Daily Papers

Reinforcement Learning from Verifiable Rewards (RLVR) has emerged as a promising framework for enhancing the reasoning capabilities of large language models. However, existing approaches such as GRPO often suffer from zero gradients. This problem arises primarily due to fixed clipping bounds for token-level probability ratios and the standardization of identical rewards, which can lead to ineffective gradient updates and underutilization of generated responses. In this work, we propose Dynamic Clipping Policy Optimization (DCPO), which introduces a dynamic clipping strategy that adaptively adjusts the clipping bounds based on token-specific prior probabilities to enhance token-level exploration, and a smooth advantage standardization technique that standardizes rewards across cumulative training steps to improve the response-level effective utilization of generated responses. DCPO achieved state-of-the-art performance on four benchmarks based on four different models. In particular, DCPO achieved an Avg@1 of 46.7 under greedy decoding and an Avg@32 of 38.8 under 32 times sampling on the AIME24 benchmark, surpassing both DAPO (36.7/31.6) and GRPO (36.7/32.1) on the Qwen2.5-Math-7B model. On the AIME25 benchmark based on Qwen2.5-14B, DCPO achieves a performance of (23.3/19.0), surpassing GRPO (13.3/10.5) and DAPO (20.0/15.3). Furthermore, DCPO achieved an average 28% improvement in the nonzero advantage over GRPO in four models, doubled the training efficiency over DAPO, and significantly reduced the token clipping ratio by an order of magnitude compared to both GRPO and DAPO, while achieving superior performance. These results highlight DCPO's effectiveness in leveraging generated data more efficiently for reinforcement learning in large language models.

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.

One of the most striking findings in modern research on large language models (LLMs) is that scaling up compute during training leads to better results. However, less attention has been given to the benefits of scaling compute during inference. This survey focuses on these inference-time approaches. We explore three areas under a unified mathematical formalism: token-level generation algorithms, meta-generation algorithms, and efficient generation. Token-level generation algorithms, often called decoding algorithms, operate by sampling a single token at a time or constructing a token-level search space and then selecting an output. These methods typically assume access to a language model's logits, next-token distributions, or probability scores. Meta-generation algorithms work on partial or full sequences, incorporating domain knowledge, enabling backtracking, and integrating external information. Efficient generation methods aim to reduce token costs and improve the speed of generation. Our survey unifies perspectives from three research communities: traditional natural language processing, modern LLMs, and machine learning systems.

The problem of pre-training data detection for large language models (LLMs) has received growing attention due to its implications in critical issues like copyright violation and test data contamination. The current state-of-the-art approach, Min-K%, measures the raw token probability which we argue may not be the most informative signal. Instead, we propose Min-K%++ to normalize the token probability with statistics of the categorical distribution over the whole vocabulary, which accurately reflects the relative likelihood of the target token compared with other candidate tokens in the vocabulary. Theoretically, we back up our method by showing that the statistic it estimates is explicitly optimized during LLM training, thus serving as a reliable indicator for detecting training data. Empirically, on the WikiMIA benchmark, Min-K%++ outperforms the SOTA Min-K% by 6.2% to 10.5% in detection AUROC averaged over five models. On the more challenging MIMIR benchmark, Min-K%++ consistently improves upon Min-K% and performs on par with reference-based method, despite not requiring an extra reference model.

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.

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.

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.

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.

Recent advancements in large language models (LLMs) have significantly enhanced their reasoning capabilities. However, they continue to struggle with basic character-level tasks, such as counting letters in words, a problem rooted in their tokenization process. While existing benchmarks have highlighted this weakness through basic character operations, such failures are often dismissed due to lacking practical relevance. Yet, many real-world applications, such as navigating text-based maps or interpreting structured tables, rely heavily on precise sub-token understanding. In this regard, we introduce SubTokenTest, a comprehensive benchmark that assesses sub-token understanding through practical, utility-driven tasks. Our benchmark includes ten tasks across four domains and isolates tokenization-related failures by decoupling performance from complex reasoning. We provide a comprehensive evaluation of nine advanced LLMs. Additionally, we investigate the impact of test-time scaling on sub-token reasoning and explore how character-level information is encoded within the hidden states.

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.

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.

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.

Many commercial Large Language Models (LLMs) are often closed-source, limiting developers to prompt tuning for aligning content generation with specific applications. While these models currently do not provide access to token logits, we argue that if such access were available, it would enable more powerful adaptation techniques beyond prompt engineering. In this paper, we propose a token-level probability reweighting framework that, given access to logits and a small amount of task-specific data, can effectively steer black-box LLMs toward application-specific content generation. Our approach views next-token prediction through the lens of supervised classification. We show that aligning black-box LLMs with task-specific data can be formulated as a label noise correction problem, leading to Plugin model -- an autoregressive probability reweighting model that operates solely on logits. We provide theoretical justification for why reweighting logits alone is sufficient for task adaptation. Extensive experiments with multiple datasets, LLMs, and reweighting models demonstrate the effectiveness of our method, advocating for broader access to token logits in closed-source models.

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.

In large language models (LLMs), each block operates on the residual stream to map input token sequences to output token distributions. However, most of the interpretability literature focuses on internal latent representations, leaving token-space dynamics underexplored. The high dimensionality and categoricity of token distributions hinder their analysis, as standard statistical descriptors are not suitable. We show that the entropy of logit-lens predictions overcomes these issues. In doing so, it provides a per-layer scalar, permutation-invariant metric. We introduce Entropy-Lens to distill the token-space dynamics of the residual stream into a low-dimensional signal. We call this signal the entropy profile. We apply our method to a variety of model sizes and families, showing that (i) entropy profiles uncover token prediction dynamics driven by expansion and pruning strategies; (ii) these dynamics are family-specific and invariant under depth rescaling; (iii) they are characteristic of task type and output format; (iv) these strategies have unequal impact on downstream performance, with the expansion strategy usually being more critical. Ultimately, our findings further enhance our understanding of the residual stream, enabling a granular assessment of how information is processed across model depth.

Autoregressive (AR) modeling, known for its next-token prediction paradigm, underpins state-of-the-art language and visual generative models. Traditionally, a ``token'' is treated as the smallest prediction unit, often a discrete symbol in language or a quantized patch in vision. However, the optimal token definition for 2D image structures remains an open question. Moreover, AR models suffer from exposure bias, where teacher forcing during training leads to error accumulation at inference. In this paper, we propose xAR, a generalized AR framework that extends the notion of a token to an entity X, which can represent an individual patch token, a cell (a ktimes k grouping of neighboring patches), a subsample (a non-local grouping of distant patches), a scale (coarse-to-fine resolution), or even a whole image. Additionally, we reformulate discrete token classification as continuous entity regression, leveraging flow-matching methods at each AR step. This approach conditions training on noisy entities instead of ground truth tokens, leading to Noisy Context Learning, which effectively alleviates exposure bias. As a result, xAR offers two key advantages: (1) it enables flexible prediction units that capture different contextual granularity and spatial structures, and (2) it mitigates exposure bias by avoiding reliance on teacher forcing. On ImageNet-256 generation benchmark, our base model, xAR-B (172M), outperforms DiT-XL/SiT-XL (675M) while achieving 20times faster inference. Meanwhile, xAR-H sets a new state-of-the-art with an FID of 1.24, running 2.2times faster than the previous best-performing model without relying on vision foundation modules (\eg, DINOv2) or advanced guidance interval sampling.

Critic-free methods like GRPO reduce memory demands by estimating advantages from multiple rollouts but tend to converge slowly, as critical learning signals are diluted by an abundance of uninformative samples and tokens. To tackle this challenge, we propose the Dynamic Dual-Level Down-Sampling (D^3S) framework that prioritizes the most informative samples and tokens across groups to improve the efficient of policy optimization. D^3S operates along two levels: (1) the sample-level, which selects a subset of rollouts to maximize advantage variance (Var(A)). We theoretically proven that this selection is positively correlated with the upper bound of the policy gradient norms, yielding higher policy gradients. (2) the token-level, which prioritizes tokens with a high product of advantage magnitude and policy entropy (|A_{i,t}|times H_{i,t}), focusing updates on tokens where the policy is both uncertain and impactful. Moreover, to prevent overfitting to high-signal data, D^3S employs a dynamic down-sampling schedule inspired by curriculum learning. This schedule starts with aggressive down-sampling to accelerate early learning and gradually relaxes to promote robust generalization. Extensive experiments on Qwen2.5 and Llama3.1 demonstrate that integrating D^3S into advanced RL algorithms achieves state-of-the-art performance and generalization while requiring fewer samples and tokens across diverse reasoning benchmarks. Our code is added in the supplementary materials and will be made publicly available.

Pretrained language models (LLMs) are often constrained by their fixed tokenization schemes, leading to inefficiencies and performance limitations, particularly for multilingual or specialized applications. This tokenizer lock-in presents significant challenges. standard methods to overcome this often require prohibitive computational resources. Although tokenizer replacement with heuristic initialization aims to reduce this burden, existing methods often require exhaustive residual fine-tuning and still may not fully preserve semantic nuances or adequately address the underlying compression inefficiencies. Our framework introduces two innovations: first, Tokenadapt, a model-agnostic tokenizer transplantation method, and second, novel pre-tokenization learning for multi-word Supertokens to enhance compression and reduce fragmentation. Tokenadapt initializes new unique token embeddings via a hybrid heuristic that combines two methods: a local estimate based on subword decomposition using the old tokenizer, and a global estimate utilizing the top-k semantically similar tokens from the original vocabulary. This methodology aims to preserve semantics while significantly minimizing retraining requirements. Empirical investigations validate both contributions: the transplantation heuristic successfully initializes unique tokens, markedly outperforming conventional baselines and sophisticated methods including Transtokenizer and ReTok, while our Supertokens achieve notable compression gains. Our zero-shot perplexity results demonstrate that the TokenAdapt hybrid initialization consistently yields lower perplexity ratios compared to both ReTok and TransTokenizer baselines across different base models and newly trained target tokenizers. TokenAdapt typically reduced the overall perplexity ratio significantly compared to ReTok, yielding at least a 2-fold improvement in these aggregate scores.

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.

Reinforcement Learning with Verifiable Rewards (RLVR) offers a promising framework for optimizing large language models in reasoning tasks. However, existing RLVR algorithms focus on different granularities, and each has complementary strengths and limitations. Group Relative Policy Optimization (GRPO) updates the policy with token-level importance ratios, which preserves fine-grained credit assignment but often suffers from high variance and instability. In contrast, Group Sequence Policy Optimization (GSPO) applies single sequence-level importance ratios across all tokens in a response that better matches sequence-level rewards, but sacrifices token-wise credit assignment. In this paper, we propose Dynamic Hybrid Policy Optimization (DHPO) to bridge GRPO and GSPO within a single clipped surrogate objective. DHPO combines token-level and sequence-level importance ratios using weighting mechanisms. We explore two variants of the mixing mechanism, including an averaged mixing and an entropy-guided mixing. To further stabilize training, we employ a branch-specific clipping strategy that constrains token-level and sequence-level ratios within separate trust regions before mixing, preventing outliers in either branch from dominating the update. Across seven challenging mathematical reasoning benchmarks, experiments on both dense and MoE models from the Qwen3 series show that DHPO consistently outperforms GRPO and GSPO. We will release our code upon acceptance of this paper.

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.

Large language models (LLMs) owe much of their stellar performance to expansive input contexts, yet such verbosity inflates monetary costs, carbon footprint, and inference-time latency. Much of this overhead manifests from the redundant low-utility tokens present in typical prompts, as only a fraction of tokens typically carries the majority of the semantic weight. We address this inefficiency by introducing FrugalPrompt, a novel prompt compression framework for LLMs, which retains only the most semantically significant tokens. Leveraging two state-of-the-art token attribution methods, GlobEnc and DecompX, we assign salience scores to every token in an input sequence, rank them to preserve the top-k% tokens in their original order, and obtain a sparse frugalized prompt. We evaluate the approach across four NLP tasks: Sentiment Analysis, Commonsense QA, Summarization, and Mathematical Reasoning, using a suite of frontier LLMs. For the first three tasks, a 20% prompt reduction incurs only a marginal loss in task performance, demonstrating that contemporary LLMs can reconstruct elided context from high-salience cues. In contrast, performance on mathematical reasoning deteriorates sharply, reflecting a stronger dependence on complete token continuity. Further analysis with bottom-k% and random-k% tokens reveals asymmetric performance patterns that may suggest potential task contamination effects, wherein models may resort to shallow memorized patterns from pretraining exposure for conventional NLP tasks. We posit that our work contributes to a more nuanced understanding of LLM behavior in performance-efficiency trade-offs, and delineate the boundary between tasks tolerant to contextual sparsity and those requiring exhaustive context. Our source code and models are available at: https://github.com/Starscream-11813/Frugal-ICL.

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.

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.

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.

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.

As a significant part of post-training of the Large Language Models (LLMs), Reinforcement Learning from Verifiable Reward (RLVR) has greatly improved LLMs' reasoning skills. However, some RLVR algorithms, such as GRPO (Group Relative Policy Optimization) and GSPO (Group Sequence Policy Optimization), are observed to suffer from unstable policy updates and low usage of sampling data, respectively. The importance ratio of GRPO is calculated at the token level, which focuses more on optimizing a single token. This will be easily affected by outliers, leading to model training collapse. GSPO proposed the calculation of the response level importance ratio, which solves the problem of high variance and training noise accumulation in the calculation of the GRPO importance ratio. However, since all the response tokens share a common importance ratio, extreme values can easily raise or lower the overall mean, leading to the entire response being mistakenly discarded, resulting in a decrease in the utilization of sampled data. This paper introduces SSPO, which applies sentence-level importance ratio, taking the balance between GRPO and GSPO. SSPO not only avoids training collapse and high variance, but also prevents the whole response tokens from being abandoned by the clipping mechanism. Furthermore, we apply sentence entropy to PPO-CLIP to steadily adjust the clipping bounds, encouraging high-entropy tokens to explore and narrow the clipping range of low-entropy tokens. In particular, SSPO achieves an average score of 46.57 across five datasets, surpassing GRPO (43.01) and GSPO (44.42), and wins state-of-the-art performance on three datasets. These results highlight SSPO's effectiveness in leveraging generated data by taking the essence of GSPO but rejecting its shortcomings.

Tokenization is the first - and often underappreciated - layer of computation in language models. While Chain-of-Thought (CoT) prompting enables transformer models to approximate recurrent computation by externalizing intermediate steps, we show that the success of such reasoning is fundamentally bounded by the structure of tokenized inputs. This work presents a theoretical and empirical investigation into how tokenization schemes, particularly subword-based methods like byte-pair encoding (BPE), impede symbolic computation by merging or obscuring atomic reasoning units. We introduce the notion of Token Awareness to formalize how poor token granularity disrupts logical alignment and prevents models from generalizing symbolic procedures. Through systematic evaluation on arithmetic and symbolic tasks, we demonstrate that token structure dramatically affect reasoning performance, causing failure even with CoT, while atomically-aligned formats unlock strong generalization, allowing small models (e.g., GPT-4o-mini) to outperform larger systems (e.g., o1) in structured reasoning. Our findings reveal that symbolic reasoning ability in LLMs is not purely architectural, but deeply conditioned on token-level representations.

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.

Visual Language Models require substantial computational resources for inference due to the additional input tokens needed to represent visual information. However, these visual tokens often contain redundant and unimportant information, resulting in an unnecessarily high number of tokens. To address this, we introduce PACT, a method that reduces inference time and memory usage by pruning irrelevant tokens and merging visually redundant ones at an early layer of the language model. Our approach uses a novel importance metric to identify unimportant tokens without relying on attention scores, making it compatible with FlashAttention. We also propose a novel clustering algorithm, called Distance Bounded Density Peak Clustering, which efficiently clusters visual tokens while constraining the distances between elements within a cluster by a predefined threshold. We demonstrate the effectiveness of PACT through extensive experiments.

Large Vision-Language Models (VLMs) enable strong multimodal reasoning but incur heavy inference costs from redundant visual tokens. Token pruning alleviates this issue, yet existing approaches face limitations. Attention-based methods rely on raw attention scores, which are often unstable across layers and heads and can lead to redundant selections. Diversity-based methods improve robustness by selecting tokens far apart in feature space but risk dropping regions needed for accurate prediction. We propose \ours, a training-free framework built on a simple intuition: tokens with higher sensitivity are more likely to influence the model's output, and they should also capture complementary visual cues rather than overlapping information. To achieve this, we estimate token sensitivity using zeroth-order perturbations at the projection layer, a shallow and computationally light component of the model. This approach measures how small random perturbations affect the projection outputs, allowing us to approximate each token's influence through lightweight forward passes without backpropagation. Extensive experiments across multiple VLMs and benchmarks show that \ours consistently outperforms prior methods, pruning up to 94.4\% of tokens while maintaining accuracy and significantly improving efficiency, achieving up to 2.30x faster end-to-end inference over the baseline.

Large language models (LLMs) have demonstrated impressive reasoning capabilities by scaling test-time compute via long Chain-of-Thought (CoT). However, recent findings suggest that raw token counts are unreliable proxies for reasoning quality: increased generation length does not consistently correlate with accuracy and may instead signal "overthinking," leading to performance degradation. In this work, we quantify inference-time effort by identifying deep-thinking tokens -- tokens where internal predictions undergo significant revisions in deeper model layers prior to convergence. Across four challenging mathematical and scientific benchmarks (AIME 24/25, HMMT 25, and GPQA-diamond) and a diverse set of reasoning-focused models (GPT-OSS, DeepSeek-R1, and Qwen3), we show that deep-thinking ratio (the proportion of deep-thinking tokens in a generated sequence) exhibits a robust and consistently positive correlation with accuracy, substantially outperforming both length-based and confidence-based baselines. Leveraging this insight, we introduce Think@n, a test-time scaling strategy that prioritizes samples with high deep-thinking ratios. We demonstrate that Think@n matches or exceeds standard self-consistency performance while significantly reducing inference costs by enabling the early rejection of unpromising generations based on short prefixes.

Reasoning has become a central paradigm for large language models (LLMs), consistently boosting accuracy across diverse benchmarks. Yet its suitability for precision-sensitive tasks remains unclear. We present the first systematic study of reasoning for classification tasks under strict low false positive rate (FPR) regimes. Our analysis covers two tasks--safety detection and hallucination detection--evaluated in both fine-tuned and zero-shot settings, using standard LLMs and Large Reasoning Models (LRMs). Our results reveal a clear trade-off: Think On (reasoning-augmented) generation improves overall accuracy, but underperforms at the low-FPR thresholds essential for practical use. In contrast, Think Off (no reasoning during inference) dominates in these precision-sensitive regimes, with Think On surpassing only when higher FPRs are acceptable. In addition, we find token-based scoring substantially outperforms self-verbalized confidence for precision-sensitive deployments. Finally, a simple ensemble of the two modes recovers the strengths of each. Taken together, our findings position reasoning as a double-edged tool: beneficial for average accuracy, but often ill-suited for applications requiring strict precision.

Latent tokens are gaining attention for enhancing reasoning in large language models (LLMs), yet their internal mechanisms remain unclear. This paper examines the problem from a reliability perspective, uncovering fundamental weaknesses: latent tokens function as uninterpretable placeholders rather than encoding faithful reasoning. While resistant to perturbation, they promote shortcut usage over genuine reasoning. We focus on Chain-of-Continuous-Thought (COCONUT), which claims better efficiency and stability than explicit Chain-of-Thought (CoT) while maintaining performance. We investigate this through two complementary approaches. First, steering experiments perturb specific token subsets, namely COCONUT and explicit CoT. Unlike CoT tokens, COCONUT tokens show minimal sensitivity to steering and lack reasoning-critical information. Second, shortcut experiments evaluate models under biased and out-of-distribution settings. Results on MMLU and HotpotQA demonstrate that COCONUT consistently exploits dataset artifacts, inflating benchmark performance without true reasoning. These findings reposition COCONUT as a pseudo-reasoning mechanism: it generates plausible traces that conceal shortcut dependence rather than faithfully representing reasoning processes.

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).

Long chain-of-thought (CoT) trajectories provide rich supervision signals for distilling reasoning from teacher to student LLMs. However, both prior work and our experiments show that trajectories from stronger teachers do not necessarily yield better students, highlighting the importance of data-student suitability in distillation. Existing methods assess suitability primarily through student likelihood, favoring trajectories that closely align with the model's current behavior but overlooking more informative ones. Addressing this, we propose Rank-Surprisal Ratio (RSR), a simple metric that captures both alignment and informativeness to assess the suitability of a reasoning trajectory. RSR is motivated by the observation that effective trajectories typically combine low absolute probability with relatively high-ranked tokens under the student model, balancing learning signal strength and behavioral alignment. Concretely, RSR is defined as the ratio of a trajectory's average token-wise rank to its average negative log-likelihood, and is straightforward to compute and interpret. Across five student models and reasoning trajectories from 11 diverse teachers, RSR strongly correlates with post-training performance (average Spearman 0.86), outperforming existing metrics. We further demonstrate its practical utility in both trajectory selection and teacher selection.

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.

Estimating probability distribution is one of the core issues in the NLP field. However, in both deep learning (DL) and pre-DL eras, unlike the vast applications of linear-chain CRF in sequence labeling tasks, very few works have applied tree-structure CRF to constituency parsing, mainly due to the complexity and inefficiency of the inside-outside algorithm. This work presents a fast and accurate neural CRF constituency parser. The key idea is to batchify the inside algorithm for loss computation by direct large tensor operations on GPU, and meanwhile avoid the outside algorithm for gradient computation via efficient back-propagation. We also propose a simple two-stage bracketing-then-labeling parsing approach to improve efficiency further. To improve the parsing performance, inspired by recent progress in dependency parsing, we introduce a new scoring architecture based on boundary representation and biaffine attention, and a beneficial dropout strategy. Experiments on PTB, CTB5.1, and CTB7 show that our two-stage CRF parser achieves new state-of-the-art performance on both settings of w/o and w/ BERT, and can parse over 1,000 sentences per second. We release our code at https://github.com/yzhangcs/crfpar.

To address this gap, our study introduces the concept of causal epistemic consistency, which focuses on the self-consistency of Large Language Models (LLMs) in differentiating intermediates with nuanced differences in causal reasoning. We propose a suite of novel metrics -- intensity ranking concordance, cross-group position agreement, and intra-group clustering -- to evaluate LLMs on this front. Through extensive empirical studies on 21 high-profile LLMs, including GPT-4, Claude3, and LLaMA3-70B, we have favoring evidence that current models struggle to maintain epistemic consistency in identifying the polarity and intensity of intermediates in causal reasoning. Additionally, we explore the potential of using internal token probabilities as an auxiliary tool to maintain causal epistemic consistency. In summary, our study bridges a critical gap in AI research by investigating the self-consistency over fine-grained intermediates involved in causal reasoning.

The number of tokens it takes to encode parallel text in different languages is known to vary. These disparities are called token premiums. Having high token premiums leads to less throughput during training and increases costs at inference. In this paper, we show that even after controlling for dataset size, vocabulary size, and data content, monolingual tokenizers exhibit a wide range of token premiums across languages. To understand the cross-linguistic differences that cause these token premiums, we train a suite of approximately 7,000 comparable monolingual tokenizers for 97 languages, manipulating tokenization algorithm, vocabulary size, and dataset size. We measure token premiums and test for a relationship between factors such as data similarity (between tokenizer training and evaluation), vocabulary size, and pre-tokenization. We also investigate the role of language-specific features such as writing system and word length. We find that similarity between training and test data does not impact token premiums, but vocabulary size and pre-tokenization do. While simply increasing vocabulary size does not lead to reduced token premium effects, we can determine an ``optimal'' vocabulary size for each language to achieve significantly reduced token premium effects. We also train superword tokenizers which allow merges over whitespaces, and we find that they both reduce token premium effects and improve compression overall. Thus, intervening on the vocabulary size or the pre-tokenizer significantly reduces crosslingual token premium effects.

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.

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.

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.

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.

Large language model (LLM) tokenizers act as structured compressors: by mapping text to discrete token sequences, they determine token count (and thus compute and context usage) and the statistical structure seen by downstream models. Despite their central role in LLM pipelines, the link between tokenization, compression efficiency and induced structure is not well understood. We empirically demonstrate that tokenizer training scale redistributes entropy: as training data grows, the token stream becomes more diverse in aggregate (higher unigram entropy) yet markedly more predictable in-context (lower higher-order conditional entropies), indicating that tokenization absorbs substantial short-range regularity although these gains degrade under train-test domain mismatch. To ground these observations, we first benchmark i) pretrained GPT-family tokenizers as black-box compressors across various domains, and ii) learned tokenizers across configurations spanning vocabulary size, training scale, and domain. Next, we study tokenization as a transform for universal compression and introduce a compression-aware BPE variant. Finally, we adopt a channel lens and introduce capacity-utilization metrics to analyze tokenizer behaviour and outline implications for downstream modeling. Put together, our results expose various trade-offs between compression, induced structure, and robustness under domain shift, and motivate principled, compression-aware tokenizer design.

Estimating the difficulty of input questions as perceived by large language models (LLMs) is essential for accurate performance evaluation and adaptive inference. Existing methods typically rely on repeated response sampling, auxiliary models, or fine-tuning the target model itself, which may incur substantial computational costs or compromise generality. In this paper, we propose a novel approach for difficulty estimation that leverages only the hidden representations produced by the target LLM. We model the token-level generation process as a Markov chain and define a value function to estimate the expected output quality given any hidden state. This allows for efficient and accurate difficulty estimation based solely on the initial hidden state, without generating any output tokens. Extensive experiments across both textual and multimodal tasks demonstrate that our method consistently outperforms existing baselines in difficulty estimation. Moreover, we apply our difficulty estimates to guide adaptive reasoning strategies, including Self-Consistency, Best-of-N, and Self-Refine, achieving higher inference efficiency with fewer generated tokens.

In this paper, we introduce an event-driven trading strategy that predicts stock movements by detecting corporate events from news articles. Unlike existing models that utilize textual features (e.g., bag-of-words) and sentiments to directly make stock predictions, we consider corporate events as the driving force behind stock movements and aim to profit from the temporary stock mispricing that may occur when corporate events take place. The core of the proposed strategy is a bi-level event detection model. The low-level event detector identifies events' existences from each token, while the high-level event detector incorporates the entire article's representation and the low-level detected results to discover events at the article-level. We also develop an elaborately-annotated dataset EDT for corporate event detection and news-based stock prediction benchmark. EDT includes 9721 news articles with token-level event labels as well as 303893 news articles with minute-level timestamps and comprehensive stock price labels. Experiments on EDT indicate that the proposed strategy outperforms all the baselines in winning rate, excess returns over the market, and the average return on each transaction.

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.

Language models (LM) are capable of remarkably complex linguistic tasks; however, numerical reasoning is an area in which they frequently struggle. An important but rarely evaluated form of reasoning is understanding probability distributions. In this paper, we focus on evaluating the probabilistic reasoning capabilities of LMs using idealized and real-world statistical distributions. We perform a systematic evaluation of state-of-the-art LMs on three tasks: estimating percentiles, drawing samples, and calculating probabilities. We evaluate three ways to provide context to LMs 1) anchoring examples from within a distribution or family of distributions, 2) real-world context, 3) summary statistics on which to base a Normal approximation. Models can make inferences about distributions, and can be further aided by the incorporation of real-world context, example shots and simplified assumptions, even if these assumptions are incorrect or misspecified. To conduct this work, we developed a comprehensive benchmark distribution dataset with associated question-answer pairs that we will release publicly.

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.

Recent advancements in large video-language models have revolutionized video understanding tasks. However, their efficiency is significantly constrained by processing high volumes of visual tokens. Existing token compression strategies apply a fixed compression ratio, ignoring the variability in semantic density among different video clips. Consequently, this lead to inadequate representation of information-rich clips due to insufficient tokens and unnecessary computation on static or content-poor ones. To address this, we propose LangDC, a Language-aware Dynamic Token Compressor. LangDC leverages a lightweight language model to describe video clips, converting them into soft caption tokens as visual representations. Trained with our proposed semantic density-aware supervision, LangDC aims to 1) cover key visual cues necessary for downstream task reasoning and 2) dynamically adjust compression ratios based on scene richness, reflected by descriptions length. Our design mimics how humans dynamically express what they see: complex scenes (seeing more) elicit more detailed language to convey nuances (saying more), whereas simpler scenes are described with fewer words. Experimental results show that our method reduces FLOPs by 49% compared to VideoGPT+ while maintaining competitive performance. Furthermore, qualitative results demonstrate our approach adaptively adjusts the token compression ratio based on video segment richness.

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.

Feature attribution methods (FAs), such as gradients and attention, are widely employed approaches to derive the importance of all input features to the model predictions. Existing work in natural language processing has mostly focused on developing and testing FAs for encoder-only language models (LMs) in classification tasks. However, it is unknown if it is faithful to use these FAs for decoder-only models on text generation, due to the inherent differences between model architectures and task settings respectively. Moreover, previous work has demonstrated that there is no `one-wins-all' FA across models and tasks. This makes the selection of a FA computationally expensive for large LMs since input importance derivation often requires multiple forward and backward passes including gradient computations that might be prohibitive even with access to large compute. To address these issues, we present a model-agnostic FA for generative LMs called Recursive Attribution Generator (ReAGent). Our method updates the token importance distribution in a recursive manner. For each update, we compute the difference in the probability distribution over the vocabulary for predicting the next token between using the original input and using a modified version where a part of the input is replaced with RoBERTa predictions. Our intuition is that replacing an important token in the context should have resulted in a larger change in the model's confidence in predicting the token than replacing an unimportant token. Our method can be universally applied to any generative LM without accessing internal model weights or additional training and fine-tuning, as most other FAs require. We extensively compare the faithfulness of ReAGent with seven popular FAs across six decoder-only LMs of various sizes. The results show that our method consistently provides more faithful token importance distributions.

Large Language Models (LLMs) are widely deployed in real-world applications, yet little is known about their training dynamics at the token level. Evaluation typically relies on aggregated training loss, measured at the batch level, which overlooks subtle per-token biases arising from (i) varying token-level dynamics and (ii) structural biases introduced by hyperparameters. While weight decay is commonly used to stabilize training, we reveal that it silently introduces performance biases detectable only at the token level. In fact, we empirically show across different dataset sizes, model architectures and sizes ranging from 270M to 3B parameters that as weight decay increases, low-frequency tokens are disproportionately depreciated. This is particularly concerning, as these neglected low-frequency tokens represent the vast majority of the token distribution in most languages, calling for novel regularization techniques that ensure fairness across all available tokens.

As post-training techniques evolve, large language models (LLMs) are increasingly augmented with structured multi-step reasoning abilities, often optimized through reinforcement learning. These reasoning-enhanced models outperform standard LLMs on complex tasks and now underpin many commercial LLM APIs. However, to protect proprietary behavior and reduce verbosity, providers typically conceal the reasoning traces while returning only the final answer. This opacity introduces a critical transparency gap: users are billed for invisible reasoning tokens, which often account for the majority of the cost, yet have no means to verify their authenticity. This opens the door to token count inflation, where providers may overreport token usage or inject synthetic, low-effort tokens to inflate charges. To address this issue, we propose CoIn, a verification framework that audits both the quantity and semantic validity of hidden tokens. CoIn constructs a verifiable hash tree from token embedding fingerprints to check token counts, and uses embedding-based relevance matching to detect fabricated reasoning content. Experiments demonstrate that CoIn, when deployed as a trusted third-party auditor, can effectively detect token count inflation with a success rate reaching up to 94.7%, showing the strong ability to restore billing transparency in opaque LLM services. The dataset and code are available at https://github.com/CASE-Lab-UMD/LLM-Auditing-CoIn.

Tokenization is a fundamental preprocessing step in Natural Language Processing (NLP), significantly impacting the capability of large language models (LLMs) to capture linguistic and semantic nuances. This study introduces a novel evaluation framework addressing tokenization challenges specific to morphologically-rich and low-resource languages such as Turkish. Utilizing the Turkish MMLU (TR-MMLU) dataset, comprising 6,200 multiple-choice questions from the Turkish education system, we assessed tokenizers based on vocabulary size, token count, processing time, language-specific token percentages (\%TR), and token purity (\%Pure). These newly proposed metrics measure how effectively tokenizers preserve linguistic structures. Our analysis reveals that language-specific token percentages exhibit a stronger correlation with downstream performance (e.g., MMLU scores) than token purity. Furthermore, increasing model parameters alone does not necessarily enhance linguistic performance, underscoring the importance of tailored, language-specific tokenization methods. The proposed framework establishes robust and practical tokenization standards for morphologically complex languages.

Vision Large Language Models (VLLMs) incur high computational costs due to their reliance on hundreds of visual tokens to represent images. While token pruning offers a promising solution for accelerating inference, this paper, however, identifies a key observation: in deeper layers (e.g., beyond the 20th), existing training-free pruning methods perform no better than random pruning. We hypothesize that this degradation is caused by "vanishing token information", where visual tokens progressively lose their salience with increasing network depth. To validate this hypothesis, we quantify a token's information content by measuring the change in the model output probabilities upon its removal. Using this proposed metric, our analysis of the information of visual tokens across layers reveals three key findings: (1) As layers deepen, the information of visual tokens gradually becomes uniform and eventually vanishes at an intermediate layer, which we term as "information horizon", beyond which the visual tokens become redundant; (2) The position of this horizon is not static; it extends deeper for visually intensive tasks, such as Optical Character Recognition (OCR), compared to more general tasks like Visual Question Answering (VQA); (3) This horizon is also strongly correlated with model capacity, as stronger VLLMs (e.g., Qwen2.5-VL) employ deeper visual tokens than weaker models (e.g., LLaVA-1.5). Based on our findings, we show that simple random pruning in deep layers efficiently balances performance and efficiency. Moreover, integrating random pruning consistently enhances existing methods. Using DivPrune with random pruning achieves state-of-the-art results, maintaining 96.9% of Qwen-2.5-VL-7B performance while pruning 50% of visual tokens. The code will be publicly available at https://github.com/YahongWang1/Information-Horizon.

Scaling laws in language modeling traditionally quantify training loss as a function of dataset size and model parameters, providing compute-optimal estimates but often neglecting the impact of data quality on model generalization. In this paper, we extend the conventional understanding of scaling law by offering a microscopic view of data quality within the original formulation -- effective training tokens -- which we posit to be a critical determinant of performance for parameter-constrained language models. Specifically, we formulate the proposed term of effective training tokens to be a combination of two readily-computed indicators of text: (i) text diversity and (ii) syntheticity as measured by a teacher model. We pretrained over 200 models of 25M to 1.5B parameters on a diverse set of sampled, synthetic data, and estimated the constants that relate text quality, model size, training tokens, and eight reasoning task accuracy scores. We demonstrated the estimated constants yield +0.83 Pearson correlation with true accuracies, and analyzed it in scenarios involving widely-used data techniques such as data sampling and synthesis which aim to improve data quality.

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.

Tasks that require character-level reasoning, such as counting or locating characters within words, remain challenging for contemporary language models. A common conjecture is that language models' reliance on subword units, rather than characters, contributes to their struggles with character-level tasks, yet recent studies offer conflicting conclusions about the role of tokenization, leaving its impact unclear. To address this gap, we introduce CharBench, a comprehensive benchmark of character-level tasks that is two orders of magnitude larger than existing alternatives. We evaluate a diverse range of leading open-weight and proprietary models on CharBench and find that it presents a significant challenge to modern LLMs, with an average accuracy of 43.6% and 32.3% on some tasks. We present an in-depth analysis of how intrinsic properties of words and their segmentations into tokens correspond to model performance. For counting tasks, we find that tokenization properties are weakly correlated with correctness, while the length of the queried word and the actual character count play a more significant part. In contrast, for tasks requiring intra-word positional understanding, performance is negatively correlated with the length of the token containing the queried character, suggesting that longer tokens obscure character position information for LLMs. We encourage future work to build on the benchmark and evaluation methodology introduced here as tools for improving model performance on such tasks.

Practicing conversations with large language models (LLMs) presents a promising alternative to traditional in-person language learning. However, most LLMs generate text at a near-native level of complexity, making them ill-suited for beginner learners (CEFR: A1-A2). In this paper, we investigate whether controllable generation techniques -- specifically modular methods that do not require model fine-tuning -- can adapt LLM outputs to better support absolute beginners. We evaluate these methods through both automatic metrics and a user study with university-level learners of Japanese. Our findings show that while prompting alone fails to control output difficulty, the use of future discriminators (Yang and Klein, 2021) significantly improves output comprehensibility (from 40.4\% to 84.3\%). We further introduce a novel token-level evaluation metric, Token Miss Rate (TMR), that quantifies the proportion of incomprehensible tokens per utterance and correlates strongly with human judgments. To support future research in AI-assisted language learning, we release our code, models, annotation tools, and dataset.

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.

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.

Large Language Models (LLMs) achieve impressive reasoning capabilities at the cost of substantial inference overhead, posing substantial deployment challenges. Although distilled Small Language Models (SLMs) significantly enhance efficiency, their performance suffers as they fail to follow LLMs' reasoning paths. Luckily, we reveal that only a small fraction of tokens genuinely diverge reasoning paths between LLMs and SLMs. Most generated tokens are either identical or exhibit neutral differences, such as minor variations in abbreviations or expressions. Leveraging this insight, we introduce **Roads to Rome (R2R)**, a neural token routing method that selectively utilizes LLMs only for these critical, path-divergent tokens, while leaving the majority of token generation to the SLM. We also develop an automatic data generation pipeline that identifies divergent tokens and generates token-level routing labels to train the lightweight router. We apply R2R to combine R1-1.5B and R1-32B models from the DeepSeek family, and evaluate on challenging math, coding, and QA benchmarks. With an average activated parameter size of 5.6B, R2R surpasses the average accuracy of R1-7B by 1.6x, outperforming even the R1-14B model. Compared to R1-32B, it delivers a 2.8x wall-clock speedup with comparable performance, advancing the Pareto frontier of test-time scaling efficiency. Our code is available at https://github.com/thu-nics/R2R.

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.

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.

On-policy distillation (OPD) has become a core technique in the post-training of large language models, yet its training dynamics remain poorly understood. This paper provides a systematic investigation of OPD dynamics and mechanisms. We first identify that two conditions govern whether OPD succeeds or fails: (i) the student and teacher should share compatible thinking patterns; and (ii) even with consistent thinking patterns and higher scores, the teacher must offer genuinely new capabilities beyond what the student has seen during training. We validate these findings through weak-to-strong reverse distillation, showing that same-family 1.5B and 7B teachers are distributionally indistinguishable from the student's perspective. Probing into the token-level mechanism, we show that successful OPD is characterized by progressive alignment on high-probability tokens at student-visited states, a small shared token set that concentrates most of the probability mass (97%-99%). We further propose two practical strategies to recover failing OPD: off-policy cold start and teacher-aligned prompt selection. Finally, we show that OPD's apparent free lunch of dense token-level reward comes at a cost, raising the question of whether OPD can scale to long-horizon distillation.

Representing continuous time is a critical and under-explored challenge in modeling temporal event sequences with large language models (LLMs). Various strategies like byte-level representations or calendar tokens have been proposed. However, the optimal approach remains unclear, especially given the diverse statistical distributions of real-world event data, which range from smooth log-normal to discrete, spiky patterns. This paper presents the first empirical study of temporal tokenization for event sequences, comparing distinct encoding strategies: naive numeric strings, high-precision byte-level representations, human-semantic calendar tokens, classic uniform binning, and adaptive residual scalar quantization. We evaluate these strategies by fine-tuning LLMs on real-world datasets that exemplify these diverse distributions. Our analysis reveals that no single strategy is universally superior; instead, prediction performance depends heavily on aligning the tokenizer with the data's statistical properties, with log-based strategies excelling on skewed distributions and human-centric formats proving robust for mixed modalities.

Large Language Models (LLMs) have recently achieved remarkable progress by leveraging Reinforcement Learning and extended Chain-of-Thought (CoT) techniques. However, the challenge of performing efficient language reasoning--especially during inference with extremely long outputs--has drawn increasing attention from the research community. In this work, we propose a dynamic ratio-based training pipeline that does not rely on sophisticated data annotations or interpolation between multiple models. We continuously balance the weights between the model's System-1 and System-2 data to eliminate redundant reasoning processes while preserving the model's reasoning capability. We validate our approach across models on DeepSeek-R1-Distill-7B and DeepSeek-R1-Distill-14B and on a diverse set of benchmarks with varying difficulty levels. Our method significantly reduces the number of output tokens by nearly 40% while maintaining the accuracy of the reasoning. Our code and data will be available soon.

Large language models (LLMs) demonstrate great performance in text generation. However, LLMs are still suffering from hallucinations. In this work, we propose an inference-time method, Self-Highlighted Hesitation (SH2), to help LLMs decode more truthfully. SH2 is based on a simple fact rooted in information theory that for an LLM, the tokens predicted with lower probabilities are prone to be more informative than others. Our analysis shows that the tokens assigned with lower probabilities by an LLM are more likely to be closely related to factual information, such as nouns, proper nouns, and adjectives. Therefore, we propose to ''highlight'' the factual information by selecting the tokens with the lowest probabilities and concatenating them to the original context, thus forcing the model to repeatedly read and hesitate on these tokens before generation. During decoding, we also adopt contrastive decoding to emphasize the difference in the output probabilities brought by the hesitation. Experimental results demonstrate that our SH2, requiring no additional data or models, can effectively help LLMs elicit factual knowledge and distinguish hallucinated contexts. Significant and consistent improvements are achieved by SH2 for LLaMA-7b and LLaMA2-7b on multiple hallucination tasks.

In infilling tasks, sub-tokens, representing instances where a complete token is segmented into two parts, often emerge at the boundaries of prefixes, middles, and suffixes. Traditional methods focused on training models at the token level, leading to sub-optimal performance in character-level infilling tasks during the inference stage. Alternately, some approaches considered character-level infilling, but they relied on predicting sub-tokens in inference, yet this strategy diminished ability in character-level infilling tasks due to the large perplexity of the model on sub-tokens. In this paper, we introduce FIM-SE, which stands for Fill-In-the-Middle with both Starting and Ending character constraints. The proposed method addresses character-level infilling tasks by utilizing a line-level format to avoid predicting any sub-token in inference. In addition, we incorporate two special tokens to signify the rest of the incomplete lines, thereby enhancing generation guidance. Extensive experiments demonstrate that our proposed approach surpasses previous methods, offering a significant advantage. Code is available at https://github.com/SenseLLM/FIM-SE.

Diffusion Language Models (DLMs) have recently emerged as a strong alternative to autoregressive language models (LMs). DLMs offer comparable accuracy with faster inference speed via parallel decoding. However, standard DLM decoding strategies relying on high-confidence tokens encounter an inherent information-theoretic bottleneck that restricts decoding progress and ultimately slows generation. We demonstrate both theoretically and empirically that prioritizing high-confidence tokens is inherently inefficient. High-probability tokens carry negligible information and strictly relying on them limits the effective progress made in each decoding round. We prove that the number of decoding rounds must grow linearly with the sample's total information (negative log-likelihood) and inversely with the per-round information budget, establishing a bits-to-rounds principle. We also propose Explore-Then-Exploit (ETE), a training-free decoding strategy that maximizes information throughput and decoding efficiency. ETE combines cross-block decoding with targeted exploration of high-uncertainty tokens to reshape the conditional distribution and trigger cascades of confident predictions. Experiments verify our theoretical bounds and demonstrate that ETE consistently reduces the required number of decoding rounds compared to confidence-only baselines without compromising generation quality.

Tokenization is associated with many poorly understood shortcomings in language models (LMs), yet remains an important component for long sequence scaling purposes. This work studies how tokenization impacts model performance by analyzing and comparing the stochastic behavior of tokenized models with their byte-level, or token-free, counterparts. We discover that, even when the two models are statistically equivalent, their predictive distributions over the next byte can be substantially different, a phenomenon we term as "tokenization bias''. To fully characterize this phenomenon, we introduce the Byte-Token Representation Lemma, a framework that establishes a mapping between the learned token distribution and its equivalent byte-level distribution. From this result, we develop a next-byte sampling algorithm that eliminates tokenization bias without requiring further training or optimization. In other words, this enables zero-shot conversion of tokenized LMs into statistically equivalent token-free ones. We demonstrate its broad applicability with two use cases: fill-in-the-middle (FIM) tasks and model ensembles. In FIM tasks where input prompts may terminate mid-token, leading to out-of-distribution tokenization, our method mitigates performance degradation and achieves an approximately 18% improvement in FIM coding benchmarks, consistently outperforming the standard token healing fix. For model ensembles where each model employs a distinct vocabulary, our approach enables seamless integration, resulting in improved performance (up to 3.7%) over individual models across various standard baselines in reasoning, knowledge, and coding.

By encoding time series as a string of numerical digits, we can frame time series forecasting as next-token prediction in text. Developing this approach, we find that large language models (LLMs) such as GPT-3 and LLaMA-2 can surprisingly zero-shot extrapolate time series at a level comparable to or exceeding the performance of purpose-built time series models trained on the downstream tasks. To facilitate this performance, we propose procedures for effectively tokenizing time series data and converting discrete distributions over tokens into highly flexible densities over continuous values. We argue the success of LLMs for time series stems from their ability to naturally represent multimodal distributions, in conjunction with biases for simplicity, and repetition, which align with the salient features in many time series, such as repeated seasonal trends. We also show how LLMs can naturally handle missing data without imputation through non-numerical text, accommodate textual side information, and answer questions to help explain predictions. While we find that increasing model size generally improves performance on time series, we show GPT-4 can perform worse than GPT-3 because of how it tokenizes numbers, and poor uncertainty calibration, which is likely the result of alignment interventions such as RLHF.

Large language models such as GPT and Llama are trained with a next-token prediction loss. In this work, we suggest that training language models to predict multiple future tokens at once results in higher sample efficiency. More specifically, at each position in the training corpus, we ask the model to predict the following n tokens using n independent output heads, operating on top of a shared model trunk. Considering multi-token prediction as an auxiliary training task, we measure improved downstream capabilities with no overhead in training time for both code and natural language models. The method is increasingly useful for larger model sizes, and keeps its appeal when training for multiple epochs. Gains are especially pronounced on generative benchmarks like coding, where our models consistently outperform strong baselines by several percentage points. Our 13B parameter models solves 12 % more problems on HumanEval and 17 % more on MBPP than comparable next-token models. Experiments on small algorithmic tasks demonstrate that multi-token prediction is favorable for the development of induction heads and algorithmic reasoning capabilities. As an additional benefit, models trained with 4-token prediction are up to 3 times faster at inference, even with large batch sizes.

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.

Chain-of-Thought (CoT) has been proven effective in enhancing the reasoning capabilities of large language models (LLMs). Recent advancements, such as OpenAI's o1 and DeepSeek-R1, suggest that scaling up the length of CoT sequences during inference could further boost LLM reasoning performance. However, due to the autoregressive nature of LLM decoding, longer CoT outputs lead to a linear increase in inference latency, adversely affecting user experience, particularly when the CoT exceeds 10,000 tokens. To address this limitation, we analyze the semantic importance of tokens within CoT outputs and reveal that their contributions to reasoning vary. Building on this insight, we propose TokenSkip, a simple yet effective approach that enables LLMs to selectively skip less important tokens, allowing for controllable CoT compression. Extensive experiments across various models and tasks demonstrate the effectiveness of TokenSkip in reducing CoT token usage while preserving strong reasoning performance. Notably, when applied to Qwen2.5-14B-Instruct, TokenSkip reduces reasoning tokens by 40% (from 313 to 181) on GSM8K, with less than a 0.4% performance drop.

Recent advancements in multimodal large reasoning models (MLRMs) have significantly improved performance in visual question answering. However, we observe that transition words (e.g., because, however, and wait) are closely associated with hallucinations and tend to exhibit high-entropy states. We argue that adequate contextual reasoning information can be directly extracted from the token probability distribution. Inspired by superposed representation theory, we propose leveraging latent superposed reasoning to integrate multiple candidate semantics and maintain latent reasoning trajectories. The hypothesis is that reliance on discrete textual inputs may drive the model toward sequential explicit reasoning, underutilizing dense contextual cues during high-entropy reasoning stages. Therefore, we propose constructing rich semantic representations from the token probability distributions to enhance in-context reasoning. With this goal, we present Latent Entropy-Aware Decoding (LEAD), an efficient plug-and-play decoding strategy that leverages semantic context to achieve reliable reasoning. The heart of our method lies in entropy-aware reasoning mode switching. The model employs probability-weighted continuous embeddings under high-entropy states and transitions back to discrete token embeddings as entropy decreases. Moreover, we propose a prior-guided visual anchor injection strategy that encourages the model to focus on visual information. Extensive experiments show that LEAD effectively mitigates hallucinations across various MLRMs on multiple benchmarks.

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.

The prefill stage in long-context LLM inference remains a computational bottleneck. Recent token-ranking heuristics accelerate inference by selectively processing a subset of semantically relevant tokens. However, existing methods suffer from unstable token importance estimation, often varying between layers. Evaluating token-ranking quality independently from heuristic-specific architectures is challenging. To address this, we introduce an Answer-Informed Oracle, which defines ground-truth token importance by measuring attention from generated answers back to the prompt. This oracle reveals that existing heuristics exhibit high variance across layers: rankings can degrade sharply at specific layers, a failure mode invisible to end-to-end benchmarks. The diagnosis suggests a simple fix: aggregate scores across layers rather than relying on any single one. We implement this as Cross-Layer Attention Aggregation (CLAA), which closes the gap to the oracle upper bound and reduces Time-to-First-Token (TTFT) by up to 39\% compared to the Full KV Cache baseline.

Though Large Language Models (LLMs) have shown remarkable abilities in mathematics reasoning, they are still struggling with performing numeric operations accurately, such as addition and multiplication. Numbers can be tokenized into tokens in various ways by different LLMs and affect the numeric operations performance. Currently, there are two representatives: 1) Tokenize into 1-digit, and 2) Tokenize into 1sim 3 digit. The difference is roughly equivalent to using different numeral systems (namely base 10 or base 10^{3}). In light of this, we study the scaling behavior of different numeral systems in the context of transformer-based large language models. We empirically show that a base 10 system is consistently more data-efficient than a base 10^{2} or 10^{3} system across training data scale, model sizes under from-scratch training settings, while different number systems have very similar fine-tuning performances. We attribute this to higher token frequencies of a base 10 system. Additionally, we reveal extrapolation behavior patterns on addition and multiplication. We identify that base 100 and base 1000 systems struggle on token-level discernment and token-level operations. We also sheds light on the mechanism learnt by the models.

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.

State-of-the-art language models are autoregressive and operate on subword units known as tokens. Specifically, one must encode the conditioning string into a list of tokens before passing to the language models for next-token prediction. We show that popular encoding schemes, such as maximum prefix encoding (MPE) and byte-pair-encoding (BPE), induce a sampling bias that cannot be mitigated with more training or data. To counter this universal problem, for each encoding scheme above, we propose a novel algorithm to obtain unbiased estimates from any language model trained on tokenized data. Our methods do not require finetuning the model, and the complexity, defined as the number of model runs, scales linearly with the sequence length in the case of MPE. As a result, we show that one can simulate token-free behavior from a tokenized language model. We empirically verify the correctness of our method through a Markov-chain setup, where it accurately recovers the transition probabilities, as opposed to the conventional method of directly prompting tokens into the language model.

Rubric-based Reinforcement Learning (RL) has emerged as a promising approach for aligning Large Language Models (LLMs) with complex, open-domain instruction following tasks. However, existing methods predominantly rely on response-level rewards, introducing severe reward sparsity and reward ambiguity problems. To address these issues, we propose Rubrics to Tokens (RTT), a novel rubric-based RL framework that bridges coarse response-level scores and fine-grained token-level credit assignment. RTT introduces a Token-Level Relevance Discriminator to predict which tokens in the response are responsible for a specific constraint, and optimizes the policy model via RTT-GRPO, which integrates response-level and token-level advantages within a unified framework. Furthermore, when transitioning from one-dimensional, outcome-level reward to three-dimensional reward space in the token-level rubric-based RL, we propose a novel group normalization method, called Intra-sample Token Group Normalization, to accommodate this shift. Extensive experiments and benchmarks demonstrate that RTT consistently outperforms other baselines in both instruction- and rubric-level accuracy across different models.

Multimodal Large Language Models (MLLMs) have demonstrated impressive capabilities, yet they encounter significant computational bottlenecks due to the massive volume of visual tokens. Consequently, visual token pruning, which substantially reduces the token count, has emerged as a critical technique for accelerating MLLM inference. Existing approaches focus on token importance, diversity, or an intuitive combination of both, without a principled framework for their optimal integration. To address this issue, we first conduct a systematic analysis to characterize the trade-off between token importance and semantic diversity. Guided by this analysis, we propose the Importance and Diversity Pruner (IDPruner), which leverages the Maximal Marginal Relevance (MMR) algorithm to achieve a Pareto-optimal balance between these two objectives. Crucially, our method operates without requiring attention maps, ensuring full compatibility with FlashAttention and efficient deployment via one-shot pruning. We conduct extensive experiments across various model architectures and multimodal benchmarks, demonstrating that IDPruner achieves state-of-the-art performance and superior generalization across diverse architectures and tasks. Notably, on Qwen2.5-VL-7B-Instruct, IDPruner retains 95.18\% of baseline performance when pruning 75\% of the tokens, and still maintains 86.40\% even under an extreme 90\% pruning ratio. Our code is available at https://github.com/Tencent/AngelSlim.

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.

The use of continuous instead of discrete tokens during the Chain-of-Thought (CoT) phase of reasoning LLMs has garnered attention recently, based on the intuition that a continuous mixture of discrete tokens could simulate a superposition of several reasoning paths simultaneously. Theoretical results have formally proven that continuous tokens have much greater expressivity and can solve specific problems more efficiently. However, practical use of continuous tokens has been limited by strong training difficulties: previous works either just use continuous tokens at inference time on a pre-trained discrete-token model, or must distill the continuous CoT from ground-truth discrete CoTs and face computational costs that limit the CoT to very few tokens. This is the first work introducing a scalable method to learn continuous CoTs via reinforcement learning (RL), without distilling from reference discrete CoTs. We use "soft" tokens: mixtures of tokens together with noise on the input embedding to provide RL exploration. Computational overhead is minimal, enabling us to learn continuous CoTs with hundreds of tokens. On math reasoning benchmarks with Llama and Qwen models up to 8B, training with continuous CoTs match discrete-token CoTs for pass@1 and surpass them for pass@32, showing greater CoT diversity. In systematic comparisons, the best-performing scenario is to train with continuous CoT tokens then use discrete tokens for inference, meaning the "soft" models can be deployed in a standard way. Finally, we show continuous CoT RL training better preserves the predictions of the base model on out-of-domain tasks, thus providing a softer touch to the base model.

We study the fractal structure of language, aiming to provide a precise formalism for quantifying properties that may have been previously suspected but not formally shown. We establish that language is: (1) self-similar, exhibiting complexities at all levels of granularity, with no particular characteristic context length, and (2) long-range dependent (LRD), with a Hurst parameter of approximately H=0.70. Based on these findings, we argue that short-term patterns/dependencies in language, such as in paragraphs, mirror the patterns/dependencies over larger scopes, like entire documents. This may shed some light on how next-token prediction can lead to a comprehension of the structure of text at multiple levels of granularity, from words and clauses to broader contexts and intents. We also demonstrate that fractal parameters improve upon perplexity-based bits-per-byte (BPB) in predicting downstream performance. We hope these findings offer a fresh perspective on language and the mechanisms underlying the success of LLMs.

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.

The next-token prediction (NTP) objective has been foundational in the development of modern large language models (LLMs), driving advances in fluency and generalization. However, NTP operates at the token level, treating deviations from a single reference continuation as errors even when alternative continuations are equally plausible or semantically equivalent (e.g., ``mom'' vs. ``mother''). As a result, token-level loss can penalize valid abstractions, paraphrases, or conceptually correct reasoning paths, biasing models toward surface form rather than underlying meaning. This mismatch between the training signal and semantic correctness motivates learning objectives that operate over higher-level representations. We propose a shift from token-level to concept-level prediction, where concepts group multiple surface forms of the same idea (e.g., ``mom,'' ``mommy,'' ``mother'' rightarrow MOTHER). We introduce various methods for integrating conceptual supervision into LLM training and show that concept-aware models achieve lower perplexity, improved robustness under domain shift, and stronger performance than NTP-based models on diverse NLP benchmarks. This suggests concept-level supervision as an improved training signal that better aligns LLMs with human semantic abstractions.

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.

Human cognition typically involves thinking through abstract, fluid concepts rather than strictly using discrete linguistic tokens. Current reasoning models, however, are constrained to reasoning within the boundaries of human language, processing discrete token embeddings that represent fixed points in the semantic space. This discrete constraint restricts the expressive power and upper potential of such reasoning models, often causing incomplete exploration of reasoning paths, as standard Chain-of-Thought (CoT) methods rely on sampling one token per step. In this work, we introduce Soft Thinking, a training-free method that emulates human-like "soft" reasoning by generating soft, abstract concept tokens in a continuous concept space. These concept tokens are created by the probability-weighted mixture of token embeddings, which form the continuous concept space, enabling smooth transitions and richer representations that transcend traditional discrete boundaries. In essence, each generated concept token encapsulates multiple meanings from related discrete tokens, implicitly exploring various reasoning paths to converge effectively toward the correct answer. Empirical evaluations on diverse mathematical and coding benchmarks consistently demonstrate the effectiveness and efficiency of Soft Thinking, improving pass@1 accuracy by up to 2.48 points while simultaneously reducing token usage by up to 22.4% compared to standard CoT. Qualitative analysis further reveals that Soft Thinking outputs remain highly interpretable and readable, highlighting the potential of Soft Thinking to break the inherent bottleneck of discrete language-based reasoning. Code is available at https://github.com/eric-ai-lab/Soft-Thinking.

Hallucination, the generation of untruthful content, is one of the major concerns regarding foundational models. Detecting hallucinations at the token level is vital for real-time filtering and targeted correction, yet the variation of hallucination signals within token sequences is not fully understood. Leveraging the RAGTruth corpus with token-level annotations and reproduced logits, we analyse how these signals depend on a token's position within hallucinated spans, contributing to an improved understanding of token-level hallucination. Our results show that the first hallucinated token carries a stronger signal and is more detectable than conditional tokens. We release our analysis framework, along with code for logit reproduction and metric computation at https://github.com/jakobsnl/RAGTruth_Xtended.

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.

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.

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.

The rapid advancement in large language models (LLMs) has significantly enhanced their ability to generate coherent and contextually relevant text, raising concerns about the misuse of AI-generated content and making it critical to detect it. However, the task remains challenging, particularly in unseen domains or with unfamiliar LLMs. Leveraging LLM next-token distribution outputs offers a theoretically appealing approach for detection, as they encapsulate insights from the models' extensive pre-training on diverse corpora. Despite its promise, zero-shot methods that attempt to operationalize these outputs have met with limited success. We hypothesize that one of the problems is that they use the mean to aggregate next-token distribution metrics across tokens, when some tokens are naturally easier or harder to predict and should be weighted differently. Based on this idea, we propose the Perplexity Attention Weighted Network (PAWN), which uses the last hidden states of the LLM and positions to weight the sum of a series of features based on metrics from the next-token distribution across the sequence length. Although not zero-shot, our method allows us to cache the last hidden states and next-token distribution metrics on disk, greatly reducing the training resource requirements. PAWN shows competitive and even better performance in-distribution than the strongest baselines (fine-tuned LMs) with a fraction of their trainable parameters. Our model also generalizes better to unseen domains and source models, with smaller variability in the decision boundary across distribution shifts. It is also more robust to adversarial attacks, and if the backbone has multilingual capabilities, it presents decent generalization to languages not seen during supervised training, with LLaMA3-1B reaching a mean macro-averaged F1 score of 81.46% in cross-validation with nine languages.

During the finetuning stage of text generation tasks, standard cross-entropy loss treats all tokens equally. This can lead models to overemphasize high-frequency, low-information tokens, neglecting lower-frequency tokens crucial for specificity and informativeness in generated content. This paper introduces a novel loss function, Power-Law Decay Loss (PDL), specifically designed to optimize the finetuning process for text generation. The core motivation for PDL stems from observations in information theory and linguistics: the informativeness of a token is often inversely proportional to its frequency of occurrence. PDL re-weights the contribution of each token in the standard cross-entropy loss based on its frequency in the training corpus, following a power-law decay. Specifically, the weights for high-frequency tokens are reduced, while low-frequency, information-dense tokens are assigned higher weights. This mechanism guides the model during finetuning to focus more on learning and generating tokens that convey specific and unique information, thereby enhancing the quality, diversity, and informativeness of the generated text. We theoretically elaborate on the motivation and construction of PDL and discuss its potential applications and advantages across various text generation finetuning tasks, such as abstractive summarization, dialogue systems, and style transfer.

Recent advancements in reinforcement learning, particularly through Group Relative Policy Optimization (GRPO), have significantly improved multimodal large language models for complex reasoning tasks. However, two critical limitations persist: 1) they often produce unfocused, verbose reasoning chains that obscure salient spatiotemporal cues and 2) binary rewarding fails to account for partially correct answers, resulting in high reward variance and inefficient learning. In this paper, we propose TW-GRPO, a novel framework that enhances visual reasoning with focused thinking and dense reward granularity. Specifically, we employs a token weighting mechanism that prioritizes tokens with high informational density (estimated by intra-group variance), suppressing redundant tokens like generic reasoning prefixes. Furthermore, we reformulate RL training by shifting from single-choice to multi-choice QA tasks, where soft rewards enable finer-grained gradient estimation by distinguishing partial correctness. Additionally, we propose question-answer inversion, a data augmentation strategy to generate diverse multi-choice samples from existing benchmarks. Experiments demonstrate state-of-the-art performance on several video reasoning and general understanding benchmarks. Notably, TW-GRPO achieves 50.4\% accuracy on CLEVRER (18.8\% improvement over Video-R1) and 65.8\% on MMVU. Our codes are available at https://github.com/longmalongma/TW-GRPO.

Despite the remarkable performance of multimodal large language models (MLLMs) across diverse tasks, the substantial training and inference costs impede their advancement. The majority of computation stems from the overwhelming volume of vision tokens processed by the transformer decoder. In this paper, we propose to build efficient MLLMs by leveraging the Mixture-of-Depths (MoD) mechanism, where each transformer decoder layer selects essential vision tokens to process while skipping redundant ones. However, integrating MoD into MLLMs is non-trivial. To address the challenges of training and inference stability as well as limited training data, we adapt the MoD module with two novel designs: tanh-gated weight normalization (TanhNorm) and symmetric token reweighting (STRing). Moreover, we observe that vision tokens exhibit higher redundancy in deeper layer and thus design a progressive ratio decay (PRD) strategy, which gradually reduces the token retention ratio layer by layer, employing a shifted cosine schedule. This crucial design fully unleashes the potential of MoD, significantly boosting the efficiency and performance of our models. To validate the effectiveness of our approach, we conduct extensive experiments with two baseline models across 14 benchmarks. Our model, p-MoD, matches or even surpasses the performance of the baseline models, with only 55.6% TFLOPs and 53.8% KV cache storage during inference, and 77.7% GPU hours during training.

Every act of language generation compresses a rich internal state into a single token sequence. We call this process intention collapse: a many-to-one projection from a high dimensional intention space I into an external language space L. We formalize intention collapse for contemporary language models, define three simple, model agnostic intention metrics (intention entropy Hint, effective dimensionality dimeff, and latent knowledge recoverability Recov), and propose an empirical agenda for studying how inference time computation shapes internal intentions before they are verbalized. We also report a first small scale experiment. Using a 4 bit Mistral 7B model on 200 GSM8K problems, we compare a direct answer baseline, a chain of thought (CoT) regime, and a babble control. CoT raises accuracy from 5.5 percent to 53 percent, sharply reduces pre collapse intention entropy (from 1.42 to 0.37 bits), and shows higher global effective dimensionality than the other regimes despite producing fewer tokens than babble. At the same time, Hint has little item level predictive power, and a linear probe on I achieves AUROC 0.65 in the CoT regime but only about chance in the baseline regime, where it collapses to the majority class. These preliminary results indicate that intention level metrics can distinguish inference regimes and expose latent information that is partly lost during collapse, while also revealing important limitations of our current proxies

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.

Vision Language Models (VLMs) have demonstrated strong capabilities across various visual understanding and reasoning tasks. However, their real-world deployment is often constrained by high latency during inference due to substantial compute required to process the large number of input tokens (predominantly from the image) by the LLM. To reduce inference costs, one can either downsize the LLM or reduce the number of input image-tokens, the latter of which has been the focus of many recent works around token compression. However, it is unclear what the optimal trade-off is, as both the factors directly affect the VLM performance. We first characterize this optimal trade-off between the number of visual tokens and LLM parameters by establishing scaling laws that capture variations in performance with these two factors. Our results reveal a surprising trend: for visual reasoning tasks, the inference-optimal behavior in VLMs, i.e., minimum downstream error at any given fixed inference compute, is achieved when using the largest LLM that fits within the inference budget while minimizing visual token count - often to a single token. While the token reduction literature has mainly focused on maintaining base model performance by modestly reducing the token count (e.g., 5-10times), our results indicate that the compute-optimal inference regime requires operating under even higher token compression ratios. Based on these insights, we take some initial steps towards building approaches tailored for high token compression settings. Code is available at https://github.com/locuslab/llava-token-compression.

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.

The rapid proliferation of Large Language Models (LLMs) and diverse specialized benchmarks necessitates a shift from fragmented, task-specific metrics to a holistic, competitive ranking system that effectively aggregates performance across multiple ability dimensions. Primarily using static scoring, current evaluation methods are fundamentally limited. They struggle to determine the proper mix ratio across diverse benchmarks, and critically, they fail to capture a model's dynamic competitive fitness or its vulnerability when confronted with sequential, high-stakes tasks. To address this, we introduce the novel Competitive Swiss-System Dynamics (CSD) framework. CSD simulates a multi-round, sequential contest where models are dynamically paired across a curated sequence of benchmarks based on their accumulated win-loss record. And Monte Carlo Simulation (N=100,000 iterations) is used to approximate the statistically robust Expected Win Score (E[S_m]), which eliminates the noise of random pairing and early-round luck. Furthermore, we implement a Failure Sensitivity Analysis by parameterizing the per-round elimination quantity (T_k), which allows us to profile models based on their risk appetite--distinguishing between robust generalists and aggressive specialists. We demonstrate that CSD provides a more nuanced and context-aware ranking than traditional aggregate scoring and static pairwise models, representing a vital step towards risk-informed, next-generation LLM evaluation.

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.

LLMs process text as sequences of tokens that roughly correspond to words, where less common words are represented by multiple tokens. However, individual tokens are often semantically unrelated to the meanings of the words/concepts they comprise. For example, Llama-2-7b's tokenizer splits the word "northeastern" into the tokens ['_n', 'ort', 'he', 'astern'], none of which correspond to semantically meaningful units like "north" or "east." Similarly, the overall meanings of named entities like "Neil Young" and multi-word expressions like "break a leg" cannot be directly inferred from their constituent tokens. Mechanistically, how do LLMs convert such arbitrary groups of tokens into useful higher-level representations? In this work, we find that last token representations of named entities and multi-token words exhibit a pronounced "erasure" effect, where information about previous and current tokens is rapidly forgotten in early layers. Using this observation, we propose a method to "read out" the implicit vocabulary of an autoregressive LLM by examining differences in token representations across layers, and present results of this method for Llama-2-7b and Llama-3-8B. To our knowledge, this is the first attempt to probe the implicit vocabulary of an LLM.

Transformers, the backbone of modern large language models (LLMs), face inherent architectural limitations that impede their reasoning capabilities. Unlike recurrent networks, Transformers lack recurrent connections, confining them to constant-depth computation. This restriction places them in the complexity class TC^0, making them theoretically incapable of solving tasks that demand increasingly deep reasoning as input length grows. Counting, a fundamental component of many reasoning tasks, also requires reasoning depth to grow linearly to be performed inductively. While previous studies have established the upper limits of counting ability in Transformer-based expert models (i.e., models specifically trained for counting tasks), these findings do not directly extend to general-purpose LLMs due to differences in reasoning mechanisms. Recent work has highlighted how Chain of Thought (CoT) reasoning can help alleviate some of the architectural limitations of Transformers in counting tasks. However, little attention has been paid to the role of tokenization in these models. Unlike expert models that often use character-level tokenization, LLMs typically rely on byte-level (BPE) tokenizers, which fundamentally alters the way reasoning is processed. Our work investigates the impact of tokenization on the counting abilities of LLMs, uncovering substantial performance variations based on input tokenization differences. We provide both theoretical and experimental analyses, offering insights into how tokenization choices can undermine models' theoretical computability, thereby inspiring the design of new tokenization methods to enhance reasoning in LLMs.

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 its simplicity and efficacy, the high token expenditure of self-consistency can limit its practical utility. Here we investigate if self-consistency can be made more token-efficient for long chain-of-thought reasoning tasks, while preserving its parallelism, through early hypothesis pruning. Concretely, we generate all solutions in parallel, but periodically prune intermediate hypotheses that are deemed unnecessary based on two lightweight indicators: (a) the model's own confidence in individual hypotheses, and (b) lexical coverage of all current hypotheses by candidate subsets that are under consideration for continued retention. We design a fast weighted set cover algorithm that utilizes the two indicators; our evaluation of five LLMs on three math benchmarks shows that this method can improve token efficiency for all models, by 10-35% in many cases.

The ongoing debate on whether reinforcement learning with verifiable rewards (RLVR) expands or shrinks the reasoning capabilities of large language models (LLMs) remains unresolved. Some studies contend that RLVR mainly improves sampling efficiency but at the expense of diversity and exploratory capacity, resulting in capability boundary shrinkage. In contrast, others demonstrate that prolonged training can lead to the emergence of novel reasoning strategies, suggesting capability boundary expansion. To reconcile these contradictory findings, we theoretically and empirically show that both perspectives are partially valid-each aligning with a separate phase in an inherent two-stage probability mass dynamic: (1) Exploitation stage: initially, the model primarily samples explored high-reward and low-reward tokens, while rarely selecting the potentially optimal token. Positive advantage estimates increase the probability of high-reward tokens and decrease those of low-reward tokens, yet the optimal token's probability remains largely unchanged during this stage. (2) Exploration stage: as training advances, the growth rate of previously acquired high-reward tokens slows as their probabilities approach saturation. When a potentially optimal token-now receiving positive advantage estimates-is occasionally sampled, its probability increases, while those of the originally high-reward tokens decrease. This dynamic suggests that over-exploitation during the exploitation stage may lead to capability boundary shrinkage, whereas prolonged training into the exploration stage can promote an expansion of the reasoning capability boundary. Building upon our insights, we revisit the potential of only using relative negative gradients for prolonging training, providing a theoretical and empirical foundation for the development of more advanced reasoning capabilities.

The popularity of transformer-based text embeddings calls for better statistical tools for measuring distributions of such embeddings. One such tool would be a method for ranking texts within a corpus by centrality, i.e. assigning each text a number signifying how representative that text is of the corpus as a whole. However, an intrinsic center-outward ordering of high-dimensional text representations is not trivial. A statistical depth is a function for ranking k-dimensional objects by measuring centrality with respect to some observed k-dimensional distribution. We adopt a statistical depth to measure distributions of transformer-based text embeddings, transformer-based text embedding (TTE) depth, and introduce the practical use of this depth for both modeling and distributional inference in NLP pipelines. We first define TTE depth and an associated rank sum test for determining whether two corpora differ significantly in embedding space. We then use TTE depth for the task of in-context learning prompt selection, showing that this approach reliably improves performance over statistical baseline approaches across six text classification tasks. Finally, we use TTE depth and the associated rank sum test to characterize the distributions of synthesized and human-generated corpora, showing that five recent synthetic data augmentation processes cause a measurable distributional shift away from associated human-generated text.

Thinking Tokens (TT) have been proposed as an unsupervised method to facilitate reasoning in language models. However, despite their conceptual appeal, our findings show that TTs marginally improves performance and consistently underperforms compared to Chain-of-Thought (CoT) reasoning across multiple benchmarks. We hypothesize that this underperformance stems from the reliance on a single embedding for TTs, which results in inconsistent learning signals and introduces noisy gradients. This paper provides a comprehensive empirical analysis to validate this hypothesis and discusses the implications for future research on unsupervised reasoning in LLMs.

In most machine learning tasks, we evaluate a model M on a given data population S by measuring a population-level metric F(S;M). Examples of such evaluation metric F include precision/recall for (binary) recognition, the F1 score for multi-class classification, and the BLEU metric for language generation. On the other hand, the model M is trained by optimizing a sample-level loss G(S_t;M) at each learning step t, where S_t is a subset of S (a.k.a. the mini-batch). Popular choices of G include cross-entropy loss, the Dice loss, and sentence-level BLEU scores. A fundamental assumption behind this paradigm is that the mean value of the sample-level loss G, if averaged over all possible samples, should effectively represent the population-level metric F of the task, such as, that E[ G(S_t;M) ] approx F(S;M). In this paper, we systematically investigate the above assumption in several NLP tasks. We show, both theoretically and experimentally, that some popular designs of the sample-level loss G may be inconsistent with the true population-level metric F of the task, so that models trained to optimize the former can be substantially sub-optimal to the latter, a phenomenon we call it, Simpson's bias, due to its deep connections with the classic paradox known as Simpson's reversal paradox in statistics and social sciences.

Language models typically tokenize text into subwords, using a deterministic, hand-engineered heuristic of combining characters into longer surface-level strings such as 'ing' or whole words. Recent literature has repeatedly shown the limitations of such a tokenization strategy, particularly for documents not written in English and for representing numbers. On the other extreme, byte/character-level language models are much less restricted but suffer from increased sequence description lengths and a subsequent quadratic expansion in self-attention computation. Recent attempts to compress and limit these context lengths with fixed size convolutions is helpful but completely ignores the word boundary. This paper considers an alternative 'learn your tokens' scheme which utilizes the word boundary to pool bytes/characters into word representations, which are fed to the primary language model, before again decoding individual characters/bytes per word in parallel. We find that our moderately expressive and moderately fast end-to-end tokenizer outperform by over 300% both subwords and byte/character models over the intrinsic language modeling metric of next-word prediction across datasets. It particularly outshines on rare words, outperforming by a factor of 30! We extensively study the language modeling setup for all three categories of tokenizers and theoretically analyze how our end-to-end models can also be a strong trade-off in efficiency and robustness.

Large language models display remarkable capabilities in logical and mathematical reasoning, allowing them to solve complex tasks. Interestingly, these abilities emerge in networks trained on the simple task of next-token prediction. In this work, we present a theoretical framework for studying auto-regressive next-token predictors. We demonstrate that even simple models such as linear next-token predictors, trained on Chain-of-Thought (CoT) data, can approximate any function efficiently computed by a Turing machine. We introduce a new complexity measure -- length complexity -- which measures the number of intermediate tokens in a CoT sequence required to approximate some target function, and analyze the interplay between length complexity and other notions of complexity. Finally, we show experimentally that simple next-token predictors, such as linear networks and shallow Multi-Layer Perceptrons (MLPs), display non-trivial performance on text generation and arithmetic tasks. Our results demonstrate that the power of language models can be attributed, to a great extent, to the auto-regressive next-token training scheme, and not necessarily to a particular choice of architecture.

According to Algorithmic Information Theory (AIT) -- Intelligent representations compress data into the shortest possible program that can reconstruct its content, exhibiting low Kolmogorov Complexity (KC). In contrast, most visual representation learning systems use fixed-length representations for all inputs, ignoring variations in complexity or familiarity. Recent adaptive tokenization methods address this by allocating variable-length representations but typically require test-time search over multiple encodings to find the most predictive one. Inspired by Kolmogorov Complexity principles, we propose a single-pass adaptive tokenizer, KARL, which predicts the appropriate number of tokens for an image in a single forward pass, halting once its approximate KC is reached. The token count serves as a proxy for the minimum description length. KARL's training procedure closely resembles the Upside-Down Reinforcement Learning paradigm, as it learns to conditionally predict token halting based on a desired reconstruction quality. KARL matches the performance of recent adaptive tokenizers while operating in a single pass. We present scaling laws for KARL, analyzing the role of encoder/decoder size, continuous vs. discrete tokenization and more. Additionally, we offer a conceptual study drawing an analogy between Adaptive Image Tokenization and Algorithmic Information Theory, examining the predicted image complexity (KC) across axes such as structure vs. noise and in- vs. out-of-distribution familiarity -- revealing alignment with human intuition.

Masked language models (MLM) do not explicitly define a distribution over language, i.e., they are not language models per se. However, recent work has implicitly treated them as such for the purposes of generation and scoring. This paper studies methods for deriving explicit joint distributions from MLMs, focusing on distributions over two tokens, which makes it possible to calculate exact distributional properties. We find that an approach based on identifying joints whose conditionals are closest to those of the MLM works well and outperforms existing Markov random field-based approaches. We further find that this derived model's conditionals can even occasionally outperform the original MLM's conditionals.

A multilingual tokenizer is a fundamental component of multilingual neural machine translation. It is trained from a multilingual corpus. Since a skewed data distribution is considered to be harmful, a sampling strategy is usually used to balance languages in the corpus. However, few works have systematically answered how language imbalance in tokenizer training affects downstream performance. In this work, we analyze how translation performance changes as the data ratios among languages vary in the tokenizer training corpus. We find that while relatively better performance is often observed when languages are more equally sampled, the downstream performance is more robust to language imbalance than we usually expected. Two features, UNK rate and closeness to the character level, can warn of poor downstream performance before performing the task. We also distinguish language sampling for tokenizer training from sampling for model training and show that the model is more sensitive to the latter.

Recently, autoregressive (AR) image models have demonstrated remarkable generative capabilities, positioning themselves as a compelling alternative to diffusion models. However, their sequential nature leads to long inference times, limiting their practical scalability. In this work, we introduce Grouped Speculative Decoding (GSD), a novel, training-free acceleration method for AR image models. While recent studies have explored Speculative Decoding (SD) as a means to speed up AR image generation, existing approaches either provide only modest acceleration or require additional training. Our in-depth analysis reveals a fundamental difference between language and image tokens: image tokens exhibit inherent redundancy and diversity, meaning multiple tokens can convey valid semantics. However, traditional SD methods are designed to accept only a single most-likely token, which fails to leverage this difference, leading to excessive false-negative rejections. To address this, we propose a new SD strategy that evaluates clusters of visually valid tokens rather than relying on a single target token. Additionally, we observe that static clustering based on embedding distance is ineffective, which motivates our dynamic GSD approach. Extensive experiments show that GSD accelerates AR image models by an average of 3.7x while preserving image quality-all without requiring any additional training. The source code is available at https://github.com/junhyukso/GSD