical performance of DS-based classification and motivate further investigation into using DS theory to analyze AI systems, in contrast to the more common approach of using AI to model dynamical systems.

Mohamed Akrout, Dan Wilson

Department of Electrical Engineering and Computer Science University of Tennessee, Knoxville, TN, USA

Single-Token Output Distributions Dynamical Systems

Jul 13, 2026cs.CL

Production and Perception in LLMs: A Token Probability Approach

The asymmetry between language production and perception has been well-documented in psycholinguistics. Whether large language models (LLMs) exhibit a functionally analogous distinction remains an open question, particularly given that LLMs rely on the same underlying mechanism (next-token prediction) for both input and output processing. In this exploratory study, we operationalize the production-perception distinction through direct token probability measurements rather than metalinguistic prompting. Using the base Llama-3.1-8B model, we generated poems under a production prompt and re-scored the same tokens under both rephrased production prompts and perception-oriented prompts. Across an extended experiment with four production and three perception prompts, production-perception distances consistently and substantially exceeded production-production distances, with non-overlapping ranges across conditions and an overall average ratio of approximately 1.8. Near-ceiling correlations in the production-production control confirm that the effect is specific to communicative framing rather than prompt surface variation, and we show the effect replicates across five open-weight models (Llama-3.1-8B, EuroLLM-9B, gemma-2-9b-it, Mistral-7B-Instruct-v0.3, and Qwen2.5-7B-Instruct), spanning both base and instruction-tuned variants. Temporal analysis revealed that the perception prompt exerts its strongest influence at the beginning of the sequence, with divergence decaying as generated context accumulates, though the specific shape of this decay varies across prompt pairs. These findings suggest that prompt framing alone induces a production-perception distinction in LLM probability distributions, even within a decoder-only architecture.

Anna Marklová, Jiří Milička, Martina Vokáčová +1

Faculty of Arts, Charles University, Prague · Faculty of Mathematics and Physics, Charles University, Prague

Single-Token Output Distributions Linguistics Perceptually Token-Level Uncertainty Perception Probability

Jul 11, 2026cs.CR

One Token Is Enough: Fingerprinting and Verifying Large Language Models from Single-Token Output Distributions

Large language models (LLMs) are increasingly consumed through opaque serving chains - API aggregators, resellers, and inference providers - in which the client has no technical means to confirm that the model answering is the model advertised, and recent audits show that a substantial fraction of commercial endpoints deviate from the vendor's reference weights. Existing identification techniques require long generated texts, token-level log-probabilities, adversarially crafted prompts, or the model owner's cooperation. We show that far weaker evidence suffices. We define a behavioral fingerprint of an LLM as the empirical distribution of its answers to trivial one-word prompts - "name a random number between 1 and 100" - collected across four languages at a cost of one output token per query. Measuring 165 models served via a large commercial aggregator (OpenRouter), we find that (i) these distributions are highly non-uniform (median cell entropy 1.0 bit) and model-specific: split halves of the same model's samples lie an order of magnitude closer than samples of different models; (ii) Jensen-Shannon divergence between fingerprints recovers model lineage, assigning a model to its documented family with 59.5% leave-one-out accuracy against an 18.4% chance rate; and (iii) a biometric-style verification protocol achieves a 7.3% equal error rate with the full 40-cell battery, and below 11% with eight probe cells - roughly a hundred single-token queries per audit. We further report ecosystem anomalies, including a proprietary-branded flagship endpoint distributionally indistinguishable from an open-weight Qwen model. The protocol, prompts, raw data, and analysis code are released for reproduction and operational use.

Tomas Bruckner

Faculty of Informatics and Statistics, Prague University of Economics and Business, Prague, Czech Republic

Single-Token Output Distributions Fingerprint Lineages

Jul 5, 2026cs.CL

Telescope: Improving Zero Shot Detection of LLM Generated Content By Measuring Token Repetition Probability

Distinguishing Large Language Model (LLM) generated text from human writing is a critical and difficult challenge. While LLMs are trained to write like humans, we hypothesize that this training leaves an indelible mark. LLMs develop a particularly strong aversion to token repetition very early in training. This bias persists as a ''Vestigial Heuristic'' (a developmental artifact) that is activated in LLM-generated text, separating LLM from human writing. To probe this phenomenon, we introduce Telescope Perplexity, a metric that evaluates the token repetition of the model,

P(s_i | s_{1:i})

. Our empirical investigation reveals that the Telescope Perplexity signature emerges early in pre-training, and Telescope Perplexity empirically enables highly effective zero-shot LLM detection. We show state-of-the-art or competitive performance across diverse datasets (including modern evaluation sets we introduce), reference models, and perturbation schemes with greater efficiency than other methods.

Christopher Nassif, Josh F. Cooper

Virginia Tech Department of Electrical and Computer Engineering · Virginia Tech Department of Industrial and Systems Engineering

Machine-Generated Text Detection Single-Token Output Distributions Repetition Canada-France-Hawaii Telescope Data

Jun 23, 2026cs.CL

Sentence-Level Contextual Entrainment in Large Language Models

Contextual entrainment, which is a newly discovered phenomenon in large language models (LLMs), refers to the tendency of a model to assign higher probabilities to tokens that appear in its context. In this work, we extend this phenomenon from the token level to the sentence level by examining the per-token mean log-probability of a sentence instead of the probabilities of individual tokens. We investigate sentence-level contextual entrainment across 26 LLMs from seven families and two datasets, which cover both subjective and objective tasks. We find that sentence-level contextual entrainment exists. This means that the sentences in the prompt (even if they are counterfactual statements) can significantly increase their probability during model inference time. As the model size increases, contextual entrainment gradually decreases. We also find that contextual entrainment is controlled by 2% to 4% of the attention heads. Turning off these attention heads can effectively mitigate contextual entrainment without hurting the model's performance.

Yang Liu, Chenhui Chu

Kyoto University

Single-Token Output Distributions

Jun 22, 2026cs.CL

WaveDetect: Robust Framework for Machine-Generated Text Detection via Wavelet Transform

As Large Language Models asymptotically approach human-level fluency in natural language generation, solely relying on surface-level semantic artifacts for detecting LLM-generated texts has become increasingly precarious. Existing detectors often falter when facing three critical challenges: adversarial perturbations, cross-domain shifts, and the rapid temporal evolution of the foundation model. To address these issues, we propose \wavedetect, a novel framework that reformulates text detection as a signal processing task within the time-frequency domain. Unlike previous methods that analyze static token probability distributions, \wavedetect models the generated output as a probability signal, upon which a differentiable Continuous Wavelet Transform is applied to convert them into learnable spectral representations. This process reveals the intrinsic ``spectral fingerprints'' in machine-generated texts--patterns that remain invisible in time domain. Comprehensive evaluations on three well-curated datasets (RAID, EvoBench, and Domain-Shift) show that our method achieves a new state-of-the-art. It not only achieves superior accuracy but also exhibits remarkable robustness against sophisticated attacks, generalization across out-of-distribution topics and unseen evolving LLMs. Our results validate the efficacy of spectral analysis as a promising paradigm for LLM-generated texts detection.

Zhichen Liu, Kaitong Qin, Linhan He +1

Dept. of Computer Science and Engineering, Southern University of Science and Technology

Machine-Generated Text Detection Attacker Large Language Model Single-Token Output Distributions Wavelets Graph Signal Processing

Jun 7, 2026cs.CL

Hacking Generative Perplexity: Why Unconditional Text Evaluation Needs Distributional Metrics

Diffusion and continuous flow-based language models have emerged as the leading non-autoregressive alternatives to language modeling. Progress in both paradigms is overwhelmingly tracked by generative perplexity (gen-PPL): the per-token negative log-likelihood of samples under a frozen autoregressive (AR) scorer such as gpt2-large, typically paired with an empirical-entropy guardrail to rule out low-entropy collapse. We argue that this metric is unsound. By construction, gen-PPL measures only predictability under the scoring AR, not grammaticality or semantic coherence -- and the set of predictable but still low-quality sequences is combinatorially large. To make this concrete, we construct a suite of zero-parameter, deliberately naive samplers that achieve state-of-the-art gen-PPL on LM1B and OpenWebText at non-degenerate entropy, surpassing recently published diffusion and continuous-flow models while producing text that is incoherent by construction. We recommend evaluation suites that directly quantify the distributional divergence between generated and reference text, and use such a suite to re-benchmark recent non-autoregressive models, recovering a more faithful picture of the current state of the art.

Antonio Franca, Alexander Tong

AITHYRA Institute, Vienna, Austria.

Language Model Perplexity Single-Token Output Distributions Autoregressive Model

May 29, 2026cs.LG

ARCA: Adapter-Residual Credit Assignment When Token Signals Degenerate

Token-level credit assignment for language-model reinforcement learning is usually formulated as if the policy were fully trainable, while practical LLM-RL pipelines often rely on parameter-efficient fine-tuning, especially LoRA. We argue that this separation hides a structural failure mode. Under LoRA, the policy is restricted to a low-rank neighborhood of the reference model, so the per-token output-distribution differences used by common intrinsic credit signals, surprisal, entropy reduction, and policy divergence, can become degenerate after within-trajectory normalization, either approaching uniform weights or concentrating on a small set of task-agnostic positions. We formalize this behavior and propose measuring it directly with concentration diagnostics such as weight Gini and effective-token ratio. We then introduce \emph{Adapter-Residual Credit Assignment} (ARCA), a lightweight alternative that derives token salience from the adapter's own hidden-state residual,

\|h^{\text{adapted}}_t - h^{\text{base}}_t\|_2

. ARCA asks where the adapter actually changes the model, rather than where the output distribution appears uncertain or shifted, and requires no learned reward model, value head, or tree construction. In a compact MATH/Qwen3-1.7B GRPO sweep, ARCA exhibits the predicted non-degenerate middle-regime credit distribution under matched rollout budgets and remains competitive with rank-matched baselines.

Rodney Lafuente-Mercado

Scale AI

Credit Assignment Large Language Model Reinforcement Learning Single-Token Output Distributions Autoregressive Language Models Divergence

May 27, 2026cs.CL

The Fragility of Chain-of-Thought Monitoring Across Typologically Diverse Languages

Chain-of-thought (CoT) monitoring has been proposed as a promising safety mechanism for detecting misaligned behavior in large language models. However, its reliability remains largely unexplored beyond English and across diverse model families. We present the first large-scale evaluation of CoT monitorability across 13 diverse languages and seven frontier model families, comprising 16 models. Using adversarial-hint evaluations that require explicit intermediate computation, together with analysis of internal answer-token probabilities, we consistently find CoT unfaithfulness across languages and hint types, with an average rate of 95.9% across 8B--120B parameter models. We find that frontier models systematically exhibit strategic manipulation, including answer-switching, post-hoc rationalization, and procedural exploitation of hints, making their reasoning difficult to reliably monitor. These deceptive patterns remain especially pronounced in low-resource languages, revealing fundamental limitations in current CoT-based oversight. Our results show that CoT monitoring is fragile under linguistic distribution shift, providing a substantially weaker safety signal than English-only studies suggest. These findings motivate the development of more robust CoT monitors and complementary white-box monitoring techniques, particularly for mid- and low-resource languages. Our code is available \href{https://multilingual-cot-monitoring.github.io/}{\textcolor{blue}{here}}.

Eric Onyame, Runtao Zhou, Kowshik Thopalli +2

University of Virginia · Lawrence Livermore National Laboratory

Chain-of-Thought Reasoning Single-Token Output Distributions Language Pairs Adversarial Evaluation Fragility

May 25, 2026cs.CL

Cultural Value Alignment Via Latent Activation Steering in Large Language Models

Large Language Models (LLMs) often exhibit homogenized cultural perspectives. While the World Values Survey (WVS) provides a gold standard for mapping human values, traditional direct prompting of LLMs on WVS often fails to access the model's latent cultural depth, leading to safety-aligned refusals or neutral responses. Here, we propose a generalizable framework for cultural evaluation and intervention that transitions from abstract queries to scenario-based behavioral probing. By extracting implicit token probabilities across 300 situational dilemmas, we bypass surface-level alignment to map the latent coordinates of LLMs cultural value. We further introduce activation steering to shift these internal alignments during the forward pass without retraining. Across multiple LLMs, we find substantial variation in adaptability and uncover a consistent phenomenon of latent entanglement, where interventions along one cultural dimension induce shifts along another. These results suggest that cultural values are encoded as coupled structures, limiting precise alignment. This work establishes a computationally efficient framework for cultural steering, highlighting the structural complexities when navigating global value with LLMs.

Trung Duc Anh Dang, Sarah Masud

University of Copenhagen

Cultural Evolution Large Language Model Alignment Single-Token Output Distributions

May 20, 2026cs.LG

X-Token: Projection-Guided Cross-Tokenizer Knowledge Distillation

Cross-tokenizer knowledge distillation allows a student model to learn from teachers with incompatible vocabularies. Prior work operates on hidden states or logits; the latter is preferred as a drop-in replacement requiring no auxiliary components. Logit-based methods either use only the correct-token probability, missing the full 'dark knowledge' in the teacher's distribution, or operate on the full output distribution, relying on strict token partitioning and/or unprincipled heuristic ranking. We identify two key shortcomings of full-distribution, logit-based methods: (i) an uncommon-token failure, where critical tokens fall into the unmatched subset (e.g., Llama's 1100 multi-digit numerals under digit-splitting Qwen supervision) and are suppressed during training, reducing GSM8k from 12.89 to 2.56 compared to same-tokenizer KD from a weaker teacher; and (ii) over-conservative matching, where strict 1-to-1 matching excludes near-equivalent tokens across surface forms. These failures require distinct remedies: eliminating the partition when critical tokens are misaligned, and refining it when alignment is reliable. We propose X-Token, an approach with two complementary loss formulations targeting these issues. P-KL removes partitioning and aligns the student's distribution with the teacher's via a sparse projection matrix W (initialized from tokenizer-level string rules) to address the uncommon-token failure. H-KL retains the hybrid form while relaxing matching to align each student token with its top-ranked teacher mapping under W. Both objectives share W and extend naturally to multiple teachers. Empirically, on Llama-3.2-1B, X-Token outperforms the current state of the art GOLD by +3.82 average points with a Qwen3-4B teacher and by +0.5 with a Phi-4-Mini teacher. Further, a two-teacher setup (Phi-4-mini + Llama-3B) improves over single-teacher distillation by +1.3 points.

Sharath Turuvekere Sreenivas, Adithyakrishna Venkatesh Hanasoge, Mingyu Yang +4

Teacher-Student Distillation Single-Token Output Distributions Teacher Implicit Association Test

May 19, 2026cs.DC

GEM: GPU-Variability-Aware Expert to GPU Mapping for MoE Systems

Mixture-of-Expert (MoE) models enable efficient inference by employing smaller experts and activating only a subset of them per token. MoE serving engines distribute experts across multiple GPUs and route tokens to appropriate GPUs at inference time based on experts activated. They process tokens in lock-step fashion, where tokens within a batch must finish processing before proceeding to the next layer. This synchronization barrier acts as a critical bottleneck because the performance of MoE models is limited by the straggler GPU that finishes last. Stragglers emerge when too many heavily used experts are placed on the same GPU or the slowest GPU. While prior works place experts that balance token loads across GPUs, they all overlook GPU variability and often place highly used experts on the slowest GPUs. We propose GEM, GPU-variability-aware Expert Mapping, a framework for GPU variability-aware expert to GPU mapping for MoE models. GEM exploits two insights. First, we must place experts such that each GPU receives non-uniform token loads based on their variability and they all finish processing a layer at about the same time. Our studies show that there are two types of experts: consistent that are used most of the time and temporal that are often used together for the remaining time. Our second insight is that we must place simultaneously used consistent and temporal experts on different GPUs and avoid placing them on slower GPUs to reduce slowdown. GEM gathers the variability profile of GPUs for each model and task and uses the token load distributions per task to map experts to GPUs. Our experiments show that GEM improves end-to-end latency by 7.9% on average and by up to 16.5% compared to the baseline.

Sourish Wawdhane, Avinash Kumar, Poulami Das

The University of Texas at Austin

Mixture-Of-Expert Inference Mixture-Of-Experts Cpu-Gpu Hybrid Designs Graphics Processing Unit Resources Inference-Time Single-Token Output Distributions

May 6, 2026cs.CV

Computer-Aided Design Generation by Cascaded Discrete Diffusion Model

Recent deep learning approaches seek to automate CAD creation by representing a model as a sequence of discrete commands and parameters, and then generating them using autoregressive models or continuous diffusion operating in Euclidean embedding space. However, continuous diffusion perturbs representations in a continuous Euclidean domain that does not reflect the inherently discrete and heterogeneous nature of CAD tokens, often producing perturbed representations that map to semantically invalid symbols. To overcome this limitation, we propose a cascaded discrete diffusion framework for CAD generation, which consists of a command diffusion for generating CAD commands and a parameter diffusion conditioned on CAD commands. Unlike isotropic Gaussian perturbation, the forward process of our approach operates directly over categorical token distributions using delicate transition matrices. For commands, we adopt an absorbing-state transition matrix that progressively corrupts tokens to a designated symbol; for parameters, we introduce specific transition matrices tailored to heterogeneous attributes: a Gaussian kernel for coordinate continuity, a scale-invariant kernel for dimensional values, and a prior-preserving kernel for boolean attributes. The reverse process is achieved by two denoising networks: a Transformer-based encoder for command recovery, and a parameter network with extra local self-attention for command-level interaction and cross-attention for conditional injection. Experiments on the DeepCAD dataset show that the proposed approach surpasses existing autoregressive and continuous diffusion models on unconditional generation metrics, while qualitative results validate effective controllability in conditional generation tasks. Source codes will be released.

Honghu Pan, Xiaoling Luo, Yongyong Chen +2

School of Artificial Intelligence and Robotics, Hunan University · College of Computer Science and Software Engineer, Shenzhen University · School of Computer Science and Technology, Harbin Institute of Technology, Shenzhen +1

Diffusion Models Diffusion Dynamics Single-Token Output Distributions Deep Learning

May 6, 2026cs.LG

A geometric relation of the error introduced by sampling a language model's output distribution to its internal state

GPT-style language models are sensitive to single-token changes at generation points where the predicted probability distribution is spread across multiple tokens. Viewing this sensitivity as a geometric property, we derive an

\mathfrak{so}(n)

-valued 1-form that depends only on the geometry of the token embeddings. Despite this purely geometric origin, we show that its curvature is semantically meaningful: On chess reasoning tasks, the curvature couples to the world model of an off-the-shelf instruction-tuned model, with transformations clustering by board region and respecting piece importance. Our findings suggest that token space geometry directly reflects how models internally represent problems.

Albert F. Modenbach

Department of Mathematics, King’s College London, United Kingdom.

Single-Token Output Distributions Chess Distributions

May 1, 2026cs.CL

Prompt-Induced Score Variance in Zero-Shot Binary Vision-Language Safety Classification

Single-prompt first-token probabilities from zero-shot vision-language model (VLM) safety classifiers are treated as decision scores, but we show they are unreliable under semantically equivalent prompt reformulation: even when the binary label is constrained to a fixed output position, equivalent prompts can induce materially different unsafe probabilities for the same sample. Across multimodal safety benchmarks and multiple VLM families, cross-prompt variance is strongly associated with prompt-level disagreement and higher error, making it a useful fragility diagnostic. A training-free mean ensemble improves NLL on all 14 dataset-model evaluation pairs and ECE on 12/14 relative to a train-selected single-prompt baseline, and wins more head-to-head NLL comparisons than labeled temperature scaling, Platt scaling, and isotonic regression applied to the same prompt. Ranking gains are consistent against the train-selected baseline on both AUROC and AUPRC, and against the full 15-prompt distribution remain consistent on AUPRC while softening on AUROC. Labeled calibration on top of the mean provides further gains when labels are available, identifying prompt averaging as a strong label-free first stage rather than a replacement for calibration. We frame this as a reliability stress test for zero-shot VLM first-token safety scores and recommend prompt-family evaluation with mean aggregation as a standard label-free reliability baseline.

Charles Weng, Dingwen Li, Alexander Martin

Johns Hopkins University · Independent

Large Language Model Safety Zero-Shot Robustness Safety Alignment Single-Token Output Distributions Variance

Apr 24, 2026cs.LG

Reward Models Are Secretly Value Functions: Temporally Coherent Reward Modeling

Reward models in RLHF are trained to score only the final token of a response - a choice that discards rich signal from every intermediate position and produces models whose token-level outputs are noise. We argue this is a missed opportunity: a well-trained reward model's output at any token should represent the conditional expectation of the final reward given the response so far. We introduce Temporally Coherent Reward Modeling (TCRM), which induces this property via two regularization terms on top of the standard Bradley-Terry loss, with minimizers provably equal to conditional expectations. The regularizers correspond to Monte Carlo and TD value-learning objectives, establishing a direct connection to RL value functions. TCRM requires zero changes to architecture, data, or inference, yet unlocks three capabilities from one principle: interpretable token-level reward trajectories (middle-token pairwise accuracy improved from 50% to 88.9%, final-token accuracy preserved); state-of-the-art PRM performance on ProcessBench (44.9% average F1) among models trained only on outcome data; and unified reward/value modeling in PPO, reducing peak GPU memory by 27% and step time by 19% with matching LLM quality.

Alex Nikulkov

AI at Meta

Single-Token Output Distributions Value Functions

Apr 17, 2026cs.CL

Stochasticity in Tokenisation Improves Robustness

The widespread adoption of large language models (LLMs) has increased concerns about their robustness. Vulnerabilities in perturbations of tokenisation of the input indicate that models trained with a deterministic canonical tokenisation can be brittle to adversarial attacks. Recent studies suggest that stochastic tokenisation can deliver internal representations that are less sensitive to perturbations. In this paper, we analyse how stochastic tokenisations affect robustness to adversarial attacks and random perturbations. We systematically study this over a range of learning regimes (pre-training, supervised fine-tuning, and in-context learning), data sets, and model architectures. We show that pre-training and fine-tuning with uniformly sampled stochastic tokenisations improve robustness to random and adversarial perturbations. Evaluating on uniformly sampled non-canonical tokenisations reduces the accuracy of a canonically trained Llama-1b model by 29.8%. We find that training with stochastic tokenisation preserves accuracy without increasing inference cost.

Sophie Steger, Rui Li, Sofiane Ennadir +4

Institute of Signal Processing and Speech Communication, Graz University of Technology, Graz, Austria · ELLIS Institute Finland & Aalto University, Espoo, Finland · King AI Labs, Microsoft Gaming +2

Single-Token Output Distributions Stochastic

Mar 19, 2026cs.CL

The Truncation Blind Spot: How Decoding Strategies Systematically Exclude Human-Like Token Choices

Why does machine-generated text remain detectable? We investigate a mechanistic explanation at the decoding stage: standard strategies such as top-

k

and nucleus sampling restrict generation to high-probability tokens, while human writers routinely choose contextually appropriate words from deeper in the model's probability distribution. Truncation makes a measurable share of these choices unreachable; we call this the \emph{truncation blind spot}. Across five open models and three domains, 8--18% of human-selected tokens fall outside common truncation boundaries. Linguistic analysis further reveals disproportionate exclusion of content-word tokens. In a benchmark comprising 1.8 million machine generations, classifiers using only predictability and lexical diversity achieve mean AUC-ROC near 0.97, with substantial variation across decoding settings and strong transfer across generators. Probability-floor samplers substantially narrow the blind spot, demonstrating that the choice of truncation criterion matters for retaining human-used tokens. Together, these findings characterize a source of human--machine distributional mismatch and motivate decoding methods that preserve contextually appropriate low-probability choices while maintaining generation quality. Code and data are available at https://github.com/EstebanGarces/human_vs_machine.

Esteban Garces Arias, Nurzhan Sapargali, Christian Heumann +1

Department of Statistics, LMU Munich · Munich Center for Machine Learning (MCML)

Machine-Generated Text Detection Single-Token Output Distributions Truncation Decoding Blind Spots Diversity

Mar 9, 2026cs.CV

Evaluating Generative Models via One-Dimensional Code Distributions

Most evaluations of generative models rely on feature-distribution metrics such as FID, which operate on continuous recognition features that are explicitly trained to be invariant to appearance variations, and thus discard cues critical for perceptual quality. We instead evaluate models in the space of discrete visual tokens, where modern 1D image tokenizers compactly encode both semantic and perceptual information and quality manifests as predictable token statistics. We introduce Codebook Histogram Distance (CHD), a training-free distribution metric in token space, and Code Mixture Model Score (CMMS), a no-reference quality metric learned from synthetic degradations of token sequences. To stress-test metrics under broad distribution shifts, we further propose VisForm, a benchmark of 210K images spanning 62 visual forms and 12 generative models with expert annotations. Across AGIQA, HPDv2/3, and VisForm, our token-based metrics achieve state-of-the-art correlation with human judgments. We will release all code and datasets to facilitate future research, with the code publicly available at https://github.com/zexiJia/1d-Distance.

Zexi Jia, Pengcheng Luo, Yijia Zhong +2

WeChat AI, Tencent Inc., China · School of Intelligence Science and Technology, Peking University · College of Computer Science and Artificial Intelligence, Fudan University

Generative Models Long Visual-Token Sequences Single-Token Output Distributions Token-Level Uncertainty Mixture Models

Dec 14, 2024cs.CL

Tokens, the oft-overlooked appetizer: Large language models, the distributional hypothesis, and meaning

Tokenization is a necessary component within the current architecture of many language mod-els, including the transformer-based large language models (LLMs) of Generative AI, yet its impact on the model's cognition is often overlooked. We argue that LLMs demonstrate that the Distributional Hypothesis (DH) is sufficient for reasonably human-like language performance (particularly with respect to inferential lexical competence), and that the emergence of human-meaningful linguistic units among tokens and current structural constraints motivate changes to existing, linguistically-agnostic tokenization techniques, particularly with respect to their roles as (1) vehicles for conveying salient distributional patterns from human language to the model and as (2) semantic primitives. We explore tokenizations from a BPE tokenizer; extant model vocabularies obtained from Hugging Face and tiktoken; and the information in exemplar token vectors as they move through the layers of a RoBERTa (large) model. Besides creating suboptimal semantic building blocks and obscuring the model's access to the necessary distributional patterns, we describe how tokens and pretraining can act as a backdoor for bias and other unwanted content, which current alignment practices may not remediate. Additionally, we relay evidence that the tokenization algorithm's objective function impacts the LLM's cognition, despite being arguably meaningfully insulated from the main system intelligence. Finally, we discuss implications for architectural choices, meaning construction, the primacy of language for thought, and LLM cognition. [First uploaded to arXiv in December, 2024.]

Julia Witte Zimmerman, Denis Hudon, Kathryn Cramer +9

Computational Story Lab, Vermont Complex Systems Institute, University of Vermont, Burlington, VT 05405, USA · Vermont Complex Systems Institute, University of Vermont, Burlington, VT 05405, USA · Department of Computer Science, St. Michael’s College, Colchester, VT 05439, USA +3

Single-Token Output Distributions Distributional Information Transformer Architectures Generative Artificial Intelligence