Daily Papers

Reasoning distillation has emerged as an efficient and powerful paradigm for enhancing the reasoning capabilities of large language models. However, reasoning distillation may inadvertently cause benchmark contamination, where evaluation data included in distillation datasets can inflate performance metrics of distilled models. In this work, we formally define the task of distillation data detection, which is uniquely challenging due to the partial availability of distillation data. Then, we propose a novel and effective method Token Probability Deviation (TBD), which leverages the probability patterns of the generated output tokens. Our method is motivated by the analysis that distilled models tend to generate near-deterministic tokens for seen questions, while producing more low-probability tokens for unseen questions. Our key idea behind TBD is to quantify how far the generated tokens' probabilities deviate from a high reference probability. In effect, our method achieves competitive detection performance by producing lower scores for seen questions than for unseen questions. Extensive experiments demonstrate the effectiveness of our method, achieving an AUC of 0.918 and a TPR@1% FPR of 0.470 on the S1 dataset.

As the probability (and thus perplexity) of a text is calculated based on the product of the probabilities of individual tokens, it may happen that one unlikely token significantly reduces the probability (i.e., increase the perplexity) of some otherwise highly probable input, while potentially representing a simple typographical error. Also, given that perplexity is a scalar value that refers to the entire input, information about the probability distribution within it is lost in the calculation (a relatively good text that has one unlikely token and another text in which each token is equally likely they can have the same perplexity value), especially for longer texts. As an alternative to scalar perplexity this research proposes a simple algorithm used to calculate vector values based on n-gram perplexities within the input. Such representations consider the previously mentioned aspects, and instead of a unique value, the relative perplexity of each text token is calculated, and these values are combined into a single vector representing the input.

Reinforcement Learning (RL) has significantly improved large language model reasoning, but existing RL fine-tuning methods rely heavily on heuristic techniques such as entropy regularization and reweighting to maintain stability. In practice, they often experience late-stage performance collapse, leading to degraded reasoning quality and unstable training. We derive that the magnitude of token-wise policy gradients in RL is negatively correlated with token probability and local policy entropy. Building on this result, we prove that training instability is driven by a tiny fraction of tokens, approximately 0.01\%, which we term spurious tokens. When such tokens appear in correct responses, they contribute little to the reasoning outcome but inherit the full sequence-level reward, leading to abnormally amplified gradient updates. Motivated by this observation, we propose Spurious-Token-Aware Policy Optimization (STAPO) for large-scale model refining, which selectively masks such updates and renormalizes the loss over valid tokens. Across six mathematical reasoning benchmarks using Qwen 1.7B, 8B, and 14B base models, STAPO consistently demonstrates superior entropy stability and achieves an average performance improvement of 7.13\% over GRPO, 20-Entropy and JustRL.

On-policy distillation (OPD) is appealing for large language model (LLM) post-training because it evaluates teacher feedback on student-generated rollouts rather than fixed teacher traces. In long-horizon settings, however, the common sampled-token variant is fragile: it reduces distribution matching to a one-token signal and becomes increasingly unreliable as rollouts drift away from prefixes the teacher commonly visits. We revisit OPD from the estimator and implementation sides. Theoretically, token-level OPD is biased relative to sequence-level reverse-KL, but it has a much tighter worst-case variance bound; our toy study shows the same tradeoff empirically, with stronger future-reward coupling producing higher gradient variance and less stable learning. Empirically, we identify three failure modes of sampled-token OPD: an imbalanced one-token signal, unreliable teacher guidance on student-generated prefixes, and distortions caused by tokenizer or special-token mismatch. We address these issues with teacher top-K local support matching, implemented as truncated reverse-KL with top-p rollout sampling and special-token masking. Across single-task math reasoning and multi-task agentic-plus-math training, this objective yields more stable optimization and better downstream performance than sampled-token OPD.

Estimating uncertainty in Large Language Models (LLMs) is important for properly evaluating LLMs, and ensuring safety for users. However, prior approaches to uncertainty estimation focus on the final answer in generated text, ignoring intermediate steps that might dramatically impact the outcome. We hypothesize that there exist key forking tokens, such that re-sampling the system at those specific tokens, but not others, leads to very different outcomes. To test this empirically, we develop a novel approach to representing uncertainty dynamics across individual tokens of text generation, and applying statistical models to test our hypothesis. Our approach is highly flexible: it can be applied to any dataset and any LLM, without fine tuning or accessing model weights. We use our method to analyze LLM responses on 7 different tasks across 4 domains, spanning a wide range of typical use cases. We find many examples of forking tokens, including surprising ones such as punctuation marks, suggesting that LLMs are often just a single token away from saying something very different.

Despite significant progress in text anomaly detection for web applications such as spam filtering and fake news detection, existing methods are fundamentally limited to document-level analysis, unable to identify which specific parts of a text are anomalous. We introduce token-level anomaly detection, a novel paradigm that enables fine-grained localization of anomalies within text. We formally define text anomalies at both document and token-levels, and propose a unified detection framework that operates across multiple levels. To facilitate research in this direction, we collect and annotate three benchmark datasets spanning spam, reviews and grammar errors with token-level labels. Experimental results demonstrate that our framework get better performance than other 6 baselines, opening new possibilities for precise anomaly localization in text. All the codes and data are publicly available on https://github.com/charles-cao/TokenCore.

As creative writing tasks do not have singular correct answers, large language models (LLMs) trained to perform these tasks should be able to generate diverse valid outputs. However, LLM post-training often focuses on improving generation quality but neglects to facilitate output diversity. Hence, in creative writing generation, we investigate post-training approaches to promote both output diversity and quality. Our core idea is to include deviation -- the degree of difference between a training sample and all other samples with the same prompt -- in the training objective to facilitate learning from rare high-quality instances. By adopting our approach to direct preference optimization (DPO) and odds ratio preference optimization (ORPO), we demonstrate that we can promote the output diversity of trained models while minimally decreasing quality. Our best model with 8B parameters could achieve on-par diversity as a human-created dataset while having output quality similar to the best instruction-tuned models we examined, GPT-4o and DeepSeek-R1. We further validate our approaches with a human evaluation, an ablation, and a comparison to an existing diversification approach, DivPO.

Large language models (LLMs) are increasingly utilized for machine translation, yet their predictions often exhibit uncertainties that hinder interpretability and user trust. Effectively visualizing these uncertainties can enhance the usability of LLM outputs, particularly in contexts where translation accuracy is critical. This paper addresses two primary objectives: (1) providing users with token-level insights into model confidence and (2) developing a web-based visualization tool to quantify and represent translation uncertainties. To achieve these goals, we utilized the T5 model with the WMT19 dataset for translation tasks and evaluated translation quality using established metrics such as BLEU, METEOR, and ROUGE. We introduced three novel uncertainty quantification (UQ) metrics: (1) the geometric mean of token probabilities, (2) the arithmetic mean of token probabilities, and (3) the arithmetic mean of the kurtosis of token distributions. These metrics provide a simple yet effective framework for evaluating translation performance. Our analysis revealed a linear relationship between the traditional evaluation metrics and our UQ metrics, demonstrating the validity of our approach. Additionally, we developed an interactive web-based visualization that uses a color gradient to represent token confidence. This tool offers users a clear and intuitive understanding of translation quality while providing valuable insights into model performance. Overall, we show that our UQ metrics and visualization are both robust and interpretable, offering practical tools for evaluating and accessing machine translation systems.

Token-level reweighting is a simple yet effective mechanism for controlling supervised fine-tuning, but common indicators are largely one-dimensional: the ground-truth probability reflects downstream alignment, while token entropy reflects intrinsic uncertainty induced by the pre-training prior. Ignoring entropy can misidentify noisy or easily replaceable tokens as learning-critical, while ignoring probability fails to reflect target-specific alignment. RankTuner introduces a probability--entropy calibration signal, the Relative Rank Indicator, which compares the rank of the ground-truth token with its expected rank under the prediction distribution. The inverse indicator is used as a token-wise Relative Scale to reweight the fine-tuning objective, focusing updates on truly under-learned tokens without over-penalizing intrinsically uncertain positions. Experiments on multiple backbones show consistent improvements on mathematical reasoning benchmarks, transfer gains on out-of-distribution reasoning, and pre code generation performance over probability-only or entropy-only reweighting baselines.

Training large-scale machine learning models poses distinct system challenges, given both the size and complexity of today's workloads. Recently, many organizations training state-of-the-art Generative AI models have reported cases of instability during training, often taking the form of loss spikes. Numeric deviation has emerged as a potential cause of this training instability, although quantifying this is especially challenging given the costly nature of training runs. In this work, we develop a principled approach to understanding the effects of numeric deviation, and construct proxies to put observations into context when downstream effects are difficult to quantify. As a case study, we apply this framework to analyze the widely-adopted Flash Attention optimization. We find that Flash Attention sees roughly an order of magnitude more numeric deviation as compared to Baseline Attention at BF16 when measured during an isolated forward pass. We then use a data-driven analysis based on the Wasserstein Distance to provide upper bounds on how this numeric deviation impacts model weights during training, finding that the numerical deviation present in Flash Attention is 2-5 times less significant than low-precision training.

Reinforcement learning for large language models suffers from high-variance token-level importance sampling (IS) ratios, which would destabilize policy optimization at scale. To improve stability, recent methods typically use a fixed sequence-level IS ratio for all tokens in a sequence or adjust each token's IS ratio separately, thereby neglecting temporal off-policy derivation across tokens in a sequence. In this paper, we first empirically identify that local off-policy deviation is structurally inconsistent at the token level, which may distort policy-gradient updates across adjacent tokens and lead to training collapse. To address the issue, we propose Online Causal Kalman Filtering for stable and effective Policy Optimization (KPO). Concretely, we model the desired IS ratio as a latent state that evolves across tokens and apply a Kalman filter to update this state online and autoregressively based on the states of past tokens, regardless of future tokens. The resulting filtered IS ratios preserve token-wise local structure-aware variation while strongly smoothing noise spikes, yielding more stable and effective policy updates. Experimentally, KPO achieves superior results on challenging math reasoning datasets compared with state-of-the-art counterparts.

ChatGPT brings revolutionary social value but also raises concerns about the misuse of AI-generated text. Consequently, an important question is how to detect whether texts are generated by ChatGPT or by human. Existing detectors are built upon the assumption that there are distributional gaps between human-generated and AI-generated text. These gaps are typically identified using statistical information or classifiers. Our research challenges the distributional gap assumption in detectors. We find that detectors do not effectively discriminate the semantic and stylistic gaps between human-generated and AI-generated text. Instead, the "subtle differences", such as an extra space, become crucial for detection. Based on this discovery, we propose the SpaceInfi strategy to evade detection. Experiments demonstrate the effectiveness of this strategy across multiple benchmarks and detectors. We also provide a theoretical explanation for why SpaceInfi is successful in evading perplexity-based detection. And we empirically show that a phenomenon called token mutation causes the evasion for language model-based detectors. Our findings offer new insights and challenges for understanding and constructing more applicable ChatGPT detectors.

Reinforcement learning (RL) has become a cornerstone for enhancing the reasoning capabilities of large language models (LLMs), with recent innovations such as Group Relative Policy Optimization (GRPO) demonstrating exceptional effectiveness. In this study, we identify a critical yet underexplored issue in RL training: low-probability tokens disproportionately influence model updates due to their large gradient magnitudes. This dominance hinders the effective learning of high-probability tokens, whose gradients are essential for LLMs' performance but are substantially suppressed. To mitigate this interference, we propose two novel methods: Advantage Reweighting and Low-Probability Token Isolation (Lopti), both of which effectively attenuate gradients from low-probability tokens while emphasizing parameter updates driven by high-probability tokens. Our approaches promote balanced updates across tokens with varying probabilities, thereby enhancing the efficiency of RL training. Experimental results demonstrate that they substantially improve the performance of GRPO-trained LLMs, achieving up to a 46.2% improvement in K&K Logic Puzzle reasoning tasks. Our implementation is available at https://github.com/zhyang2226/AR-Lopti.

Frontier LLMs are increasingly utilised across academia, society and industry. A commonly used unit for comparing models, their inputs and outputs, and estimating inference pricing is the token. In general, tokens are used as a stable currency, assumed to be broadly consistent across tokenizers and contexts, enabling direct comparisons. However, tokenization varies significantly across models and domains of text, making naive interpretation of token counts problematic. We quantify this variation by providing a comprehensive empirical analysis of tokenization, exploring the compression of sequences to tokens across different distributions of textual data. Our analysis challenges commonly held heuristics about token lengths, finding them to be overly simplistic. We hope the insights of our study add clarity and intuition toward tokenization in contemporary LLMs.

We study the relationship between vocabulary size and text length in a corpus of 75 literary works in English, authored by six writers, distinguishing between the contributions of three grammatical classes (or ``tags,'' namely, {\it nouns}, {\it verbs}, and {\it others}), and analyze the progressive appearance of new words of each tag along each individual text. While the power-law relation prescribed by Heaps' law is satisfactorily fulfilled by total vocabulary sizes and text lengths, the appearance of new words in each text is on the whole well described by the average of random shufflings of the text, which does not obey a power law. Deviations from this average, however, are statistically significant and show a systematic trend across the corpus. Specifically, they reveal that the appearance of new words along each text is predominantly retarded with respect to the average of random shufflings. Moreover, different tags are shown to add systematically distinct contributions to this tendency, with {\it verbs} and {\it others} being respectively more and less retarded than the mean trend, and {\it nouns} following instead this overall mean. These statistical systematicities are likely to point to the existence of linguistically relevant information stored in the different variants of Heaps' law, a feature that is still in need of extensive assessment.

Multiple choice questions (MCQs) are commonly used to evaluate the capabilities of large language models (LLMs). One common way to evaluate the model response is to rank the candidate answers based on the log probability of the first token prediction. An alternative way is to examine the text output. Prior work has shown that first token probabilities lack robustness to changes in MCQ phrasing, and that first token probabilities do not match text answers for instruction-tuned models. Therefore, in this paper, we investigate the robustness of text answers. We show that the text answers are more robust to question perturbations than the first token probabilities, when the first token answers mismatch the text answers. The difference in robustness increases as the mismatch rate becomes greater. As the mismatch reaches over 50\%, the text answer is more robust to option order changes than the debiased first token probabilities using state-of-the-art debiasing methods such as PriDe. Our findings provide further evidence for the benefits of text answer evaluation over first token probability evaluation.

Rigorous statistical evaluations of large language models (LLMs), including valid error bars and significance testing, are essential for meaningful and reliable performance assessment. Currently, when such statistical measures are reported, they typically rely on the Central Limit Theorem (CLT). In this position paper, we argue that while CLT-based methods for uncertainty quantification are appropriate when benchmarks consist of thousands of examples, they fail to provide adequate uncertainty estimates for LLM evaluations that rely on smaller, highly specialized benchmarks. In these small-data settings, we demonstrate that CLT-based methods perform very poorly, usually dramatically underestimating uncertainty (i.e. producing error bars that are too small). We give recommendations for alternative frequentist and Bayesian methods that are both easy to implement and more appropriate in these increasingly common scenarios. We provide a simple Python library for these Bayesian methods at https://github.com/sambowyer/bayes_evals .

Next token prediction paradigm has been prevailing for autoregressive models in the era of LLMs. The current default sampling choice for popular LLMs is temperature scaling together with nucleus sampling to balance diversity and coherence. Nevertheless, such approach leads to inferior performance in various NLP tasks when the model is not certain about testing questions. To this end, we propose a brand new training-free decoding strategy, dubbed as Cautious Next Token Prediction (CNTP). In the decoding process, if the model has comparatively high prediction entropy at a certain step, we sample multiple trials starting from the step independently and stop when encountering any punctuation. Then we select the trial with the lowest perplexity score viewed as the most probable and reliable trial path given the model's capacity. The trial number is negatively correlated with the prediction confidence, i.e., the less confident the model is, the more trials it should sample. This is consistent with human beings' behaviour: when feeling uncertain or unconfident, one tends to think more creatively, exploring multiple thinking paths, to cautiously select the path one feels most confident about. Extensive experiments on both LLMs and MLLMs show that our proposed CNTP approach outperforms existing standard decoding strategies consistently by a clear margin. Moreover, the integration of CNTP with self consistency can further improve over vanilla self consistency. We believe our proposed CNTP has the potential to become one of the default choices for LLM decoding. Code is available at https://github.com/wyzjack/CNTP.

Recent reasoning Large Language Models (LLMs) demonstrate remarkable problem-solving abilities but often generate long thinking traces whose utility is unclear. Our work aims to improve their efficiency, enabling them to reach high performance without overthinking. First, we analyze the entropy of token probabilities in reasoning traces. Across three models, we observe a consistent U-shaped entropy pattern: high entropy on easy problems despite high accuracy, low entropy on problems with medium difficulty, and high entropy on hard problems reflecting uncertainty. Specifically, we notice 22--25\% entropy reduction from easy to medium difficulty regions, suggesting an {overthinking} phenomenon on easy instances. Building on these insights, we introduce DiffAdapt, a lightweight framework that selects Easy/Normal/Hard inference strategies per question based on their difficulty and reasoning trace entropy. Each inference strategy consists of a fixed prompt, temperature and maximum token length. In contrast to existing efficiency optimization methods, our approach does not fine-tune base LLM but a small probe that classifies LLM's final hidden state, allowing inexpensive adaptation. We comprehensively evaluate our method on five models and eight benchmarks. Our method achieves comparable or improved accuracy while reducing token usage by up to 22.4\%, establishing a practical path toward compute-efficient reasoning.

As the scale of training corpora for large language models (LLMs) grows, model developers become increasingly reluctant to disclose details on their data. This lack of transparency poses challenges to scientific evaluation and ethical deployment. Recently, pretraining data detection approaches, which infer whether a given text was part of an LLM's training data through black-box access, have been explored. The Min-K\% Prob method, which has achieved state-of-the-art results, assumes that a non-training example tends to contain a few outlier words with low token probabilities. However, the effectiveness may be limited as it tends to misclassify non-training texts that contain many common words with high probabilities predicted by LLMs. To address this issue, we introduce a divergence-based calibration method, inspired by the divergence-from-randomness concept, to calibrate token probabilities for pretraining data detection. We compute the cross-entropy (i.e., the divergence) between the token probability distribution and the token frequency distribution to derive a detection score. We have developed a Chinese-language benchmark, PatentMIA, to assess the performance of detection approaches for LLMs on Chinese text. Experimental results on English-language benchmarks and PatentMIA demonstrate that our proposed method significantly outperforms existing methods. Our code and PatentMIA benchmark are available at https://github.com/zhang-wei-chao/DC-PDD.

Why do language models sometimes prefer correct statements even when trained on mixed-quality data? We introduce the Compression--Consistency Principle: next-token prediction favors hypotheses that allow shorter and more internally consistent descriptions of the training data. Truth bias emerges only when false alternatives are structurally harder to compress. We test this using small GPT-2-style character-level transformers (3.5M--86M parameters) on synthetic math corpora with controlled mixtures of correct and incorrect rules. In the random-error setting, models strongly prefer correct completions in paired evaluation: 83.1% accuracy at balanced data and 67.0% even when correct rules appear in only 10% of the corpus. Replacing random errors with a coherent but mathematically incorrect rule system largely eliminates the preference (near-chance accuracy). In a more natural-language-like synthetic world, the effect is weaker but still present (57.7%). Additional experiments show that embedding verification steps can restore preference for correctness even at small scale, while increasing the number of consistent rules produces a graded improvement in accuracy. Our results suggest that what appears as a "truth bias" is largely a side effect of compression pressure and preference for internal consistency, rather than an intrinsic drive toward truth. Full code and data are available at https://github.com/Rai220/compression-drives-truth.

Recent advancements in reinforcement learning from human feedback have shown that utilizing fine-grained token-level reward models can substantially enhance the performance of Proximal Policy Optimization (PPO) in aligning large language models. However, it is challenging to leverage such token-level reward as guidance for Direct Preference Optimization (DPO), since DPO is formulated as a sequence-level bandit problem. To address this challenge, this work decomposes the sequence-level PPO into a sequence of token-level proximal policy optimization problems and then frames the problem of token-level PPO with token-level reward guidance, from which closed-form optimal token-level policy and the corresponding token-level reward can be derived. Using the obtained reward and Bradley-Terry model, this work establishes a framework of computable loss functions with token-level reward guidance for DPO, and proposes a practical reward guidance based on the induced DPO reward. This formulation enables different tokens to exhibit varying degrees of deviation from reference policy based on their respective rewards. Experiment results demonstrate that our method achieves substantial performance improvements over DPO, with win rate gains of up to 7.5 points on MT-Bench, 6.2 points on AlpacaEval 2, and 4.3 points on Arena-Hard. Code is available at https://github.com/dvlab-research/TGDPO.

We consider multi-draft speculative sampling, where the proposal sequences are sampled independently from different draft models. At each step, a token-level draft selection scheme takes a list of valid tokens as input and produces an output token whose distribution matches that of the target model. Previous works have demonstrated that the optimal scheme (which maximizes the probability of accepting one of the input tokens) can be cast as a solution to a linear program. In this work we show that the optimal scheme can be decomposed into a two-step solution: in the first step an importance sampling (IS) type scheme is used to select one intermediate token; in the second step (single-draft) speculative sampling is applied to generate the output token. For the case of two identical draft models we further 1) establish a necessary and sufficient condition on the distributions of the target and draft models for the acceptance probability to equal one and 2) provide an explicit expression for the optimal acceptance probability. Our theoretical analysis also motives a new class of token-level selection scheme based on weighted importance sampling. Our experimental results demonstrate consistent improvements in the achievable block efficiency and token rates over baseline schemes in a number of scenarios.

Despite the widespread use of Transformer-based text embedding models in NLP tasks, surprising 'sticky tokens' can undermine the reliability of embeddings. These tokens, when repeatedly inserted into sentences, pull sentence similarity toward a certain value, disrupting the normal distribution of embedding distances and degrading downstream performance. In this paper, we systematically investigate such anomalous tokens, formally defining them and introducing an efficient detection method, Sticky Token Detector (STD), based on sentence and token filtering. Applying STD to 40 checkpoints across 14 model families, we discover a total of 868 sticky tokens. Our analysis reveals that these tokens often originate from special or unused entries in the vocabulary, as well as fragmented subwords from multilingual corpora. Notably, their presence does not strictly correlate with model size or vocabulary size. We further evaluate how sticky tokens affect downstream tasks like clustering and retrieval, observing significant performance drops of up to 50%. Through attention-layer analysis, we show that sticky tokens disproportionately dominate the model's internal representations, raising concerns about tokenization robustness. Our findings show the need for better tokenization strategies and model design to mitigate the impact of sticky tokens in future text embedding applications.

Recent Large Language Model (LLM) post-training methods rely on token-level clipping mechanisms during Reinforcement Learning (RL). However, we identify a fundamental flaw in this Outcome-Supervised RL (OSRL) paradigm: the Importance Sampling (IS) ratios of positive-advantage tokens are mismatched, leading to unbalanced token weighting for positive and negative tokens. This mismatch suppresses the update of low-probability tokens while over-amplifying already high-probability ones. To address this, we propose Asymmetric Importance Sampling Policy Optimization (ASPO), which uses a simple yet effective strategy that flips the IS ratios of positive-advantage tokens, aligning their update direction with the learning dynamics of negative ones. AIS further incorporates a soft dual-clipping mechanism to stabilize extreme updates while maintaining gradient flow. Comprehensive experiments on coding and mathematical reasoning benchmarks demonstrate that ASPO significantly mitigates premature convergence, improves training stability, and enhances final performance over strong GRPO-based baselines. Our analysis provides new insights into the role of token-level weighting in OSRL and highlights the critical importance of correcting IS in LLM RL. The code and models of ASPO are available at https://github.com/wizard-III/Archer2.0.

When using agent-task datasets to enhance agent capabilities for Large Language Models (LLMs), current methodologies often treat all tokens within a sample equally. However, we argue that tokens serving different roles - specifically, reasoning tokens versus boilerplate tokens (e.g., those governing output format) - differ significantly in importance and learning complexity, necessitating their disentanglement and distinct treatment. To address this, we propose a novel Shuffle-Aware Discriminator (SHAD) for adaptive token discrimination. SHAD classifies tokens by exploiting predictability differences observed after shuffling input-output combinations across samples: boilerplate tokens, due to their repetitive nature among samples, maintain predictability, whereas reasoning tokens do not. Using SHAD, we propose the Reasoning-highlighted Fine-Tuning (RFT) method, which adaptively emphasizes reasoning tokens during fine-tuning, yielding notable performance gains over common Supervised Fine-Tuning (SFT).

The disconnect between tokenizer creation and model training in language models has been known to allow for certain inputs, such as the infamous SolidGoldMagikarp token, to induce unwanted behaviour. Although such `glitch tokens' that are present in the tokenizer vocabulary, but are nearly or fully absent in training, have been observed across a variety of different models, a consistent way of identifying them has been missing. We present a comprehensive analysis of Large Language Model (LLM) tokenizers, specifically targeting this issue of detecting untrained and under-trained tokens. Through a combination of tokenizer analysis, model weight-based indicators, and prompting techniques, we develop effective methods for automatically detecting these problematic tokens. Our findings demonstrate the prevalence of such tokens across various models and provide insights into improving the efficiency and safety of language models.

Large Language Models (LLMs) have exhibited remarkable performance on reasoning tasks. They utilize autoregressive token generation to construct reasoning trajectories, enabling the development of a coherent chain of thought. In this work, we explore the impact of individual tokens on the final outcomes of reasoning tasks. We identify the existence of ``critical tokens'' that lead to incorrect reasoning trajectories in LLMs. Specifically, we find that LLMs tend to produce positive outcomes when forced to decode other tokens instead of critical tokens. Motivated by this observation, we propose a novel approach - cDPO - designed to automatically recognize and conduct token-level rewards for the critical tokens during the alignment process. Specifically, we develop a contrastive estimation approach to automatically identify critical tokens. It is achieved by comparing the generation likelihood of positive and negative models. To achieve this, we separately fine-tune the positive and negative models on various reasoning trajectories, consequently, they are capable of identifying identify critical tokens within incorrect trajectories that contribute to erroneous outcomes. Moreover, to further align the model with the critical token information during the alignment process, we extend the conventional DPO algorithms to token-level DPO and utilize the differential likelihood from the aforementioned positive and negative model as important weight for token-level DPO learning.Experimental results on GSM8K and MATH500 benchmarks with two-widely used models Llama-3 (8B and 70B) and deepseek-math (7B) demonstrate the effectiveness of the propsoed approach cDPO.

Reinforcement learning with verifiable rewards (RLVR) has substantially improved the reasoning capabilities of large language models. While existing analyses identify that RLVR-induced changes are sparse, they primarily focus on the magnitude of these updates, largely overlooking their direction. In this work, we argue that the direction of updates is a more critical lens for understanding RLVR's effects, which can be captured by the signed, token-level log probability difference Δlog p between the base and final RLVR models. Through statistical analysis and token-replacement interventions, we demonstrate that Δlog p more effectively identifies sparse, yet reasoning-critical updates than magnitude-based metrics (\eg divergence or entropy). Building on this insight, we propose two practical applications: (1) a test-time extrapolation method that amplifies the policy along the learned Δlog p direction to improve reasoning accuracy without further training; (2) a training-time reweighting method that focuses learning on low-probability (corresponding to higher Δlog p) tokens, which improves reasoning performance across models and benchmarks. Our work establishes the direction of change as a key principle for analyzing and improving RLVR.

Generative models, widely utilized in various applications, can often struggle with prompts corresponding to partial tokens. This struggle stems from tokenization, where partial tokens fall out of distribution during inference, leading to incorrect or nonsensical outputs. This paper examines a technique to alleviate the tokenization artifact on text completion in generative models, maintaining performance even in regular non-subword cases. The method, termed token alignment, involves backtracking to the last complete tokens and ensuring the model's generation aligns with the prompt. This approach showcases marked improvement across many partial token scenarios, including nuanced cases like space-prefix and partial indentation, with only a minor time increase. The technique and analysis detailed in this paper contribute to the continuous advancement of generative models in handling partial inputs, bearing relevance for applications like code completion and text autocompletion.

In modern large language models (LLMs), LLM alignment is of crucial importance and is typically achieved through methods such as reinforcement learning from human feedback (RLHF) and direct preference optimization (DPO). However, in most existing methods for LLM alignment, all tokens in the response are optimized using a sparse, response-level reward or preference annotation. The ignorance of token-level rewards may erroneously punish high-quality tokens or encourage low-quality tokens, resulting in suboptimal performance and slow convergence speed. To address this issue, we propose AlignDistil, an RLHF-equivalent distillation method for token-level reward optimization. Specifically, we introduce the reward learned by DPO into the RLHF objective and theoretically prove the equivalence between this objective and a token-level distillation process, where the teacher distribution linearly combines the logits from the DPO model and a reference model. On this basis, we further bridge the accuracy gap between the reward from the DPO model and the pure reward model, by building a contrastive DPO reward with a normal and a reverse DPO model. Moreover, to avoid under- and over-optimization on different tokens, we design a token adaptive logit extrapolation mechanism to construct an appropriate teacher distribution for each token. Experimental results demonstrate the superiority of our AlignDistil over existing methods and showcase fast convergence due to its token-level distributional reward optimization.

Autoregressive language models accumulate errors due to their fixed, irrevocable left-to-right token generation. To address this, we propose a new sampling method called Resample-Previous-Tokens (RPT). RPT mitigates error accumulation by iteratively revisiting and potentially replacing tokens in a window of previously generated text. This method can be integrated into existing autoregressive models, preserving their next-token-prediction quality and speed. Fine-tuning a pretrained 8B parameter model with RPT for only 100B resulted in ~10% relative improvements on reasoning and coding benchmarks compared to the standard sampling.

Reasoning failures in large language models (LLMs) are typically measured only at the end of a generation, yet many failures manifest as a process-level breakdown: the model "loses the thread" mid-reasoning. We study whether such breakdowns are detectable from inference-time observables available in standard APIs (token log probabilities), without any training or fine-tuning. We define a simple instability signal that combines consecutive-step distributional shift (JSD) and uncertainty (entropy), summarize each trace by its peak instability strength, and show that this signal reliably predicts failure. Across GSM8K and HotpotQA, instability strength predicts wrong answers with above-chance AUC and yields monotonic bucket-level accuracy decline at scale across model sizes. Crucially, we show that instability is not uniformly harmful: early instability can reflect subsequent stabilization and a correct final answer (corrective instability), whereas late instability is more often followed by failure (destructive instability), even at comparable peak magnitudes, indicating that recoverability depends not only on how strongly the distribution changes but also on when such changes occur relative to the remaining decoding horizon. The method is model-agnostic, training-free, and reproducible, and is presented as a diagnostic lens rather than a corrective or control mechanism.

Despite their widespread use, the mechanisms by which large language models (LLMs) represent and regulate uncertainty in next-token predictions remain largely unexplored. This study investigates two critical components believed to influence this uncertainty: the recently discovered entropy neurons and a new set of components that we term token frequency neurons. Entropy neurons are characterized by an unusually high weight norm and influence the final layer normalization (LayerNorm) scale to effectively scale down the logits. Our work shows that entropy neurons operate by writing onto an unembedding null space, allowing them to impact the residual stream norm with minimal direct effect on the logits themselves. We observe the presence of entropy neurons across a range of models, up to 7 billion parameters. On the other hand, token frequency neurons, which we discover and describe here for the first time, boost or suppress each token's logit proportionally to its log frequency, thereby shifting the output distribution towards or away from the unigram distribution. Finally, we present a detailed case study where entropy neurons actively manage confidence in the setting of induction, i.e. detecting and continuing repeated subsequences.

When fine-tuning pre-trained Large Language Models (LLMs) to align with human values and intentions, maximizing the estimated reward can lead to superior performance, but it also introduces potential risks due to deviations from the reference model's intended behavior. Most existing methods typically introduce KL divergence to constrain deviations between the trained model and the reference model; however, this may not be sufficient in certain applications that require tight risk control. In this paper, we introduce Risk-aware Direct Preference Optimization (Ra-DPO), a novel approach that incorporates risk-awareness by employing a class of nested risk measures. This approach formulates a constrained risk-aware advantage function maximization problem and then converts the Bradley-Terry model into a token-level representation. The objective function maximizes the likelihood of the policy while suppressing the deviation between a trained model and the reference model using a sequential risk ratio, thereby enhancing the model's risk-awareness. Experimental results across three open-source datasets: IMDb Dataset, Anthropic HH Dataset, and AlpacaEval, demonstrate the proposed method's superior performance in balancing alignment performance and model drift. Our code is opensourced at https://github.com/zlj123-max/Ra-DPO.

Large Language Models (LLMs) have demonstrated impressive problem-solving capabilities in mathematics through step-by-step reasoning chains. However, they are susceptible to reasoning errors that impact the quality of subsequent reasoning chains and the final answer due to language models' autoregressive token-by-token generating nature. Recent works have proposed adopting external verifiers to guide the generation of reasoning paths, but existing works utilize models that have been trained with step-by-step labels to assess the correctness of token-by-token reasoning chains. Consequently, they struggle to recognize discriminative details of tokens within a reasoning path and lack the ability to evaluate whether an intermediate reasoning path is on a promising track toward the correct final answer. To amend the lack of sound and token-grained math-verification signals, we devise a novel training scheme for verifiers that apply token-level supervision with the expected cumulative reward (i.e., value). Furthermore, we propose a practical formulation of the cumulative reward by reducing it to finding the probability of future correctness of the final answer and thereby enabling the empirical estimation of the value. Experimental results on mathematical reasoning benchmarks show that Token-Supervised Value Model (TVM) can outperform step-by-step verifiers on GSM8K and MATH with Mistral and Llama.

While Reinforcement Learning with Verifiable Rewards (RLVR) can enhance LLM reasoning, its training process poses a critical risk: entropy collapse. This phenomenon is a rapid loss of policy diversity, stemming from the exploration-exploitation imbalance and leading to a lack of generalization. Recent entropy-intervention methods aim to prevent entropy collapse, yet their underlying mechanisms remain unclear. In this paper, we conduct a quantitative analysis to reveal token-level entropy changes and how existing entropy intervention methods help avoid entropy collapse. Our findings point out a fundamental limitation of existing methods: they attempt to control entropy dynamics indirectly. By only affecting related factors, such as the advantage signal and generation probability, their effectiveness is inherently limited and could potentially fail. To address this limitation, we introduce an entropy-change-aware reweighting scheme, namely Stabilizing Token-level Entropy-changE via Reweighting (STEER), that adaptively stabilizes entropy dynamics through fine-grained token-level adjustments. Our approach mitigates over-exploitation while fostering robust exploration. Extensive experiments demonstrate that STEER significantly mitigates entropy collapse, stabilizes entropy dynamics, and achieves stronger downstream performance across various mathematical reasoning benchmarks \footnote{Our code is available at https://github.com/zz-haooo/STEER.

We propose (G)I-DLE, a new approach to constrained decoding that leverages KL divergence minimization to preserve the intrinsic conditional probability distribution of autoregressive language models while excluding undesirable tokens. Unlike conventional methods that naively set banned tokens' logits to -infty, which can distort the conversion from raw logits to posterior probabilities and increase output variance, (G)I-DLE re-normalizes the allowed token probabilities to minimize such distortion. We validate our method on the K2-Eval dataset, specifically designed to assess Korean language fluency, logical reasoning, and cultural appropriateness. Experimental results on Qwen2.5 models (ranging from 1.5B to 14B) demonstrate that G-IDLE not only boosts mean evaluation scores but also substantially reduces the variance of output quality.

Words of estimative probability (WEP) are expressions of a statement's plausibility (probably, maybe, likely, doubt, likely, unlikely, impossible...). Multiple surveys demonstrate the agreement of human evaluators when assigning numerical probability levels to WEP. For example, highly likely corresponds to a median chance of 0.90+-0.08 in Fagen-Ulmschneider (2015)'s survey. In this work, we measure the ability of neural language processing models to capture the consensual probability level associated to each WEP. Firstly, we use the UNLI dataset (Chen et al., 2020) which associates premises and hypotheses with their perceived joint probability p, to construct prompts, e.g. "[PREMISE]. [WEP], [HYPOTHESIS]." and assess whether language models can predict whether the WEP consensual probability level is close to p. Secondly, we construct a dataset of WEP-based probabilistic reasoning, to test whether language models can reason with WEP compositions. When prompted "[EVENTA] is likely. [EVENTB] is impossible.", a causal language model should not express that [EVENTA&B] is likely. We show that both tasks are unsolved by off-the-shelf English language models, but that fine-tuning leads to transferable improvement.

With the expanding application of Large Language Models (LLMs) in various domains, it becomes imperative to comprehensively investigate their unforeseen behaviors and consequent outcomes. In this study, we introduce and systematically explore the phenomenon of "glitch tokens", which are anomalous tokens produced by established tokenizers and could potentially compromise the models' quality of response. Specifically, we experiment on seven top popular LLMs utilizing three distinct tokenizers and involving a totally of 182,517 tokens. We present categorizations of the identified glitch tokens and symptoms exhibited by LLMs when interacting with glitch tokens. Based on our observation that glitch tokens tend to cluster in the embedding space, we propose GlitchHunter, a novel iterative clustering-based technique, for efficient glitch token detection. The evaluation shows that our approach notably outperforms three baseline methods on eight open-source LLMs. To the best of our knowledge, we present the first comprehensive study on glitch tokens. Our new detection further provides valuable insights into mitigating tokenization-related errors in LLMs.

Classifier-free guidance (CFG) has become an essential component of modern diffusion models to enhance both generation quality and alignment with input conditions. However, CFG requires specific training procedures and is limited to conditional generation. To address these limitations, we propose Token Perturbation Guidance (TPG), a novel method that applies perturbation matrices directly to intermediate token representations within the diffusion network. TPG employs a norm-preserving shuffling operation to provide effective and stable guidance signals that improve generation quality without architectural changes. As a result, TPG is training-free and agnostic to input conditions, making it readily applicable to both conditional and unconditional generation. We further analyze the guidance term provided by TPG and show that its effect on sampling more closely resembles CFG compared to existing training-free guidance techniques. Extensive experiments on SDXL and Stable Diffusion 2.1 show that TPG achieves nearly a 2times improvement in FID for unconditional generation over the SDXL baseline, while closely matching CFG in prompt alignment. These results establish TPG as a general, condition-agnostic guidance method that brings CFG-like benefits to a broader class of diffusion models. The code is available at https://github.com/TaatiTeam/Token-Perturbation-Guidance

Reward guidance has been applied to great success in the test-time adaptation of continuous diffusion models; it updates each denoising step using the gradients from a downstream reward model. We study reward guidance for discrete diffusion language models, where one cannot differentiate through the natural outputs of the model because they are discrete tokens. Existing approaches either replace these discrete tokens with continuous relaxations, or employ techniques like the straight-through estimator. In this work, we show the downsides of both these methods. The former degrades gradient feedback because the reward model has never been trained with continuous inputs. The latter involves incorrect optimization because the gradient evaluated at discrete tokens is used to update continuous logits. Our key innovation is to go beyond this tradeoff by introducing a novel mechanism called EntRGi: Entropy aware Reward Guidance that dynamically regulates the gradients from the reward model. By modulating the continuous relaxation using the model's confidence, our approach substantially improves reward guidance while providing reliable inputs to the reward model. We empirically validate our approach on a 7B-parameter diffusion language model across 3 diverse reward models and 3 multi-skill benchmarks, showing consistent improvements over state-of-the-art methods.

Deterministic inference is a comforting ideal in classical software: the same program on the same input should always produce the same output. As large language models move into real-world deployment, this ideal has been imported wholesale into inference stacks. Recent work from the Thinking Machines Lab has presented a detailed analysis of nondeterminism in LLM inference, showing how batch-invariant kernels and deterministic attention can enforce bitwise-identical outputs, positioning deterministic inference as a prerequisite for reproducibility and enterprise reliability. In this paper, we take the opposite stance. We argue that, for LLMs, deterministic inference kills. It kills the ability to model uncertainty, suppresses emergent abilities, collapses reasoning into a single brittle path, and weakens safety alignment by hiding tail risks. LLMs implement conditional distributions over outputs, not fixed functions. Collapsing these distributions to a single canonical completion may appear reassuring, but it systematically conceals properties central to artificial cognition. We instead advocate Stochastic CHAOS, treating distributional variability as a signal to be measured and controlled. Empirically, we show that deterministic inference is systematically misleading. Single-sample deterministic evaluation underestimates both capability and fragility, masking failure probability under paraphrases and noise. Phase-like transitions associated with emergent abilities disappear under greedy decoding. Multi-path reasoning degrades when forced onto deterministic backbones, reducing accuracy and diagnostic insight. Finally, deterministic evaluation underestimates safety risk by hiding rare but dangerous behaviors that appear only under multi-sample evaluation.

Large language models (LLMs) have shown remarkable capabilities in code generation. However, the effects of hallucinations (e.g., output noise) make it particularly challenging for LLMs to generate high-quality code in one pass. In this work, we propose a simple and effective uncertainty-aware selective contrastive decoding (USCD) mechanism to improve the quality of one-pass code generation in LLMs and reduce the impact of output noise. To be specific, we first elaborately designed a negative prompt (namely lame prompt) to output noise by removing input-output examples from the standard few-shot prompt. Our preliminary study shows that the Jensen-Shannon divergence (JS divergence) between token distribution uncertainty and the output noise is relatively low (approximately 0.25), indicating their high relevance. Then, we selectively eliminate output noise induced by lame prompts based on the uncertainty of the prediction distribution from the standard prompt. Notably, our proposed plug-and-play mechanism is an inference-only method, enjoying appealing flexibility. Extensive experiments on widely used benchmarks, e.g., HumanEval, MBPP, and MultiPL-E, upon several LLMs (i.e., Inocder-6b, CodeLlama-7b, WizardCoder-15b, StarCoder, and Llama2-7b), demonstrate that our proposed USCD significantly improves one-pass code generation, with an average pass@1 scores increase of 16.59\%. We will release code and data on GitHub.

Uncertainty quantification (UQ) for open-ended language generation remains a critical yet underexplored challenge, especially under black-box constraints where internal model signals are inaccessible. In this paper, we introduce Token-Entropy Conformal Prediction (TECP), a novel framework that leverages token-level entropy as a logit-free, reference-free uncertainty measure and integrates it into a split conformal prediction (CP) pipeline to construct prediction sets with formal coverage guarantees. Unlike existing approaches that rely on semantic consistency heuristics or white-box features, TECP directly estimates epistemic uncertainty from the token entropy structure of sampled generations and calibrates uncertainty thresholds via CP quantiles to ensure provable error control. Empirical evaluations across six large language models and two benchmarks (CoQA and TriviaQA) demonstrate that TECP consistently achieves reliable coverage and compact prediction sets, outperforming prior self-consistency-based UQ methods. Our method provides a principled and efficient solution for trustworthy generation in black-box LLM settings.

Large Language Models (LLMs) can significantly improve their reasoning capabilities by interacting with external tools, a paradigm known as Tool-Integrated Reasoning (TIR). However, extending TIR to multi-turn scenarios using Reinforcement Learning (RL) is often hindered by training instability and performance collapse. We identify that such instability is primarily caused by a distributional drift from external tool feedback, leading to the generation of low-probability tokens. This issue compounds over successive turns, causing catastrophic gradient norm explosions that derail the training process. To address this challenge, we introduce SimpleTIR , a plug-and-play algorithm that stabilizes multi-turn TIR training. Its core strategy is to identify and filter out trajectories containing void turns, i.e., turns that yield neither a code block nor a final answer. By removing these problematic trajectories from the policy update, SimpleTIR effectively blocks the harmful, high-magnitude gradients, thus stabilizing the learning dynamics. Extensive experiments show that SimpleTIR achieves state-of-the-art performance on challenging math reasoning benchmarks, notably elevating the AIME24 score from a text-only baseline of 22.1 to 50.5 when starting from the Qwen2.5-7B base model. Furthermore, by avoiding the constraints of supervised fine-tuning, SimpleTIR encourages the model to discover diverse and sophisticated reasoning patterns, such as self-correction and cross-validation.

Tool-based Agentic Reinforcement Learning (TARL) has emerged as a promising paradigm for training search agents to interact with external tools for a multi-turn information-seeking process autonomously. However, we identify a critical training instability that leads to catastrophic model collapse: Importance Sampling Distribution Drift(ISDD). In Group Relative Policy Optimization(GRPO), a widely adopted TARL algorithm, ISDD manifests as a precipitous decline in the importance sampling ratios, which nullifies gradient updates and triggers irreversible training failure. To address this, we propose Search Agent Policy Optimization (SAPO), which stabilizes training via a conditional token-level KL constraint. Unlike hard clipping, which ignores distributional divergence, SAPO selectively penalizes the KL divergence between the current and old policies. Crucially, this penalty is applied only to positive tokens with low probabilities where the policy has shifted excessively, thereby preventing distribution drift while preserving gradient flow. Remarkably, SAPO requires only one-line code modification to standard GRPO, ensuring immediate deployability. Extensive experiments across seven QA benchmarks demonstrate that SAPO achieves +10.6\% absolute improvement (+31.5\% relative) over Search-R1, yielding consistent gains across varying model scales (1.5B, 14B) and families (Qwen, LLaMA).

While Large Language Models (LLMs) have demonstrated remarkable potential in natural language generation and instruction following, a persistent challenge lies in their susceptibility to "hallucinations", which erodes trust in their outputs. Although Uncertainty Quantification (UQ) presents a promising solution, its accurate implementation within the context of LLMs remains a significant hurdle. To address this critical roadblock, our research originates from a fundamental heuristic insight: tokens within auto-regressive LLM-generated text do not equally reflect the underlying meaning. Some tokens carry greater relevance and representativeness than others, owing to the phenomenon of "linguistic redundancy", wherein a select few keywords suffice to convey the essence of lengthy sentences. Regrettably, existing methodologies treat all tokens with equal importance when estimating uncertainty, disregarding these inherent generative inequalities. Our analysis reveals a significant issue with state-of-the-art: numerous tokens (and sentences) of limited semantic significance receive equal or even excessive weighting during uncertainty estimation. To rectify this bias, we propose to jointly Shifting Attention to more Relevant (SAR) components, at both the token- and the sentence-levels for accurate uncertainty estimation. We conduct extensive experiments involving a range of popular "off-the-shelf" LLMs, including instruction-tuned LLMs such as Vicuna, WizardLM, and LLaMA-2-chat, as well as pretrained LLMs like OPT and LLaMA, with model sizes extending up to 33B parameters. We carry out evaluation across various free-form question-answering tasks, encompassing domains such as reading comprehension, science Q&A, and medical Q&A. Our experimental results demonstrate the superior performance of SAR in addressing the challenges of uncertainty estimation within the realm of LLMs.

Quality Estimation (QE) is estimating the quality of model output when the ground truth reference is not available. Looking at model uncertainty from its own output probabilities is the most trivial and low-effort way to estimate the output quality. However, for generative model, output probabilities might not be the best quality estimator. At an output step, there can be multiple correct options, making the probability distribution spread out more. Thus, lower token probability does not necessarily mean lower output quality. In other words, the model can be considered underconfident. In this paper, we propose a QE approach called Dominant Mass Probability (DMP}, that boosts the model confidence in cases where there are multiple viable output options. We show that, with no increase in complexity, DMP is notably better than sequence probability when estimating the quality of different models (Whisper, Llama, etc.) on different tasks (translation, summarization, etc.). Compared to sequence probability, DMP achieves on average +0.208 improvement in Pearson correlation to ground-truth quality.

Agentic systems are evaluated on benchmarks where agents interact with environments to solve tasks. Most papers report a pass@1 score computed from a single run per task, assuming this gives a reliable performance estimate. We test this assumption by collecting 60,000 agentic trajectories on SWE-Bench-Verified, spanning three models and two scaffolds. We find substantial variance: single-run pass@1 estimates vary by 2.2 to 6.0 percentage points depending on which run is selected, with standard deviations exceeding 1.5 percentage points even at temperature 0. This variance has critical implications: reported improvements of 2--3 percentage points may reflect evaluation noise rather than genuine algorithmic progress. Through token-level analysis, we show that trajectories diverge early, often within the first few percent of tokens, and that these small differences cascade into different solution strategies. To enable reliable evaluation of agentic systems, we recommend three concrete practices: (1) estimate pass@1 from multiple independent runs per task, especially when measuring small improvements, (2) use statistical power analysis to determine the number of runs needed to detect expected effect sizes, and (3) consider metrics like pass@k (optimistic bound) and pass^k (pessimistic bound) with k>1 to better characterize the full performance envelope. While these practices increase evaluation cost, they are essential for distinguishing genuine scientific progress from statistical noise.

A key component of building safe and reliable language models is enabling the models to appropriately refuse to follow certain instructions or answer certain questions. We may want models to output refusal messages for various categories of user queries, for example, ill-posed questions, instructions for committing illegal acts, or queries which require information past the model's knowledge horizon. Engineering models that refuse to answer such questions is complicated by the fact that an individual may want their model to exhibit varying levels of sensitivity for refusing queries of various categories, and different users may want different refusal rates. The current default approach involves training multiple models with varying proportions of refusal messages from each category to achieve the desired refusal rates, which is computationally expensive and may require training a new model to accommodate each user's desired preference over refusal rates. To address these challenges, we propose refusal tokens, one such token for each refusal category or a single refusal token, which are prepended to the model's responses during training. We then show how to increase or decrease the probability of generating the refusal token for each category during inference to steer the model's refusal behavior. Refusal tokens enable controlling a single model's refusal rates without the need of any further fine-tuning, but only by selectively intervening during generation.

Recent advancements have shown that reinforcement learning (RL) can substantially improve the reasoning abilities of large language models (LLMs). The effectiveness of such RL training, however, depends critically on the exploration space defined by the pre-trained model's token-output distribution. In this paper, we revisit the standard cross-entropy loss, interpreting it as a specific instance of policy gradient optimization applied within a single-step episode. To systematically study how the pre-trained distribution shapes the exploration potential for subsequent RL, we propose a generalized pre-training objective that adapts on-policy RL principles to supervised learning. By framing next-token prediction as a stochastic decision process, we introduce a reward-shaping strategy that explicitly balances diversity and precision. Our method employs a positive reward scaling factor to control probability concentration on ground-truth tokens and a rank-aware mechanism that treats high-ranking and low-ranking negative tokens asymmetrically. This allows us to reshape the pre-trained token-output distribution and investigate how to provide a more favorable exploration space for RL, ultimately enhancing end-to-end reasoning performance. Contrary to the intuition that higher distribution entropy facilitates effective exploration, we find that imposing a precision-oriented prior yields a superior exploration space for RL.

Recent advances in language models (LMs) have led to significant improvements in quality on complex NLP tasks, but at the expense of increased inference costs. Cascading offers a simple strategy to achieve more favorable cost-quality tradeoffs: here, a small model is invoked for most "easy" instances, while a few "hard" instances are deferred to the large model. While the principles underpinning cascading are well-studied for classification tasks - with deferral based on predicted class uncertainty favored theoretically and practically - a similar understanding is lacking for generative LM tasks. In this work, we initiate a systematic study of deferral rules for LM cascades. We begin by examining the natural extension of predicted class uncertainty to generative LM tasks, namely, the predicted sequence uncertainty. We show that this measure suffers from the length bias problem, either over- or under-emphasizing outputs based on their lengths. This is because LMs produce a sequence of uncertainty values, one for each output token; and moreover, the number of output tokens is variable across examples. To mitigate this issue, we propose to exploit the richer token-level uncertainty information implicit in generative LMs. We argue that naive predicted sequence uncertainty corresponds to a simple aggregation of these uncertainties. By contrast, we show that incorporating token-level uncertainty through learned post-hoc deferral rules can significantly outperform such simple aggregation strategies, via experiments on a range of natural language benchmarks with FLAN-T5 models. We further show that incorporating embeddings from the smaller model and intermediate layers of the larger model can give an additional boost in the overall cost-quality tradeoff.

Reinforcement learning with verifiable rewards (RLVR) has significantly improved reasoning in large language models (LLMs), yet the token-level mechanisms underlying these improvements remain unclear. We present a systematic empirical study of RLVR's distributional effects organized around three main analyses: (1) token-level characterization of distributional shifts between base and RL models, (2) the impact of token-level distributional shifts on sequence-level reasoning performance through cross-sampling interventions, and (3) fine-grained mechanics of these shifts at the token level. We find that RL fine-tuning induces highly sparse and targeted changes, with only a small fraction of token distributions exhibiting meaningful divergence between the base and RL policies. We further characterize the structure and evolution of these shifts through analyses of token entropy, positional concentration, and reallocation of probability mass. To assess the functional importance of these sparse changes, we conduct cross-sampling experiments that selectively swap token choices between the base and RL models with varying intervention budgets. We show that inserting only a small fraction of RL-sampled tokens into base generations progressively recovers RL performance gains, while injecting a similarly small number of base token choices into otherwise RL-generated sequences collapses performance to base levels, isolating a small set of token-level decisions directly responsible for RLVR's performance gains. Finally, we explore divergence-weighted variants of the advantage signal as a diagnostic intervention, finding that they can yield improvements over baselines. Together, our results shed light on the distributional changes induced by RLVR and provide a fine-grained, token-level lens for understanding RLVR fine-tuning as a targeted refinement process.

To align conditional text generation model outputs with desired behaviors, there has been an increasing focus on training the model using reinforcement learning (RL) with reward functions learned from human annotations. Under this framework, we identify three common cases where high rewards are incorrectly assigned to undesirable patterns: noise-induced spurious correlation, naturally occurring spurious correlation, and covariate shift. We show that even though learned metrics achieve high performance on the distribution of the data used to train the reward function, the undesirable patterns may be amplified during RL training of the text generation model. While there has been discussion about reward gaming in the RL or safety community, in this discussion piece, we would like to highlight reward gaming in the natural language generation (NLG) community using concrete conditional text generation examples and discuss potential fixes and areas for future work.

In this work, we derive sharp non-asymptotic deviation bounds for weighted sums of Dirichlet random variables. These bounds are based on a novel integral representation of the density of a weighted Dirichlet sum. This representation allows us to obtain a Gaussian-like approximation for the sum distribution using geometry and complex analysis methods. Our results generalize similar bounds for the Beta distribution obtained in the seminal paper Alfers and Dinges [1984]. Additionally, our results can be considered a sharp non-asymptotic version of the inverse of Sanov's theorem studied by Ganesh and O'Connell [1999] in the Bayesian setting. Based on these results, we derive new deviation bounds for the Dirichlet process posterior means with application to Bayesian bootstrap. Finally, we apply our estimates to the analysis of the Multinomial Thompson Sampling (TS) algorithm in multi-armed bandits and significantly sharpen the existing regret bounds by making them independent of the size of the arms distribution support.

Reasoning models generate chain-of-thought (CoT) tokens before their final output, but how this affects their vulnerability to jailbreak attacks remains unclear. While traditional language models make refusal decisions at the prompt-response boundary, we find evidence that DeepSeek-R1-Distill-Llama-8B makes these decisions within its CoT generation. We identify a linear direction in activation space during CoT token generation that predicts whether the model will refuse or comply -- termed the "caution" direction because it corresponds to cautious reasoning patterns in the generated text. Ablating this direction from model activations increases harmful compliance, effectively jailbreaking the model. We additionally show that intervening only on CoT token activations suffices to control final outputs, and that incorporating this direction into prompt-based attacks improves success rates. Our findings suggest that the chain-of-thought itself is a promising new target for adversarial manipulation in reasoning models. Code available at https://github.com/ky295/reasoning-manipulation

Fine-tuning large language models (LLMs) on reasoning benchmarks via reinforcement learning requires a specific reward function, often binary, for each benchmark. This comes with two potential limitations: the need to design the reward, and the potentially sparse nature of binary rewards. Here, we systematically investigate rewards derived from the probability or log-probability of emitting the reference answer (or any other prompt continuation present in the data), which have the advantage of not relying on specific verifiers and being available at scale. Several recent works have advocated for the use of similar rewards (e.g., VeriFree, JEPO, RLPR, NOVER). We systematically compare variants of likelihood-based rewards with standard baselines, testing performance both on standard mathematical reasoning benchmarks, and on long-form answers where no external verifier is available. We find that using the log-probability of the reference answer as the reward for chain-of-thought (CoT) learning is the only option that performs well in all setups. This reward is also consistent with the next-token log-likelihood loss used during pretraining. In verifiable settings, log-probability rewards bring comparable or better success rates than reinforcing with standard binary rewards, and yield much better perplexity. In non-verifiable settings, they perform on par with SFT. On the other hand, methods based on probability, such as VeriFree, flatline on non-verifiable settings due to vanishing probabilities of getting the correct answer. Overall, this establishes log-probability rewards as a viable method for CoT fine-tuning, bridging the short, verifiable and long, non-verifiable answer settings.

Large language models (LLMs) are notorious for hallucinating, i.e., producing erroneous claims in their output. Such hallucinations can be dangerous, as occasional factual inaccuracies in the generated text might be obscured by the rest of the output being generally factual, making it extremely hard for the users to spot them. Current services that leverage LLMs usually do not provide any means for detecting unreliable generations. Here, we aim to bridge this gap. In particular, we propose a novel fact-checking and hallucination detection pipeline based on token-level uncertainty quantification. Uncertainty scores leverage information encapsulated in the output of a neural network or its layers to detect unreliable predictions, and we show that they can be used to fact-check the atomic claims in the LLM output. Moreover, we present a novel token-level uncertainty quantification method that removes the impact of uncertainty about what claim to generate on the current step and what surface form to use. Our method Claim Conditioned Probability (CCP) measures only the uncertainty of particular claim value expressed by the model. Experiments on the task of biography generation demonstrate strong improvements for CCP compared to the baselines for six different LLMs and three languages. Human evaluation reveals that the fact-checking pipeline based on uncertainty quantification is competitive with a fact-checking tool that leverages external knowledge.

Ensembling Large Language Models (LLMs) has gained attention as a promising approach to surpass the performance of individual models by leveraging their complementary strengths. In particular, aggregating models' next-token probability distributions to select the next token has been shown to be effective in various tasks. However, while successful for short-form answers, its application to long-form generation remains underexplored. In this paper, we show that using existing ensemble methods in long-form generation requires a careful choice of ensembling positions, since the standard practice of ensembling at every token often degrades performance. We identify two key factors for determining these positions: tokenization mismatch across models and consensus in their next-token probability distributions. Based on this, we propose SAFE, (Stable And Fast LLM Ensembling), a framework that selectively ensembles by jointly considering these factors. To further improve stability, we introduce a probability sharpening strategy that consolidates probabilities spread across multiple sub-word tokens representing the same word into a single representative token. Our experiments on diverse benchmarks, including MATH500 and BBH, demonstrate that SAFE outperforms existing methods in both accuracy and efficiency, with gains achieved even when ensembling fewer than 1% of tokens.

Code generation using large language models (LLMs) is highly sensitive to the choice of tokens during decoding, especially at points of uncertainty that critically affect the generated program's logic. Conventional decoding methods such as greedy search and beam search apply uniform treatment to all tokens, neglecting the unique uncertainty characteristics inherent in code generation, which can result in suboptimal outputs. In this work, we conduct an empirical analysis demonstrating that a significant portion of generation errors arises from incorrect token ranking at high-uncertainty steps, where the ground truth token exists in the candidate set but fails to be ranked first. Inspired by this insight, we introduce AdaDec, an adaptive decoding framework guided by token-level uncertainty quantified via Shannon entropy. AdaDec dynamically learns uncertainty thresholds tailored to each model and employs a pause-then-rerank mechanism with lookahead when the uncertainty surpasses these thresholds. Evaluation on the HumanEval and MBPP benchmarks reveals that AdaDec achieves up to a 15.5% improvement in Pass@1 accuracy compared to greedy decoding, matches or outperforms traditional beam search, and reduces both computational overhead and latency through targeted, selective pausing. Our findings suggest that uncertainty-aware adaptive decoding holds considerable potential for enhancing both the reliability and efficiency of code generation with LLMs.

Pre-tokenization, the initial step in many modern tokenization pipelines, segments text into smaller units called pretokens, typically splitting on whitespace and punctuation. While this process encourages having full, individual words as tokens, it introduces a fundamental limitation in most tokenization algorithms such as Byte Pair Encoding (BPE). Specifically, pre-tokenization causes the distribution of tokens in a corpus to heavily skew towards common, full-length words. This skewed distribution limits the benefits of expanding to larger vocabularies, since the additional tokens appear with progressively lower counts. To overcome this barrier, we propose BoundlessBPE, a modified BPE algorithm that relaxes the pretoken boundary constraint. Our approach selectively merges two complete pretokens into a larger unit we term a superword. Superwords are not necessarily semantically cohesive. For example, the pretokens " of" and " the" might be combined to form the superword " of the". This merging strategy results in a substantially more uniform distribution of tokens across a corpus than standard BPE, and compresses text more effectively, with an approximate 20% increase in bytes per token.

Reinforcement learning (RL) is a pivotal task for enhancing Large Language Model (LLM) reasoning. Conventional algorithms, however, typically adhere to a coarse-grained credit assignment paradigm, applying a uniform reward to all tokens in a sequence, a critical flaw in long-chain reasoning tasks. In this paper, we address this challenge and propose Dynamic Entropy Weighting, a novel mechanism that facilitates fine-grained rewards through two new algorithms: Group Token Policy Optimization (GTPO), which assigns an entropy-weighted reward to each token, and the analogous algorithm Sequence-Level GRPO (GRPO-S). Our approach is founded on the hypothesis that high policy entropy within a reasoning path is a powerful heuristic for cognitive effort at pivotal junctures, which can be repurposed into a learning signal. By repurposing policy entropy for reward shaping, we achieve true per-token credit assignment. Experimental results across challenging reasoning benchmarks validate the superiority of our approach, showing our methods significantly outperform a strong DAPO baseline and confirming our entropy-weighting mechanism as the key driver of this performance boost.

Reinforcement learning (RL) post-training has increasingly demonstrated strong ability to elicit reasoning behaviors in large language models (LLMs). For training efficiency, rollouts are typically generated in an off-policy manner using an older sampling policy and then used to update the current target policy. To correct the resulting discrepancy between the sampling and target policies, most existing RL objectives rely on a token-level importance sampling ratio, primarily due to its computational simplicity and numerical stability. However, we observe that token-level correction often leads to unstable training dynamics when the degree of off-policyness is large. In this paper, we revisit LLM policy optimization under off-policy conditions and show that the theoretically rigorous correction term is the prefix importance ratio, and that relaxing it to a token-level approximation can induce instability in RL post-training. To stabilize LLM optimization under large off-policy drift, we propose a simple yet effective objective, Minimum Prefix Ratio (MinPRO). MinPRO replaces the unstable cumulative prefix ratio with a non-cumulative surrogate based on the minimum token-level ratio observed in the preceding prefix. Extensive experiments on both dense and mixture-of-experts LLMs, across multiple mathematical reasoning benchmarks, demonstrate that MinPRO substantially improves training stability and peak performance in off-policy regimes.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a powerful approach to enhancing the reasoning capabilities of Large Language Models (LLMs), while its mechanisms are not yet well understood. In this work, we undertake a pioneering exploration of RLVR through the novel perspective of token entropy patterns, comprehensively analyzing how different tokens influence reasoning performance. By examining token entropy patterns in Chain-of-Thought (CoT) reasoning, we observe that only a small fraction of tokens exhibit high entropy, and these tokens act as critical forks that steer the model toward diverse reasoning pathways. Furthermore, studying how entropy patterns evolve during RLVR training reveals that RLVR largely adheres to the base model's entropy patterns, primarily adjusting the entropy of high-entropy tokens. These findings highlight the significance of high-entropy tokens (i.e., forking tokens) to RLVR. We ultimately improve RLVR by restricting policy gradient updates to forking tokens and uncover a finding even beyond the 80/20 rule: utilizing only 20% of the tokens while maintaining performance comparable to full-gradient updates on the Qwen3-8B base model and significantly surpassing full-gradient updates on the Qwen3-32B (+11.04 on AIME'25 and +7.71 on AIME'24) and Qwen3-14B (+4.79 on AIME'25 and +5.21 on AIME'24) base models, highlighting a strong scaling trend. In contrast, training exclusively on the 80% lowest-entropy tokens leads to a marked decline in performance. These findings indicate that the efficacy of RLVR primarily arises from optimizing the high-entropy tokens that decide reasoning directions. Collectively, our results highlight the potential to understand RLVR through a token-entropy perspective and optimize RLVR by leveraging high-entropy minority tokens to further improve LLM reasoning.

Can a mere next-token predictor faithfully model human intelligence? We crystallize this intuitive concern, which is fragmented in the literature. As a starting point, we argue that the two often-conflated phases of next-token prediction -- autoregressive inference and teacher-forced training -- must be treated distinctly. The popular criticism that errors can compound during autoregressive inference, crucially assumes that teacher-forcing has learned an accurate next-token predictor. This assumption sidesteps a more deep-rooted problem we expose: in certain classes of tasks, teacher-forcing can simply fail to learn an accurate next-token predictor in the first place. We describe a general mechanism of how teacher-forcing can fail, and design a minimal planning task where both the Transformer and the Mamba architecture empirically fail in that manner -- remarkably, despite the task being straightforward to learn. We provide preliminary evidence that this failure can be resolved when training to predict multiple tokens in advance. We hope this finding can ground future debates and inspire explorations beyond the next-token prediction paradigm. We make our code available under https://github.com/gregorbachmann/Next-Token-Failures

Large language models (LLMs) are increasingly deployed as multi-step decision-making agents, where effective reward design is essential for guiding learning. Although recent work explores various forms of reward shaping and step-level credit assignment, a key signal remains largely overlooked: the intrinsic uncertainty of LLMs. Uncertainty reflects model confidence, reveals where exploration is needed, and offers valuable learning cues even in failed trajectories. We introduce SELAUR: Self Evolving LLM Agent via Uncertainty-aware Rewards, a reinforcement learning framework that incorporates uncertainty directly into the reward design. SELAUR integrates entropy-, least-confidence-, and margin-based metrics into a combined token-level uncertainty estimate, providing dense confidence-aligned supervision, and employs a failure-aware reward reshaping mechanism that injects these uncertainty signals into step- and trajectory-level rewards to improve exploration efficiency and learning stability. Experiments on two benchmarks, ALFWorld and WebShop, show that our method consistently improves success rates over strong baselines. Ablation studies further demonstrate how uncertainty signals enhance exploration and robustness.

Distinct-n scoreLi2016 is a widely used automatic metric for evaluating diversity in language generation tasks. However, we observed that the original approach for calculating distinct scores has evident biases that tend to assign higher penalties to longer sequences. We refine the calculation of distinct scores by scaling the number of distinct tokens based on their expectations. We provide both empirical and theoretical evidence to show that our method effectively removes the biases existing in the original distinct score. Our experiments show that our proposed metric, Expectation-Adjusted Distinct (EAD), correlates better with human judgment in evaluating response diversity. To foster future research, we provide an example implementation at https://github.com/lsy641/Expectation-Adjusted-Distinct.

We introduce a simple, yet novel entropy-based framework to drive token efficiency in large language models during reasoning tasks. Our approach uses Shannon entropy from token-level logprobs as a confidence signal to enable early stopping, achieving 25-50% computational savings while maintaining task accuracy. Crucially, we demonstrate that entropy-based confidence calibration represents an emergent property of advanced post-training optimization present in modern reasoning models but notably absent in standard instruction-tuned and pre-trained models (Llama 3.3 70B). We show that the entropy threshold to stop reasoning varies from model to model but can be calculated easily in one shot using only a few examples from existing reasoning datasets. Our results indicate that advanced reasoning models often know that they've gotten a correct answer early on, and that this emergent confidence awareness can be exploited to save tokens and reduce latency. The framework demonstrates consistent performance across reasoning-optimized model families with 25-50% computational cost reduction while preserving accuracy, revealing that confidence mechanisms represent a distinguishing characteristic of modern post-trained reasoning systems versus their predecessors.

Large language models (LLMs) reason over discrete token ID sequences, yet modern subword tokenizers routinely produce non-unique encodings: multiple token ID sequences can detokenize to identical surface strings. This representational mismatch creates an unmeasured fragility wherein reasoning processes can fail. LLMs may treat two internal representations as distinct "words" even when they are semantically identical at the text level. In this work, we show that tokenization can betray LLM reasoning through one-to-many token ID mappings. We introduce a tokenization-consistency probe that requires models to replace designated target words in context while leaving all other content unchanged. The task is intentionally simple at the surface level, enabling us to attribute failures to tokenizer-detokenizer artifacts rather than to knowledge gaps or parameter limitations. Through analysis of over 11000 replacement trials across state-of-the-art open-source LLMs, we find a non-trivial rate of outputs exhibit phantom edits: cases where models operate under the illusion of correct reasoning, a phenomenon arising from tokenizer-induced representational defects. We further analyze these cases and provide a taxonomy of eight systematic tokenizer artifacts, including whitespace-boundary shifts and intra-word resegmentation. These findings indicate that part of apparent reasoning deficiency originates in the tokenizer layer, motivating tokenizer-level remedies before incurring the cost of training ever-larger models on ever-larger corpora.

Accurately quantifying a large language model's (LLM) predictive uncertainty is crucial for judging the reliability of its answers. While most existing research focuses on short, directly answerable questions with closed-form outputs (e.g., multiple-choice), involving intermediate reasoning steps in LLM responses is increasingly important. This added complexity complicates uncertainty quantification (UQ) because the probabilities assigned to answer tokens are conditioned on a vast space of preceding reasoning tokens. Direct marginalization is infeasible, and the dependency inflates probability estimates, causing overconfidence in UQ. To address this, we propose UQAC, an efficient method that narrows the reasoning space to a tractable size for marginalization. UQAC iteratively constructs an "attention chain" of tokens deemed "semantically crucial" to the final answer via a backtracking procedure. Starting from the answer tokens, it uses attention weights to identify the most influential predecessors, then iterates this process until reaching the input tokens. Similarity filtering and probability thresholding further refine the resulting chain, allowing us to approximate the marginal probabilities of the answer tokens, which serve as the LLM's confidence. We validate UQAC on multiple reasoning benchmarks with advanced open-source LLMs, demonstrating that it consistently delivers reliable UQ estimates with high computational efficiency.

A unique aspect of ColBERT is its use of [MASK] tokens in queries to score documents (query augmentation). Prior work shows [MASK] tokens weighting non-[MASK] query terms, emphasizing certain tokens over others , rather than introducing whole new terms as initially proposed. We begin by demonstrating that a term weighting behavior previously reported for [MASK] tokens in ColBERTv1 holds for ColBERTv2. We then examine the effect of changing the number of [MASK] tokens from zero to up to four times past the query input length used in training, both for first stage retrieval, and for scoring candidates, observing an initial decrease in performance with few [MASK]s, a large increase when enough [MASK]s are added to pad queries to an average length of 32, then a plateau in performance afterwards. Additionally, we compare baseline performance to performance when the query length is extended to 128 tokens, and find that differences are small (e.g., within 1% on various metrics) and generally statistically insignificant, indicating performance does not collapse if ColBERT is presented with more [MASK] tokens than expected.

With adversarial or otherwise normal prompts, existing large language models (LLM) can be pushed to generate toxic discourses. One way to reduce the risk of LLMs generating undesired discourses is to alter the training of the LLM. This can be very restrictive due to demanding computation requirements. Other methods rely on rule-based or prompt-based token elimination, which are limited as they dismiss future tokens and the overall meaning of the complete discourse. Here, we center detoxification on the probability that the finished discourse is ultimately considered toxic. That is, at each point, we advise against token selections proportional to how likely a finished text from this point will be toxic. To this end, we formally extend the dead-end theory from the recent reinforcement learning (RL) literature to also cover uncertain outcomes. Our approach, called rectification, utilizes a separate but significantly smaller model for detoxification, which can be applied to diverse LLMs as long as they share the same vocabulary. Importantly, our method does not require access to the internal representations of the LLM, but only the token probability distribution at each decoding step. This is crucial as many LLMs today are hosted in servers and only accessible through APIs. When applied to various LLMs, including GPT-3, our approach significantly improves the generated discourse compared to the base LLMs and other techniques in terms of both the overall language and detoxification performance.

While language models have exceptional capabilities at text generation, they lack a natural inductive bias for emitting numbers and thus struggle in tasks involving reasoning over quantities, especially arithmetics. This has particular relevance in scientific datasets where combinations of text and numerical data are abundant. One fundamental limitation is the nature of the CE loss, which assumes a nominal (categorical) scale and thus cannot convey proximity between generated number tokens. As a remedy, we here present two versions of a number token loss. The first is based on an L_p loss between the ground truth token value and the weighted sum of the predicted class probabilities. The second loss minimizes the Wasserstein-1 distance between the distribution of the predicted output probabilities and the ground truth distribution. These regression-like losses can easily be added to any language model and extend the CE objective during training. We compare the proposed schemes on a mathematics dataset against existing tokenization, encoding, and decoding schemes for improving number representation in language models. Our results reveal a significant improvement in numerical accuracy when equipping a standard T5 model with the proposed loss schemes.

Frontier models that generate extended reasoning traces inadvertently produce rich token sequences that can facilitate model distillation. Recognizing this vulnerability, model owners may seek sampling strategies that limit the effectiveness of distillation without compromising model performance. Antidistillation sampling provides exactly this capability. By strategically modifying a model's next-token probability distribution, antidistillation sampling poisons reasoning traces, rendering them significantly less effective for distillation while preserving the model's practical utility. For further details, see https://antidistillation.com.

This paper addresses a practical task: High-Resolution Image Anomaly Detection (HRIAD). In comparison to conventional image anomaly detection for low-resolution images, HRIAD imposes a heavier computational burden and necessitates superior global information capture capacity. To tackle HRIAD, this paper translates image anomaly detection into visual token prediction and proposes VarAD based on visual autoregressive modeling for token prediction. Specifically, VarAD first extracts multi-hierarchy and multi-directional visual token sequences, and then employs an advanced model, Mamba, for visual autoregressive modeling and token prediction. During the prediction process, VarAD effectively exploits information from all preceding tokens to predict the target token. Finally, the discrepancies between predicted tokens and original tokens are utilized to score anomalies. Comprehensive experiments on four publicly available datasets and a real-world button inspection dataset demonstrate that the proposed VarAD achieves superior high-resolution image anomaly detection performance while maintaining lightweight, rendering VarAD a viable solution for HRIAD. Code is available at https://github.com/caoyunkang/VarAD{https://github.com/caoyunkang/VarAD}.

The problem of estimating an unknown discrete distribution from its samples is a fundamental tenet of statistical learning. Over the past decade, it attracted significant research effort and has been solved for a variety of divergence measures. Surprisingly, an equally important problem, estimating an unknown Markov chain from its samples, is still far from understood. We consider two problems related to the min-max risk (expected loss) of estimating an unknown k-state Markov chain from its n sequential samples: predicting the conditional distribution of the next sample with respect to the KL-divergence, and estimating the transition matrix with respect to a natural loss induced by KL or a more general f-divergence measure. For the first measure, we determine the min-max prediction risk to within a linear factor in the alphabet size, showing it is Omega(kloglog n / n) and O(k^2loglog n / n). For the second, if the transition probabilities can be arbitrarily small, then only trivial uniform risk upper bounds can be derived. We therefore consider transition probabilities that are bounded away from zero, and resolve the problem for essentially all sufficiently smooth f-divergences, including KL-, L_2-, Chi-squared, Hellinger, and Alpha-divergences.

Different large language models (LLMs) exhibit diverse strengths and weaknesses, and LLM ensemble serves as a promising approach to integrate their complementary capabilities. Despite substantial progress in improving ensemble quality, limited attention has been paid to the robustness of ensembles against potential erroneous signals, which often arise from heterogeneous tokenization schemes and varying model expertise. Our analysis shows that ensemble failures typically arise from both the token level and the model level: the former reflects severe disagreement in token predictions, while the latter involves low confidence and pronounced disparities among models. In light of this, we propose CoRE, a plug-and-play technique that harnesses model consistency for robust LLM ensemble, which can be seamlessly integrated with diverse ensemble methods. Token-level consistency captures fine-grained disagreements by applying a low-pass filter to downweight uncertain tokens with high inconsistency, often due to token misalignment, thereby improving robustness at a granular level. Model-level consistency models global agreement by promoting model outputs with high self-confidence and minimal divergence from others, enhancing robustness at a coarser level. Extensive experiments across diverse benchmarks, model combinations, and ensemble strategies demonstrate that CoRE consistently improves ensemble performance and robustness.

As demand for LLM inference grows, it is becoming increasingly important that providers and their customers can verify that inference processes are performed correctly, without errors or tampering. However, re-running the same inference process twice often leads to different results due to benign numerical noise, making it difficult to distinguish legitimate variation from actual problems. To address this problem, we introduce Token-DiFR (Token-Divergence-From-Reference), a method for verifying inference outputs by comparing generated tokens against predictions made by a trusted reference implementation conditioned on the same random seed. Sampling seed synchronization tightly constrains valid outputs, leaving providers minimal room to deviate from correct inference, which allows output tokens themselves to serve as auditable evidence of correctness at zero additional cost to the provider. Token-DiFR reliably identifies sampling errors, simulated bugs, and model quantization, detecting 4-bit quantization with AUC > 0.999 within 300 output tokens. For applications requiring sample-efficient forward-pass verification, we additionally introduce Activation-DiFR, a scheme that uses random orthogonal projections to compress activations into compact fingerprints for subsequent verification. Activation-DiFR detects 4-bit quantization with AUC > 0.999 using just 2 output tokens, while reducing communication overhead by 25-75% relative to existing methods. We release an open-source integration with vLLM to accelerate practical deployment of verifiable inference.

Recent advances have demonstrated that integrating reinforcement learning with rule-based rewards can significantly enhance the reasoning capabilities of large language models, even without supervised fine-tuning. However, prevalent reinforcement learning algorithms such as GRPO and its variants like DAPO, suffer from a coarse granularity issue when computing the advantage. Specifically, they compute rollout-level advantages that assign identical values to every token within a sequence, failing to capture token-specific contributions and hindering effective learning. To address this limitation, we propose Key-token Advantage Estimation (KTAE) - a novel algorithm that estimates fine-grained, token-level advantages without introducing additional models. KTAE leverages the correctness of sampled rollouts and applies statistical analysis to quantify the importance of individual tokens within a sequence to the final outcome. This quantified token-level importance is then combined with the rollout-level advantage to obtain a more fine-grained token-level advantage estimation. Empirical results show that models trained with GRPO+KTAE and DAPO+KTAE outperform baseline methods across five mathematical reasoning benchmarks. Notably, they achieve higher accuracy with shorter responses and even surpass R1-Distill-Qwen-1.5B using the same base model.

Anomaly detection aims at detecting unexpected behaviours in the data. Because anomaly detection is usually an unsupervised task, traditional anomaly detectors learn a decision boundary by employing heuristics based on intuitions, which are hard to verify in practice. This introduces some uncertainty, especially close to the decision boundary, that may reduce the user trust in the detector's predictions. A way to combat this is by allowing the detector to reject examples with high uncertainty (Learning to Reject). This requires employing a confidence metric that captures the distance to the decision boundary and setting a rejection threshold to reject low-confidence predictions. However, selecting a proper metric and setting the rejection threshold without labels are challenging tasks. In this paper, we solve these challenges by setting a constant rejection threshold on the stability metric computed by ExCeeD. Our insight relies on a theoretical analysis of such a metric. Moreover, setting a constant threshold results in strong guarantees: we estimate the test rejection rate, and derive a theoretical upper bound for both the rejection rate and the expected prediction cost. Experimentally, we show that our method outperforms some metric-based methods.

Conventional wisdom holds that autoregressive models for image generation are typically accompanied by vector-quantized tokens. We observe that while a discrete-valued space can facilitate representing a categorical distribution, it is not a necessity for autoregressive modeling. In this work, we propose to model the per-token probability distribution using a diffusion procedure, which allows us to apply autoregressive models in a continuous-valued space. Rather than using categorical cross-entropy loss, we define a Diffusion Loss function to model the per-token probability. This approach eliminates the need for discrete-valued tokenizers. We evaluate its effectiveness across a wide range of cases, including standard autoregressive models and generalized masked autoregressive (MAR) variants. By removing vector quantization, our image generator achieves strong results while enjoying the speed advantage of sequence modeling. We hope this work will motivate the use of autoregressive generation in other continuous-valued domains and applications.

Supervised fine-tuning (SFT) is a fundamental post-training strategy to align Large Language Models (LLMs) with human intent. However, traditional SFT often ignores the one-to-many nature of language by forcing alignment with a single reference answer, leading to the model overfitting to non-core expressions. Although our empirical analysis suggests that introducing multiple reference answers can mitigate this issue, the prohibitive data and computational costs necessitate a strategic shift: prioritizing the mitigation of single-reference overfitting over the costly pursuit of answer diversity. To achieve this, we reveal the intrinsic connection between token probability and semantic importance: high-probability tokens carry the core logical framework, while low-probability tokens are mostly replaceable expressions. Based on this insight, we propose ProFit, which selectively masks low-probability tokens to prevent surface-level overfitting. Extensive experiments confirm that ProFit consistently outperforms traditional SFT baselines on general reasoning and mathematical benchmarks.

We investigate the relationship between the geometry of token embeddings and their role in the next token prediction within transformer models. An important aspect of this connection uses the notion of empirical measure, which encodes the distribution of token point clouds across transformer layers and drives the evolution of token representations in the mean-field interacting picture. We use metrics such as intrinsic dimension, neighborhood overlap, and cosine similarity to observationally probe these empirical measures across layers. To validate our approach, we compare these metrics to a dataset where the tokens are shuffled, which disrupts the syntactic and semantic structure. Our findings reveal a correlation between the geometric properties of token embeddings and the cross-entropy loss of next token predictions, implying that prompts with higher loss values have tokens represented in higher-dimensional spaces.

Language models are often trained to maximize the likelihood of the next token given past tokens in the training dataset. However, during inference time, they are utilized differently, generating text sequentially and auto-regressively by using previously generated tokens as input to predict the next one. Marginal differences in predictions at each step can cascade over successive steps, resulting in different distributions from what the models were trained for and potentially leading to unpredictable behavior. This paper proposes two simple approaches based on model own generation to address this discrepancy between the training and inference time. Our first approach is Batch-Scheduled Sampling, where, during training, we stochastically choose between the ground-truth token from the dataset and the model's own generated token as input to predict the next token. This is done in an offline manner, modifying the context window by interleaving ground-truth tokens with those generated by the model. Our second approach is Reference-Answer-based Correction, where we explicitly incorporate a self-correction capability into the model during training. This enables the model to effectively self-correct the gaps between the generated sequences and the ground truth data without relying on an external oracle model. By incorporating our proposed strategies during training, we have observed an overall improvement in performance compared to baseline methods, as demonstrated by our extensive experiments using summarization, general question-answering, and math question-answering tasks.

Large-scale language models often learn behaviors that are misaligned with user expectations. Generated text may contain offensive or toxic language, contain significant repetition, or be of a different sentiment than desired by the user. We consider the task of unlearning these misalignments by fine-tuning the language model on signals of what not to do. We introduce Quantized Reward Konditioning (Quark), an algorithm for optimizing a reward function that quantifies an (un)wanted property, while not straying too far from the original model. Quark alternates between (i) collecting samples with the current language model, (ii) sorting them into quantiles based on reward, with each quantile identified by a reward token prepended to the language model's input, and (iii) using a standard language modeling loss on samples from each quantile conditioned on its reward token, while remaining nearby the original language model via a KL-divergence penalty. By conditioning on a high-reward token at generation time, the model generates text that exhibits less of the unwanted property. For unlearning toxicity, negative sentiment, and repetition, our experiments show that Quark outperforms both strong baselines and state-of-the-art reinforcement learning methods like PPO (Schulman et al. 2017), while relying only on standard language modeling primitives.

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

Prompt optimization improves language models without updating their weights by searching for a better system prompt, but its effectiveness varies widely across tasks. We study what makes a task amenable to prompt optimization. We show that the reward variance across different system prompts can be decomposed into two components: variance among responses, which captures generation stochasticity, and variance among system prompts, which captures differences in system prompt quality. Prompt optimization succeeds when variance among system prompts is sufficiently large, but fails when variance among responses dominates the variance of the system prompts. Surprisingly, we further show that scaling to more user prompts can hurt optimization by reducing variance among system prompts, especially on heterogeneous datasets where different user prompts favor different system prompts. Motivated by this insight, we propose p1, a simple user prompt filtering method that selects a small subset of user prompts with high variance across candidate system prompts. This subset of user prompts allows one to distinguish a good system prompt from a bad one, making system optimization easier. Experiments on reasoning benchmarks show that p1 substantially improves prompt optimization over training on the full dataset and outperforms strong baselines such as GEPA. Notably, training on only two prompts from AIME 24 yields a system prompt that generalizes well to other reasoning benchmarks.

Diffusion language models (DLMs) have recently emerged as a strong alternative to autoregressive models by enabling parallel text generation. To improve inference efficiency and KV-cache compatibility, prior work commonly adopts block-based diffusion, decoding tokens block by block. However, this paradigm suffers from a structural limitation that we term Boundary-Induced Context Truncation (BICT): undecoded tokens near block boundaries are forced to commit without access to nearby future context, even when such context could substantially reduce uncertainty. This limitation degrades decoding certainty and generation quality, especially for tasks requiring precise reasoning, such as mathematical problem solving and code generation. We propose Deferred Commitment Decoding (DCD), a novel, training-free decoding strategy that mitigates this issue. DCD maintains a certainty-aware sliding window over masked tokens, resolving low-uncertainty tokens early while deferring high-uncertainty tokens until sufficient contextual evidence becomes available. Extensive experiments across multiple diffusion language models, benchmarks, and caching configurations show that DCD improves generation accuracy by 1.73% with comparable time on average compared to fixed block-based diffusion methods, with the most significant improvement reaching 16.5%. These results demonstrate that deferring token commitment based on uncertainty is a simple yet effective principle for improving both the quality and efficiency of diffusion language model decoding.

While speculative decoding has recently appeared as a promising direction for accelerating the inference of large language models (LLMs), the speedup and scalability are strongly bounded by the token acceptance rate. Prevalent methods usually organize predicted tokens as independent chains or fixed token trees, which fails to generalize to diverse query distributions. In this paper, we propose DySpec, a faster speculative decoding algorithm with a novel dynamic token tree structure. We begin by bridging the draft distribution and acceptance rate from intuitive and empirical clues, and successfully show that the two variables are strongly correlated. Based on this, we employ a greedy strategy to dynamically expand the token tree at run time. Theoretically, we show that our method can achieve optimal results under mild assumptions. Empirically, DySpec yields a higher acceptance rate and speedup than fixed trees. DySpec can drastically improve the throughput and reduce the latency of token generation across various data distribution and model sizes, which significantly outperforms strong competitors, including Specinfer and Sequoia. Under low temperature setting, DySpec can improve the throughput up to 9.1times and reduce the latency up to 9.4times on Llama2-70B. Under high temperature setting, DySpec can also improve the throughput up to 6.21times, despite the increasing difficulty of speculating more than one token per step for draft model.

This paper presents the Entropy-Driven Unified Process Reward Model (EDU-PRM), a novel framework that approximates state-of-the-art performance in process supervision while drastically reducing training costs. EDU-PRM introduces an entropy-guided dynamic step partitioning mechanism, using logit distribution entropy to pinpoint high-uncertainty regions during token generation dynamically. This self-assessment capability enables precise step-level feedback without manual fine-grained annotation, addressing a critical challenge in process supervision. Experiments on the Qwen2.5-72B model with only 7,500 EDU-PRM-generated training queries demonstrate accuracy closely approximating the full Qwen2.5-72B-PRM (71.1% vs. 71.6%), achieving a 98% reduction in query cost compared to prior methods. This work establishes EDU-PRM as an efficient approach for scalable process reward model training.

Using a 100-day symmetric window around the January 2025 U.S. presidential inauguration, non-parametric statistical methods with bootstrap resampling (10,000 iterations) analyze distributional properties and anomalies. Results indicate a statistically significant 3.61\% Indonesian rupiah depreciation post-inauguration, with a large effect size (Cliff's Delta = -0.9224, CI: [-0.9727, -0.8571]). Central tendency shifted markedly, yet volatility remained stable (variance ratio = 0.9061, p = 0.504). Four significant anomalies exhibiting temporal clustering are detected. These findings provide quantitative evidence of political transition effects on emerging market currencies, highlighting implications for monetary policy and currency risk management.

Diffusion models have emerged as a promising approach for text generation, with recent works falling into two main categories: discrete and continuous diffusion models. Discrete diffusion models apply token corruption independently using categorical distributions, allowing for different diffusion progress across tokens but lacking fine-grained control. Continuous diffusion models map tokens to continuous spaces and apply fine-grained noise, but the diffusion progress is uniform across tokens, limiting their ability to capture semantic nuances. To address these limitations, we propose \underline{N}on-simultan\underline{e}ous C\underline{o}ntinuous \underline{Diff}usion Models (NeoDiff), a novel diffusion model that integrates the strengths of both discrete and continuous approaches. NeoDiff introduces a Poisson diffusion process for the forward process, enabling a flexible and fine-grained noising paradigm, and employs a time predictor for the reverse process to adaptively modulate the denoising progress based on token semantics. Furthermore, NeoDiff utilizes an optimized schedule for inference to ensure more precise noise control and improved performance. Our approach unifies the theories of discrete and continuous diffusion models, offering a more principled and effective framework for text generation. Experimental results on several text generation tasks demonstrate NeoDiff's superior performance compared to baselines of non-autoregressive continuous and discrete diffusion models, iterative-based methods and autoregressive diffusion-based methods. These results highlight NeoDiff's potential as a powerful tool for generating high-quality text and advancing the field of diffusion-based text generation.

Large Language Models (LLMs) generate longform text by successively sampling the next token based on the probability distribution of the token vocabulary at each decoding step. Current popular truncation sampling methods such as top-p sampling, also known as nucleus sampling, often struggle to balance coherence and creativity in generating text, particularly when using higher temperatures. To address this issue, we propose min-p, a dynamic truncation sampling method, that establishes a minimum base percentage threshold for tokens, which the scales according to the probability of the top candidate token. Through experiments on several benchmarks, such as GPQA, GSM8K and AlpacaEval Creative Writing, we demonstrate that min-p improves the coherence and quality of generated text even at high temperatures, while also facilitating more creative and diverse outputs compared to top-p and other sampling methods. As of writing, min-p has been adopted by multiple open-source LLM implementations, and have been independently assessed by members of the open-source LLM community, further validating its practical utility and potential.

Current reinforcement learning from human feedback (RLHF) pipelines for large language model (LLM) alignment typically assign scalar rewards to sequences, using the final token as a surrogate indicator for the quality of the entire sequence. However, this leads to sparse feedback and suboptimal token-level credit assignment. In this work, we frame reward shaping as an optimization problem focused on token-level credit assignment. We propose a reward-shaping function leveraging explainability methods such as SHAP and LIME to estimate per-token rewards from the reward model. To learn parameters of this shaping function, we employ a bilevel optimization framework that integrates Bayesian Optimization and policy training to handle noise from the token reward estimates. Our experiments show that achieving a better balance of token-level reward attribution leads to performance improvements over baselines on downstream tasks and finds an optimal policy faster during training. Furthermore, we show theoretically that explainability methods that are feature additive attribution functions maintain the optimal policy as the original reward.

A common approach to explain NLP models, is to use importance measures that express which tokens are important for a prediction. Unfortunately, such explanations are often wrong despite being persuasive. Therefore, it is essential to measure their faithfulness. One such metric is if tokens are truly important, then masking them should result in worse model performance. However, token masking introduces out-of-distribution issues and existing solutions are computationally expensive and employ proxy-models. Furthermore, other metrics are very limited in scope. In this work, we propose an inherently faithfulness measurable model that addresses these challenges. This is achieved by using a novel fine-tuning method that incorporates masking, such that masking tokens become in-distribution by design. This differs from existing approaches, which are completely model-agnostic but are inapplicable in practice. We demonstrate the generality of our approach by applying it to various tasks and validate it using statistical in-distribution tests. Additionally, because masking is in-distribution, importance measures which themselves use masking become more faithful, thus our model becomes more explainable.

Large reasoning models have recently demonstrated strong performance on complex tasks that require long chain-of-thought reasoning, through supervised fine-tuning on large-scale and high-quality datasets. To construct such datasets, existing pipelines generate long reasoning data from more capable Large Language Models (LLMs) and apply manually heuristic or naturalness-based selection methods to filter high-quality samples. Despite the proven effectiveness of naturalness-based data selection, which ranks data by the average log probability assigned by LLMs, our analysis shows that, when applied to LLM reasoning datasets, it systematically prefers samples with longer reasoning steps (i.e., more tokens per step) rather than higher-quality ones, a phenomenon we term step length confounding. Through quantitative analysis, we attribute this phenomenon to low-probability first tokens in reasoning steps; longer steps dilute their influence, thereby inflating the average log probabilities. To address this issue, we propose two variant methods: ASLEC-DROP, which drops first-token probabilities when computing average log probability, and ASLEC-CASL, which applies a causal debiasing regression to remove the first tokens' confounding effect. Experiments across four LLMs and five evaluation benchmarks demonstrate the effectiveness of our approach in mitigating the step length confounding problem.

There is a growing literature on reasoning by large language models (LLMs), but the discussion on the uncertainty in their responses is still lacking. Our aim is to assess the extent of confidence that LLMs have in their answers and how it correlates with accuracy. Confidence is measured (i) qualitatively in terms of persistence in keeping their answer when prompted to reconsider, and (ii) quantitatively in terms of self-reported confidence score. We investigate the performance of three LLMs -- GPT4o, GPT4-turbo and Mistral -- on two benchmark sets of questions on causal judgement and formal fallacies and a set of probability and statistical puzzles and paradoxes. Although the LLMs show significantly better performance than random guessing, there is a wide variability in their tendency to change their initial answers. There is a positive correlation between qualitative confidence and accuracy, but the overall accuracy for the second answer is often worse than for the first answer. There is a strong tendency to overstate the self-reported confidence score. Confidence is only partially explained by the underlying token-level probability. The material effects of prompting on qualitative confidence and the strong tendency for overconfidence indicate that current LLMs do not have any internally coherent sense of confidence.

Supervised Fine-Tuning (SFT) is the standard paradigm for domain adaptation, yet it frequently incurs the cost of catastrophic forgetting. In sharp contrast, on-policy Reinforcement Learning (RL) effectively preserves general capabilities. We investigate this discrepancy and identify a fundamental distributional gap: while RL aligns with the model's internal belief, SFT forces the model to fit external supervision. This mismatch often manifests as "Confident Conflicts" tokens characterized by low probability but low entropy. In these instances, the model is highly confident in its own prediction but is forced to learn a divergent ground truth, triggering destructive gradient updates. To address this, we propose Entropy-Adaptive Fine-Tuning (EAFT). Unlike methods relying solely on prediction probability, EAFT utilizes token-level entropy as a gating mechanism to distinguish between epistemic uncertainty and knowledge conflict. This allows the model to learn from uncertain samples while suppressing gradients on conflicting data. Extensive experiments on Qwen and GLM series (ranging from 4B to 32B parameters) across mathematical, medical, and agentic domains confirm our hypothesis. EAFT consistently matches the downstream performance of standard SFT while significantly mitigating the degradation of general capabilities.

Common evaluation paradigms for language models focus on scoring single responses through accuracy metrics or proper scoring rules, failing to capture the full richness of a model's belief state. Recent work illustrates that language models hallucinate in-part because they are optimised to be good test-takers under binary scoring schemes that reward any answer over abstention. While this insight naturally leads to penalty-based approaches, they ignore crucial distinctions in how models distribute uncertainty, for example between hedging toward incorrect answers versus hedging toward "I don't know" responses. A novel evaluation metric, the Distributional Correctness Score (DCS), is introduced to solve this problem, i.e., of not considering a model's entire probability distribution over answer choices. DCS naturally distinguishes between harmful overconfidence in wrong answers and uncertainty expressed through abstention, providing scores in an interpretable default range. Through theoretical analysis and illustrative examples, DCS is demonstrated to offer a more nuanced and aligned evaluation paradigm that incentivises models to express genuine uncertainty rather than guessing. Adapting 12 existing evaluation benchmarks to DCS's variants and measuring performance on six language models reveals that for half of the tested benchmarks scores are negative across all tested models, indicating significant tendencies towards hallucination.

Numerous efforts have been made to extend the ``next token prediction'' paradigm to visual contents, aiming to create a unified approach for both image generation and understanding. Nevertheless, attempts to generate images through autoregressive modeling with discrete tokens have been plagued by issues such as low visual fidelity, distorted outputs, and failure to adhere to complex instructions when rendering intricate details. These shortcomings are likely attributed to cumulative errors during autoregressive inference or information loss incurred during the discretization process. Probably due to this challenge, recent research has increasingly shifted toward jointly training image generation with diffusion objectives and language generation with autoregressive objectives, moving away from unified modeling approaches. In this work, we demonstrate that reinforcement learning can effectively mitigate artifacts and largely enhance the generation quality of a discrete autoregressive modeling method, thereby enabling seamless integration of image and language generation. Our framework comprises a semantic image tokenizer, a unified autoregressive model for both language and images, and an offline diffusion decoder for image generation, termed X-Omni. X-Omni achieves state-of-the-art performance in image generation tasks using a 7B language model, producing images with high aesthetic quality while exhibiting strong capabilities in following instructions and rendering long texts.

The development of state-of-the-art large language models is commonly understood as a two-stage process involving pre-training and post-training. We point out the need for an additional intermediate stage called reinforcement mid-training with potential for strong performance gains. In this paper, we formally define the problem and identify three key challenges: (1) inefficient training due to excessive reasoning steps, (2) disregard of the imbalanced token entropy distribution, and (3) underutilization of token information. To address these challenges, we propose RMT, a framework for efficient, adaptive, and unified reinforcement mid-training with various innovative components. In particular, we first introduce a dynamic token budget mechanism that constrains unnecessary reasoning steps and mitigates model overthinking. Next, we design a curriculum-based adaptive sampling method that fosters a progressive learning trajectory from easy to hard tokens. Finally, we present a dual training strategy that combines reinforcement learning with next-token prediction, ensuring targeted learning on key tokens and full exploitation of all token information. Extensive experiments demonstrate the superiority of RMT over state-of-the-art methods, achieving up to +64.91% performance improvement with only 21% of the reasoning length in language modeling. We also show that checkpoints obtained after reinforcement mid-training can benefit the subsequent post-training, yielding up to +18.76% improvement in the mathematical domain.

Neural text generation is a key tool in natural language applications, but it is well known there are major problems at its core. In particular, standard likelihood training and decoding leads to dull and repetitive outputs. While some post-hoc fixes have been proposed, in particular top-k and nucleus sampling, they do not address the fact that the token-level probabilities predicted by the model are poor. In this paper we show that the likelihood objective itself is at fault, resulting in a model that assigns too much probability to sequences containing repeats and frequent words, unlike those from the human training distribution. We propose a new objective, unlikelihood training, which forces unlikely generations to be assigned lower probability by the model. We show that both token and sequence level unlikelihood training give less repetitive, less dull text while maintaining perplexity, giving superior generations using standard greedy or beam search. According to human evaluations, our approach with standard beam search also outperforms the currently popular decoding methods of nucleus sampling or beam blocking, thus providing a strong alternative to existing techniques.

Standard methods for detecting discontinuities in conditional means are not applicable to outcomes that are complex, non-Euclidean objects like distributions, networks, or covariance matrices. This article develops a nonparametric test for jumps in conditional means when outcomes lie in a non-Euclidean metric space. Using local Fr\'echet regressionx2014which generalizes standard regression to metric-space valued datax2014the method estimates a mean path on either side of a candidate cutoff, extending existing k-sample tests to a flexible regression setting. Key theoretical contributions include a central limit theorem for the local estimator of the conditional Fr\'echet variance and the asymptotic validity and consistency of the proposed test. Simulations confirm nominal size control and robust power in finite samples. Two applications demonstrate the method's value by revealing effects invisible to scalar-based tests. First, I detect a sharp change in work-from-home compositions at Washington State's income threshold for non-compete enforceability during COVID-19, highlighting remote work's role as a bargaining margin. Second, I find that countries restructure their input-output networks after losing preferential US trade access. These findings underscore that analyzing regression functions within their native metric spaces can reveal structural discontinuities that scalar summaries would miss.

The key limitation of the verification performance lies in the ability of error detection. With this intuition we designed several variants of pessimistic verification, which are simple workflows that could significantly improve the verification of open-ended math questions. In pessimistic verification we construct multiple parallel verifications for the same proof, and the proof is deemed incorrect if any one of them reports an error. This simple technique significantly improves the performance across many math verification benchmarks without incurring substantial computational resources. Its token efficiency even surpassed extended long-CoT in test-time scaling. Our case studies further indicate that the majority of false negatives in stronger models are actually caused by annotation errors in the original dataset, so our method's performance is in fact underestimated. Self-verification for mathematical problems can effectively improve the reliability and performance of language model outputs, and it also plays a critical role in enabling long-horizon mathematical tasks. We believe that research on pessimistic verification will help enhance the mathematical capabilities of language models across a wide range of tasks.

Transferring reasoning capabilities from larger language models to smaller ones through supervised fine-tuning often fails counterintuitively, with performance degrading despite access to high-quality teacher demonstrations. We identify that this failure stems from distributional misalignment: reasoning traces from larger models contain tokens that are low probability under the student's distribution, exceeding the internal representation capacity of smaller architectures and creating learning barriers rather than helpful guidance. We propose Reverse Speculative Decoding (RSD), a mechanism for generating student-friendly reasoning traces in which the teacher model proposes candidate tokens but the student model determines acceptance based on its own probability distributions, filtering low probability tokens. When applied to Qwen3-0.6B, direct distillation of s1K-1.1 reasoning trace data degrades average performance across major reasoning benchmarks by 20.5\%, while the same model trained on RSD-generated reasoning traces achieves meaningful improvements of 4.9\%. Our analysis reveals that low probability tokens constitute the critical bottleneck in reasoning ability transfer. However, cross-model experiments demonstrate that RSD traces are model-specific rather than universally applicable, indicating that distributional alignment must be tailored for each student architecture's unique internal representation.

Reinforcement learning (RL) has become a central paradigm for post-training large language models (LLMs), particularly for complex reasoning tasks, yet it often suffers from exploration collapse: policies prematurely concentrate on a small set of dominant reasoning patterns, improving pass@1 while limiting rollout-level diversity and gains in pass@k. We argue that this failure stems from regularizing local token behavior rather than diversity over sets of solutions. To address this, we propose Uniqueness-Aware Reinforcement Learning, a rollout-level objective that explicitly rewards correct solutions that exhibit rare high-level strategies. Our method uses an LLM-based judge to cluster rollouts for the same problem according to their high-level solution strategies, ignoring superficial variations, and reweights policy advantages inversely with cluster size. As a result, correct but novel strategies receive higher rewards than redundant ones. Across mathematics, physics, and medical reasoning benchmarks, our approach consistently improves pass@k across large sampling budgets and increases the area under the pass@k curve (AUC@K) without sacrificing pass@1, while sustaining exploration and uncovering more diverse solution strategies at scale.

Reinforcement Learning with Verifiable Rewards (RLVR) has propelled Large Language Models in complex reasoning, yet its scalability is often hindered by a training bottleneck where performance plateaus as policy entropy collapses, signaling a loss of exploration. Previous methods typically address this by maintaining high policy entropy, yet the precise mechanisms that govern meaningful exploration have remained underexplored. Our analysis suggests that an unselective focus on entropy risks amplifying irrelevant tokens and destabilizing training. This paper investigates the exploration dynamics within RLVR and identifies a key issue: the gradual elimination of valuable low-probability exploratory tokens, which we term \textit{reasoning sparks}. We find that while abundant in pre-trained models, these sparks are systematically extinguished during RLVR due to over-penalization, leading to a degeneracy in exploration. To address this, we introduce Low-probability Regularization (Lp-Reg). Its core mechanism regularizes the policy towards a heuristic proxy distribution. This proxy is constructed by filtering out presumed noise tokens and re-normalizing the distribution over the remaining candidates. The result is a less-noisy proxy where the probability of reasoning sparks is amplified, which then serves as a soft regularization target to shield these valuable tokens from elimination via KL divergence. Experiments show that Lp-Reg enables stable on-policy training for around 1,000 steps, a regime where baseline entropy-control methods collapse. This sustained exploration leads to state-of-the-art performance, achieving a 60.17% average accuracy on five math benchmarks, an improvement of 2.66% over prior methods. Code is available at https://github.com/CarlanLark/Lp-Reg.

Fine-tuning pre-trained Large Language Models (LLMs) is essential to align them with human values and intentions. This process often utilizes methods like pairwise comparisons and KL divergence against a reference LLM, focusing on the evaluation of full answers generated by the models. However, the generation of these responses occurs in a token level, following a sequential, auto-regressive fashion. In this paper, we introduce Token-level Direct Preference Optimization (TDPO), a novel approach to align LLMs with human preferences by optimizing policy at the token level. Unlike previous methods, which face challenges in divergence efficiency, TDPO incorporates forward KL divergence constraints for each token, improving alignment and diversity. Utilizing the Bradley-Terry model for a token-based reward system, TDPO enhances the regulation of KL divergence, while preserving simplicity without the need for explicit reward modeling. Experimental results across various text tasks demonstrate TDPO's superior performance in balancing alignment with generation diversity. Notably, fine-tuning with TDPO strikes a better balance than DPO in the controlled sentiment generation and single-turn dialogue datasets, and significantly improves the quality of generated responses compared to both DPO and PPO-based RLHF methods. Our code is open-sourced at https://github.com/Vance0124/Token-level-Direct-Preference-Optimization.

Recent advancements in large language models(LLMs), such as GPT-4 and GPT-4o, have shown exceptional performance, especially in languages with abundant resources like English, thanks to extensive datasets that ensure robust training. Conversely, these models exhibit limitations when processing under-resourced languages such as Chinese and Korean, where issues including hallucinatory responses remain prevalent. This paper traces the roots of these disparities to the tokenization process inherent to these models. Specifically, it explores how the tokenizers vocabulary, often used to speed up the tokenization process and reduce tokens but constructed independently of the actual model training data, inadequately represents non-English languages. This misrepresentation results in the propagation of under-trained or untrained tokens, which perpetuate biases and pose serious concerns related to data security and ethical standards. We aim to dissect the tokenization mechanics of GPT-4o, illustrating how its simplified token-handling methods amplify these risks and offer strategic solutions to mitigate associated security and ethical issues. Through this study, we emphasize the critical need to rethink tokenization frameworks to foster more equitable and secure AI technologies. The code and data are available at https://github.com/yeyimilk/LLMGPT4o

Multi-agent debates have been introduced to improve the accuracy of Large Language Models (LLMs) by having multiple agents discuss solutions to a problem over several rounds of debate. However, models often generate incorrect yet confident-sounding responses, which can mislead others. This issue arises partly because agents do not consider how confident their peers are. To address this, we propose DebUnc, a debate framework that uses uncertainty metrics to assess agent confidence. Confidence is then conveyed through a modified attention mechanism that adjusts token weights, or through textual prompts. Evaluations across benchmarks show that attention-based methods are particularly effective and that performance continues to improve as uncertainty estimation becomes more reliable. The code is available at https://github.com/lukeyoffe/debunc.

Token dropping is a recently-proposed strategy to speed up the pretraining of masked language models, such as BERT, by skipping the computation of a subset of the input tokens at several middle layers. It can effectively reduce the training time without degrading much performance on downstream tasks. However, we empirically find that token dropping is prone to a semantic loss problem and falls short in handling semantic-intense tasks. Motivated by this, we propose a simple yet effective semantic-consistent learning method (ScTD) to improve the token dropping. ScTD aims to encourage the model to learn how to preserve the semantic information in the representation space. Extensive experiments on 12 tasks show that, with the help of our ScTD, token dropping can achieve consistent and significant performance gains across all task types and model sizes. More encouragingly, ScTD saves up to 57% of pretraining time and brings up to +1.56% average improvement over the vanilla token dropping.

Prevalent semantic speech tokenizers, designed to capture linguistic content, are surprisingly fragile. We find they are not robust to meaning-irrelevant acoustic perturbations; even at high Signal-to-Noise Ratios (SNRs) where speech is perfectly intelligible, their output token sequences can change drastically, increasing the learning burden for downstream LLMs. This instability stems from two flaws: a brittle single-path quantization architecture and a distant training signal indifferent to intermediate token stability. To address this, we introduce StableToken, a tokenizer that achieves stability through a consensus-driven mechanism. Its multi-branch architecture processes audio in parallel, and these representations are merged via a powerful bit-wise voting mechanism to form a single, stable token sequence. StableToken sets a new state-of-the-art in token stability, drastically reducing Unit Edit Distance (UED) under diverse noise conditions. This foundational stability translates directly to downstream benefits, significantly improving the robustness of SpeechLLMs on a variety of tasks.

We explore the Iterative Inference Hypothesis (IIH) within the context of transformer-based language models, aiming to understand how a model's latent representations are progressively refined and whether observable differences are present between correct and incorrect generations. Our findings provide empirical support for the IIH, showing that the nth token embedding in the residual stream follows a trajectory of decreasing loss. Additionally, we observe that the rate at which residual embeddings converge to a stable output representation reflects uncertainty in the token generation process. Finally, we introduce a method utilizing cross-entropy to detect this uncertainty and demonstrate its potential to distinguish between correct and incorrect token generations on a dataset of idioms.

Text-to-image (T2I) models have significantly advanced in producing high-quality images. However, such models have the ability to generate images containing not-safe-for-work (NSFW) content, such as pornography, violence, political content, and discrimination. To mitigate the risk of generating NSFW content, refusal mechanisms, i.e., safety checkers, have been developed to check potential NSFW content. Adversarial prompting techniques have been developed to evaluate the robustness of the refusal mechanisms. The key challenge remains to subtly modify the prompt in a way that preserves its sensitive nature while bypassing the refusal mechanisms. In this paper, we introduce TokenProber, a method designed for sensitivity-aware differential testing, aimed at evaluating the robustness of the refusal mechanisms in T2I models by generating adversarial prompts. Our approach is based on the key observation that adversarial prompts often succeed by exploiting discrepancies in how T2I models and safety checkers interpret sensitive content. Thus, we conduct a fine-grained analysis of the impact of specific words within prompts, distinguishing between dirty words that are essential for NSFW content generation and discrepant words that highlight the different sensitivity assessments between T2I models and safety checkers. Through the sensitivity-aware mutation, TokenProber generates adversarial prompts, striking a balance between maintaining NSFW content generation and evading detection. Our evaluation of TokenProber against 5 safety checkers on 3 popular T2I models, using 324 NSFW prompts, demonstrates its superior effectiveness in bypassing safety filters compared to existing methods (e.g., 54%+ increase on average), highlighting TokenProber's ability to uncover robustness issues in the existing refusal mechanisms.

This paper evaluates whether large language models (LLMs) exhibit cognitive fan effects, similar to those discovered by Anderson in humans, after being pre-trained on human textual data. We conduct two sets of in-context recall experiments designed to elicit fan effects. Consistent with human results, we find that LLM recall uncertainty, measured via token probability, is influenced by the fan effect. Our results show that removing uncertainty disrupts the observed effect. The experiments suggest the fan effect is consistent whether the fan value is induced in-context or in the pre-training data. Finally, these findings provide in-silico evidence that fan effects and typicality are expressions of the same phenomena.

Speculative decoding accelerates inference in large language models (LLMs) by generating multiple draft tokens simultaneously. However, existing methods often struggle with token misalignment between the training and decoding phases, limiting their performance. To address this, we propose GRIFFIN, a novel framework that incorporates a token-alignable training strategy and a token-alignable draft model to mitigate misalignment. The training strategy employs a loss masking mechanism to exclude highly misaligned tokens during training, preventing them from negatively impacting the draft model's optimization. The token-alignable draft model introduces input tokens to correct inconsistencies in generated features. Experiments on LLaMA-series and Vicuna models demonstrate that GRIFFIN achieves an average acceptance length improvement of over 7\% and a speedup ratio exceeding 8%, outperforming current SoTAs as shown in Fig. 1 (a) and (b).

Recent advances in aligning Large Language Models with human preferences have benefited from larger reward models and better preference data. However, most of these methodologies rely on the accuracy of the reward model. The reward models used in Reinforcement Learning with Human Feedback (RLHF) are typically learned from small datasets using stochastic optimization algorithms, making them prone to high variability. We illustrate the inconsistencies between reward models empirically on numerous open-source datasets. We theoretically show that the fluctuation of the reward models can be detrimental to the alignment problem because the derived policies are more overfitted to the reward model and, hence, are riskier if the reward model itself is uncertain. We use concentration of measure to motivate an uncertainty-aware, conservative algorithm for policy optimization. We show that such policies are more risk-averse in the sense that they are more cautious of uncertain rewards. We theoretically prove that our proposed methodology has less risk than the vanilla method. We corroborate our theoretical results with experiments based on designing an ensemble of reward models. We use this ensemble of reward models to align a language model using our methodology and observe that our empirical findings match our theoretical predictions.

Despite their ubiquity in language generation, it remains unknown why truncation sampling heuristics like nucleus sampling are so effective. We provide a theoretical explanation for the effectiveness of the truncation sampling by proving that truncation methods that discard tokens below some probability threshold (the most common type of truncation) can guarantee that all sampled tokens have nonzero true probability. However, thresholds are a coarse heuristic, and necessarily discard some tokens with nonzero true probability as well. In pursuit of a more precise sampling strategy, we show that we can leverage a known source of model errors, the softmax bottleneck, to prove that certain tokens have nonzero true probability, without relying on a threshold. Based on our findings, we develop an experimental truncation strategy and the present pilot studies demonstrating the promise of this type of algorithm. Our evaluations show that our method outperforms its threshold-based counterparts under automatic and human evaluation metrics for low-entropy (i.e., close to greedy) open-ended text generation. Our theoretical findings and pilot experiments provide both insight into why truncation sampling works, and make progress toward more expressive sampling algorithms that better surface the generative capabilities of large language models.

Large Language Models (LLMs) have exhibited strong mathematical reasoning and computational prowess, tackling tasks ranging from basic arithmetic to advanced competition-level problems. However, frequently occurring subtle errors, such as miscalculations or incorrect substitutions, limit the models' full mathematical potential. Existing studies to improve mathematical ability typically involve distilling reasoning skills from stronger LLMs or applying preference learning to step-wise response pairs. Although these methods leverage samples of varying granularity to mitigate reasoning errors, they overlook the frequently occurring subtle errors. A major reason is that sampled preference pairs involve differences unrelated to the errors, which may distract the model from focusing on subtle errors. In this work, we propose a novel preference learning framework called eRror-Injected Self-Editing (RISE), which injects predefined subtle errors into partial tokens of correct solutions to construct hard pairs for error mitigation. In detail, RISE uses the model itself to edit a small number of tokens in the solution, injecting designed subtle errors. Then, pairs composed of self-edited solutions and their corresponding correct ones, along with pairs of correct and incorrect solutions obtained through sampling, are used together for subtle error-aware DPO training. Compared with other preference learning methods, RISE further refines the training objective to focus on predefined errors and their tokens, without requiring fine-grained sampling or preference annotation. Extensive experiments validate the effectiveness of RISE, with preference learning on Qwen2-7B-Instruct yielding notable improvements of 3.0% on GSM8K and 7.9% on MATH.