Daily Papers

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

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.

Large Language Models (LLMs) that can continually improve beyond their training budgets are able to solve increasingly difficult problems by adapting at test time, a property we refer to as extrapolation. However, standard reinforcement learning (RL) operates over fixed problem distributions and training budgets, which limits extrapolation amidst distribution shift at test time. To address this, we introduce RC, an iterative decoding algorithm that replaces standard autoregressive decoding during both training and inference. RC exploits an asymmetry between the response generation and summarization capabilities of LLMs to construct reasoning chains that consistently improve across iterations. Models trained to use RC can extrapolate and continually improve over reasoning horizons more than an order of magnitude longer than those seen during training. Empirically, training a 4B model with RC using a 16k-token training budget improves performance on HMMT 2025 from 40% to nearly 70% with 0.5m tokens at test time, outperforming both comparably sized models and many larger reasoning LLMs. Finally, we also show that models trained with RC can more effectively leverage existing scaffolds to further scale test-time performance, due to the improved summary-conditioned generation abilities learned through training.

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

Reinforcement Learning (RL) for Large Language Models (LLMs) often suffers from training collapse in long-horizon tasks due to exploding gradient variance. To mitigate this, a baseline is commonly introduced for advantage computation; however, traditional value models remain difficult to optimize, and standard group-based baselines overlook sequence heterogeneity. Although classic optimal baseline theory can achieve global variance reduction, it neglects token heterogeneity and requires prohibitive gradient-based computation. In this work, we derive the Optimal Token Baseline (OTB) from first principles, proving that gradient updates should be weighted inversely to their cumulative gradient norm. To ensure efficiency, we propose the Logit-Gradient Proxy that approximates the gradient norm using only forward-pass probabilities. Our method achieves training stability and matches the performance of large group sizes (N=32) with only N=4, reducing token consumption by over 65% across single-turn and tool-integrated reasoning tasks.

Reinforcement learning with verifiable rewards (RLVR) has become a central component of large language model (LLM) post-training. Unlike supervised fine-tuning (SFT), RLVR lets an LLM generate multiple candidate solutions and reinforces those that lead to a verifiably correct final answer. However, in practice, RLVR often requires thousands of training steps to reach strong performance, incurring substantial computation largely attributed to prolonged exploration. In this work, we make a surprising observation: during RLVR, LLMs evolve in a strongly linear manner. Specifically, both model weights and model output log-probabilities exhibit strong linear correlations with RL training steps. This suggests that RLVR predominantly amplifies trends that emerge early in training, rather than continuously discovering new behaviors throughout the entire optimization trajectory. Motivated by this linearity, we investigate whether future model states can be predicted from intermediate checkpoints via extrapolation, avoiding continued expensive training. We show that Weight Extrapolation produces models with performance comparable to standard RL training while requiring significantly less computation. Moreover, Logits Extrapolation consistently outperforms continued RL training on all four benchmarks by extrapolating beyond the step range where RL training remains stable.

We consider an extension to the classic position auctions in which sponsored creatives can be added within AI generated content rather than shown in predefined slots. New challenges arise from the natural requirement that sponsored creatives should smoothly fit into the context. With the help of advanced LLM technologies, it becomes viable to accurately estimate the benefits of adding each individual sponsored creatives into each potential positions within the AI generated content by properly taking the context into account. Therefore, we assume one click-through rate estimation for each position-creative pair, rather than one uniform estimation for each sponsored creative across all positions in classic settings. As a result, the underlying optimization becomes a general matching problem, thus the substitution effects should be treated more carefully compared to standard position auction settings, where the slots are independent with each other. In this work, we formalize a concrete mathematical model of the extended position auction problem and study the welfare-maximization and revenue-maximization mechanism design problem. Formally, we consider two different user behavior models and solve the mechanism design problems therein respectively. For the Multinomial Logit (MNL) model, which is order-insensitive, we can efficiently implement the optimal mechanisms. For the cascade model, which is order-sensitive, we provide approximately optimal solutions.

Large language models excel at reasoning but lack key aspects of introspection, including anticipating their own success and the computation required to achieve it. Humans use real-time introspection to decide how much effort to invest, when to make multiple attempts, when to stop, and when to signal success or failure. Without this, LLMs struggle to make intelligent meta-cognition decisions. Test-time scaling methods like Best-of-N drive up cost and latency by using a fixed budget of samples regardless of the marginal benefit of each one at any point in generation, and the absence of confidence signals can mislead people, prevent appropriate escalation to better tools, and undermine trustworthiness. Learned verifiers or reward models can provide confidence estimates, but do not enable adaptive inference and add substantial cost by requiring extra models or forward passes. We present ZIP-RC, which equips models with zero-overhead introspective predictions of reward and cost. At every token, ZIP-RC reuses reserved or unused logits in the same forward pass as next-token prediction to output a joint distribution over final reward and remaining length -- no extra models, architecture change, or inference overhead. This full joint distribution is used to compute a sampling utility which is the linear combination of the expected maximum reward, total compute, and latency of set of samples if generated to completion. During inference, we maximize this utility with meta-actions that determine which prefix of tokens to continue or initiate sampling from. On mixed-difficulty mathematical benchmarks, ZIP-RC improves accuracy by up to 12% over majority voting at equal or lower average cost, and traces smooth Pareto frontiers between quality, compute, and latency. By providing real-time reward-cost introspection, ZIP-RC enables adaptive, efficient reasoning.

Relative positional embeddings (RPE) have received considerable attention since RPEs effectively model the relative distance among tokens and enable length extrapolation. We propose KERPLE, a framework that generalizes relative position embedding for extrapolation by kernelizing positional differences. We achieve this goal using conditionally positive definite (CPD) kernels, a class of functions known for generalizing distance metrics. To maintain the inner product interpretation of self-attention, we show that a CPD kernel can be transformed into a PD kernel by adding a constant offset. This offset is implicitly absorbed in the Softmax normalization during self-attention. The diversity of CPD kernels allows us to derive various RPEs that enable length extrapolation in a principled way. Experiments demonstrate that the logarithmic variant achieves excellent extrapolation performance on three large language modeling datasets. Our implementation and pretrained checkpoints are released at https://github.com/chijames/KERPLE.git.

Speculative decoding is an effective and lossless approach for accelerating LLM inference. However, existing widely adopted model-based draft designs, such as EAGLE3, improve accuracy at the cost of multi-step autoregressive inference, resulting in high drafting latency and ultimately rendering the drafting stage itself a performance bottleneck. Inspired by diffusion-based large language models (dLLMs), we propose DART, which leverages parallel generation to reduce drafting latency. DART predicts logits for multiple future masked positions in parallel within a single forward pass based on hidden states of the target model, thereby eliminating autoregressive rollouts in the draft model while preserving a lightweight design. Based on these parallel logit predictions, we further introduce an efficient tree pruning algorithm that constructs high-quality draft token trees with N-gram-enforced semantic continuity. DART substantially reduces draft-stage overhead while preserving high draft accuracy, leading to significantly improved end-to-end decoding speed. Experimental results demonstrate that DART achieves a 2.03x--3.44x wall-clock time speedup across multiple datasets, surpassing EAGLE3 by 30% on average and offering a practical speculative decoding framework. Code is released at https://github.com/fvliang/DART.

The extrapolation capability of Large Language Models (LLMs) based on Rotary Position Embedding is currently a topic of considerable interest. The mainstream approach to addressing extrapolation with LLMs involves modifying RoPE by replacing 10000, the rotary base of theta_n={10000}^{-2n/d} in the original RoPE, with a larger value and providing longer fine-tuning text. In this work, we first observe that fine-tuning a RoPE-based LLM with either a smaller or larger base in pre-training context length could significantly enhance its extrapolation performance. After that, we propose \textit{Scaling Laws of RoPE-based Extrapolation}, a unified framework from the periodic perspective, to describe the relationship between the extrapolation performance and base value as well as tuning context length. In this process, we also explain the origin of the RoPE-based extrapolation issue by \textit{critical dimension for extrapolation}. Besides these observations and analyses, we achieve extrapolation up to 1 million context length within only 16K training length on LLaMA2 7B and 13B.

Transformer-based Large Language Models (LLMs) struggle to process inputs exceeding their training context window, with performance degrading due to positional out-of-distribution (O.O.D.) that disrupt attention computations. Existing solutions, fine-tuning and training-free methods, are limited by computational inefficiency, attention logit outliers or loss of local positional information. To address this, we propose Greedy Attention Logit Interpolation (GALI), a training-free length extrapolation method that maximizes the utilization of pretrained positional intervals while avoiding attention logit outliers through attention logit interpolation. The result demonstrates that GALI consistently outperforms state-of-the-art training-free methods. Our findings reveal that LLMs interpret positional intervals unevenly within their training context window, suggesting that extrapolating within a smaller positional interval range yields superior results-even for short-context tasks. GALI represents a significant step toward resolving the positional O.O.D. challenge, enabling more reliable long-text understanding in LLMs. Our implementation of GALI, along with the experiments from our paper, is open-sourced at https://github.com/AcademyCityL/GALI.

Various XAI attribution methods have been recently proposed for the transformer architecture, allowing for insights into the decision-making process of large language models by assigning importance scores to input tokens and intermediate representations. One class of methods that seems very promising in this direction includes decomposition-based approaches, i.e., XAI-methods that redistribute the model's prediction logit through the network, as this value is directly related to the prediction. In the previous literature we note though that two prominent methods of this category, namely ALTI-Logit and LRP, have not yet been analyzed in juxtaposition and hence we propose to close this gap by conducting a careful quantitative evaluation w.r.t. ground truth annotations on a subject-verb agreement task, as well as various qualitative inspections, using BERT, GPT-2 and LLaMA-3 as a testbed. Along the way we compare and extend the ALTI-Logit and LRP methods, including the recently proposed AttnLRP variant, from an algorithmic and implementation perspective. We further incorporate in our benchmark two widely-used gradient-based attribution techniques. Finally, we make our carefullly constructed benchmark dataset for evaluating attributions on language models, as well as our code, publicly available in order to foster evaluation of XAI-methods on a well-defined common ground.

Extrapolation -- the ability to make inferences that go beyond the scope of one's experiences -- is a hallmark of human intelligence. By contrast, the generalization exhibited by contemporary neural network algorithms is largely limited to interpolation between data points in their training corpora. In this paper, we consider the challenge of learning representations that support extrapolation. We introduce a novel visual analogy benchmark that allows the graded evaluation of extrapolation as a function of distance from the convex domain defined by the training data. We also introduce a simple technique, temporal context normalization, that encourages representations that emphasize the relations between objects. We find that this technique enables a significant improvement in the ability to extrapolate, considerably outperforming a number of competitive techniques.

Auto-regressive decoding makes the inference of Large Language Models (LLMs) time-consuming. We propose a simple framework, EAGLE (Extrapolation Algorithm for Greater Language-model Efficiency), for lossless acceleration. Unlike traditional speculative sampling methods, EAGLE operates the drafting process auto-regressively at the more regular (second-top-layer) feature level and addresses the sampling uncertainty issues in the next-feature prediction problems by integrating tokens from one time step ahead. The acceleration provided by EAGLE is lossless: it involves no fine-tuning of the target LLM, and the generated text maintains the same distribution as that of vanilla auto-regressive decoding. As of the submission of this paper, EAGLE is the fastest known framework within the speculative sampling family. On MT-bench, EAGLE is 3x faster than vanilla decoding, 2x faster than Lookahead, and 1.6x faster than Medusa. Using gpt-fast, EAGLE attains on average 160 tokens/s with LLaMA2-Chat 13B on a single RTX 3090 GPU, compared to 24 tokens/s of Huggingface's implementations.

We propose an acceleration scheme for large language models (LLMs) through Speculative Decoding with Semantic Adaptive Tokens (SDSAT). The primary objective of this design is to enhance the LLM model's ability to generate draft tokens more accurately without compromising the model's accuracy. The core strategies involve: 1) Fine-tune the model by incorporating semantic adaptive tokens that possess flexible decoding capabilities without changing its structure, allowing them to generate high-quality draft tokens. 2) By employing a training method that does not affect the standard tokens, the model can acquire parallel decoding abilities atop its original framework with minimal training overhead. 3) We have designed the "two-step-draft-then-verify" generation strategies using both greedy search and nucleus sampling. Experiments conducted on the CodeLlama-13B and 7B models have yielded speed increases of over 3.5X and 3.0X, respectively. Please refer to https://github.com/hasuoshenyun/SDSAT.

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

We present Entropy Adaptive Decoding (EAD), a novel approach for efficient language model inference that dynamically switches between different-sized models based on prediction uncertainty. By monitoring rolling entropy in model logit distributions, our method identifies text regions where a smaller model suffices and switches to a larger model only when prediction uncertainty exceeds a threshold. Unlike speculative decoding approaches that maintain perfect output fidelity through verification, EAD accepts controlled output divergence in exchange for computational efficiency. Our experiments on the MATH benchmark demonstrate remarkable efficiency gains across different model families. Using the LLaMA family, we maintain 96.7\% of the 11B model's performance (50.4\% vs 52.1\%) while using it for only 43\% of tokens, decreasing computational cost by 41.5\%. These gains become more pronounced with larger size differentials in the Qwen family, where we achieve 92.9\% of the 14B model's performance (74.3\% vs 80.0\%) while using it for just 25\% of tokens, decreasing computational cost by 67\%. The consistency of these results across model pairs suggests that language model computation can be significantly optimized by selectively deploying model capacity based on local generation complexity. Our findings indicate that current approaches to model inference may be unnecessarily conservative in their pursuit of perfect output fidelity, and that accepting minor performance trade-offs can enable dramatic reductions in computational costs.

Large language models have achieved remarkable success in recent years, primarily due to the implementation of self-attention mechanisms. However, traditional Softmax attention suffers from numerical instability and reduced performance as the length of inference tokens increases. This paper addresses these issues by decomposing the Softmax operation into a non-linear transformation and the l_1-norm. We identify the latter as essential for maintaining model performance. By replacing the non-linear transformation with the Softplus activation function and introducing a dynamic scale factor for different token lengths based on invariance entropy, we create a novel attention mechanism with performance better than conventional Softmax attention across various inference lengths. To further improve the length extrapolation ability of the proposed attention mechanism, we introduce a fine-tuning-free re-weighting mechanism that amplifies significant attention weights while diminishing weaker ones, enabling the model to concentrate more effectively on relevant tokens without requiring retraining. When combined with our proposed attention mechanism, this approach demonstrates significant promise in managing longer sequences, maintaining nearly constant validation loss even at 16times the training token length while ensuring numerical stability. Our code is available at: https://github.com/iminfine/freeatten.

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.

Recently, pre-trained vision-language models (e.g., CLIP) have shown great potential in few-shot learning and attracted a lot of research interest. Although efforts have been made to improve few-shot ability of CLIP, key factors on the effectiveness of existing methods have not been well studied, limiting further exploration of CLIP's potential in few-shot learning. In this paper, we first introduce a unified formulation to analyze CLIP-based few-shot learning methods from a perspective of logit bias, which encourages us to learn an effective logit bias for further improving performance of CLIP-based few-shot learning methods. To this end, we disassemble three key components involved in computation of logit bias (i.e., logit features, logit predictor, and logit fusion) and empirically analyze the effect on performance of few-shot classification. Based on analysis of key components, this paper proposes a novel AMU-Tuning method to learn effective logit bias for CLIP-based few-shot classification. Specifically, our AMU-Tuning predicts logit bias by exploiting the appropriate textbf{A}uxiliary features, which are fed into an efficient feature-initialized linear classifier with textbf{M}ulti-branch training. Finally, an textbf{U}ncertainty-based fusion is developed to incorporate logit bias into CLIP for few-shot classification. The experiments are conducted on several widely used benchmarks, and the results show AMU-Tuning clearly outperforms its counterparts while achieving state-of-the-art performance of CLIP-based few-shot learning without bells and whistles.

Recent advancements in recommender systems have focused on leveraging Large Language Models (LLMs) to improve user preference modeling, yielding promising outcomes. However, current LLM-based approaches struggle to fully leverage user behavior sequences, resulting in suboptimal preference modeling for personalized recommendations. In this study, we propose a novel Counterfactual Fine-Tuning (CFT) method to address this issue by explicitly emphasizing the role of behavior sequences when generating recommendations. Specifically, we employ counterfactual reasoning to identify the causal effects of behavior sequences on model output and introduce a task that directly fits the ground-truth labels based on these effects, achieving the goal of explicit emphasis. Additionally, we develop a token-level weighting mechanism to adjust the emphasis strength for different item tokens, reflecting the diminishing influence of behavior sequences from earlier to later tokens during predicting an item. Extensive experiments on real-world datasets demonstrate that CFT effectively improves behavior sequence modeling. Our codes are available at https://github.com/itsmeyjt/CFT.

Leveraging the models' outputs, specifically the logits, is a common approach to estimating the test accuracy of a pre-trained neural network on out-of-distribution (OOD) samples without requiring access to the corresponding ground truth labels. Despite their ease of implementation and computational efficiency, current logit-based methods are vulnerable to overconfidence issues, leading to prediction bias, especially under the natural shift. In this work, we first study the relationship between logits and generalization performance from the view of low-density separation assumption. Our findings motivate our proposed method MaNo which (1) applies a data-dependent normalization on the logits to reduce prediction bias, and (2) takes the L_p norm of the matrix of normalized logits as the estimation score. Our theoretical analysis highlights the connection between the provided score and the model's uncertainty. We conduct an extensive empirical study on common unsupervised accuracy estimation benchmarks and demonstrate that MaNo achieves state-of-the-art performance across various architectures in the presence of synthetic, natural, or subpopulation shifts.

Transformers' ability to generalize to longer sequences than they have been trained on, known as length extrapolation, degrades as sequence length increases. Most of Relative Positional Encoding (RPE) methods address this problem by either adding constant linear biases or learning general biases, lacking the ability to specialize for different sequences. In this work, inspired by ALiBi, we propose Context-aware Biases for Length Extrapolation (Cable), that learns token-specific biases for each head in decoder-based transformers. Cable learns adaptive, context-aware biases, overcoming the limitations of fixed patterns by adding dynamic biases specific to each token in the sequence. Results show that when tested on a sequence length of 1024, a GPT-3 Medium (334M parameters) with our positional encoding, trained on a sequence length of 512, achieves better perplexity (-0.65) than a similar network with sinusoidal positional encoding trained on a sequence length of 1024. This is achieved with 48% lower memory usage, and only 3.5% higher training time. Furthermore, our method notably improves the extrapolation ability of existing RPE methods on the Edu-FineWeb10B and WikiText-103 datasets. Code is available at: https://github.com/axiomlab/Cable

While large reasoning models trained with critic-free reinforcement learning and verifiable rewards (RLVR) represent the state-of-the-art, their practical utility is hampered by ``overthinking'', a critical issue where models generate excessively long reasoning paths without any performance benefit. Existing solutions that penalize length often fail, inducing performance degradation due to a fundamental misalignment between trajectory-level rewards and token-level optimization. In this work, we introduce a novel framework, DECS, built on our theoretical discovery of two previously unaddressed flaws in current length rewards: (1) the erroneous penalization of essential exploratory tokens and (2) the inadvertent rewarding of partial redundancy. Our framework's innovations include (i) a first-of-its-kind decoupled token-level reward mechanism that surgically distinguishes and penalizes redundant tokens, and (ii) a novel curriculum batch scheduling strategy to master the efficiency-efficacy equilibrium. Experimental results show DECS can achieve a dramatic reduction in reasoning tokens by over 50\% across seven benchmarks while simultaneously maintaining or even improving performance. It demonstrates conclusively that substantial gains in reasoning efficiency can be achieved without compromising a model's underlying reasoning power. Code is available at https://github.com/pixas/DECS.

Reinforcement Learning has emerged as the fundamental technique for enhancing reasoning in LLMs. However, existing algorithms apply uniform optimization to all tokens, ignoring their different roles in reasoning process. To address this limitation, we introduce Heterogeneous Adaptive Policy Optimization (HAPO), a comprehensive token-aware algorithm that dynamically adapts optimization based on token entropy. For rollout sampling, we propose Adaptive Temperature Sampling, which adjusts sampling temperature in real time, promoting exploration at high-entropy tokens while preserving coherence at low-entropy ones. For advantage calculation, we introduce Token Level Group Average that normalizes advantages at token level, jointly accounting for sequence-length as in token-mean loss while preserving non-biased treatment. We then develop Differential Advantage Redistribution that leverages entropy and importance ratios to modulate rewards-adjusting updates for tokens with clear signals. For clipping loss, we design Asymmetric Adaptive Clipping, allowing aggressive probability reduction for noisy low-entropy tokens while enabling exploration for high-entropy tokens. Through systematic investigation between entropy and training dynamics, we embedded token-level treatment into every stages to achieve fine-grained control. Extensive experiments demonstrate that HAPO consistently outperforms DAPO across multiple model scales. Our code can be found in https://github.com/starriver030515/HAPO.

Inference with modern Large Language Models (LLMs) is expensive and time-consuming, and speculative sampling has proven to be an effective solution. Most speculative sampling methods such as EAGLE use a static draft tree, implicitly assuming that the acceptance rate of draft tokens depends only on their position. Interestingly, we found that the acceptance rate of draft tokens is also context-dependent. In this paper, building upon EAGLE, we propose EAGLE-2, which introduces a new technique of context-aware dynamic draft tree into drafting modeling. This improvement leverages the fact that the draft model of EAGLE is well-calibrated: the confidence scores from the draft model approximate acceptance rates with small errors. We conducted extensive evaluations on three series of LLMs and six tasks, with EAGLE-2 achieving speedup ratios 3.05x-4.26x, which is 20%-40% faster than EAGLE-1. EAGLE-2 also ensures that the distribution of the generated text remains unchanged, making it a lossless acceleration algorithm.

Out-of-distribution (OOD) detection is critical for ensuring the reliability of deep learning models in open-world applications. While post-hoc methods are favored for their efficiency and ease of deployment, existing approaches often underexploit the rich information embedded in the model's logits space. In this paper, we propose LogitGap, a novel post-hoc OOD detection method that explicitly exploits the relationship between the maximum logit and the remaining logits to enhance the separability between in-distribution (ID) and OOD samples. To further improve its effectiveness, we refine LogitGap by focusing on a more compact and informative subset of the logit space. Specifically, we introduce a training-free strategy that automatically identifies the most informative logits for scoring. We provide both theoretical analysis and empirical evidence to validate the effectiveness of our approach. Extensive experiments on both vision-language and vision-only models demonstrate that LogitGap consistently achieves state-of-the-art performance across diverse OOD detection scenarios and benchmarks. Code is available at https://github.com/GIT-LJc/LogitGap.

Efficient fine-tuning of large language models for task-specific applications is imperative, yet the vast number of parameters in these models makes their training increasingly challenging. Despite numerous proposals for effective methods, a substantial memory overhead remains for gradient computations during updates. Can we fine-tune a series of task-specific small models and transfer their knowledge directly to a much larger model without additional training? In this paper, we explore weak-to-strong specialization using logit arithmetic, facilitating a direct answer to this question. Existing weak-to-strong methods often employ a static knowledge transfer ratio and a single small model for transferring complex knowledge, which leads to suboptimal performance. % To address this, To surmount these limitations, we propose a dynamic logit fusion approach that works with a series of task-specific small models, each specialized in a different task. This method adaptively allocates weights among these models at each decoding step, learning the weights through Kullback-Leibler divergence constrained optimization problems. We conduct extensive experiments across various benchmarks in both single-task and multi-task settings, achieving leading results. By transferring expertise from the 7B model to the 13B model, our method closes the performance gap by 96.4\% in single-task scenarios and by 86.3\% in multi-task scenarios compared to full fine-tuning of the 13B model. Notably, we achieve surpassing performance on unseen tasks. Moreover, we further demonstrate that our method can effortlessly integrate in-context learning for single tasks and task arithmetic for multi-task scenarios. (Our implementation is available in https://github.com/Facico/Dynamic-Logit-Fusion.)

While large reasoning models demonstrate strong performance on complex tasks, they lack the ability to adjust reasoning token usage based on task difficulty. This often leads to the "overthinking" problem -- excessive and unnecessary reasoning -- which, although potentially mitigated by human intervention to control the token budget, still fundamentally contradicts the goal of achieving fully autonomous AI. In this work, we propose Adaptive Reasoning Model (ARM), a reasoning model capable of adaptively selecting appropriate reasoning formats based on the task at hand. These formats include three efficient ones -- Direct Answer, Short CoT, and Code -- as well as a more elaborate format, Long CoT. To train ARM, we introduce Ada-GRPO, an adaptation of Group Relative Policy Optimization (GRPO), which addresses the format collapse issue in traditional GRPO. Ada-GRPO enables ARM to achieve high token efficiency, reducing tokens by an average of 30%, and up to 70%, while maintaining performance comparable to the model that relies solely on Long CoT. Furthermore, not only does it improve inference efficiency through reduced token generation, but it also brings a 2x speedup in training. In addition to the default Adaptive Mode, ARM supports two additional reasoning modes: 1) Instruction-Guided Mode, which allows users to explicitly specify the reasoning format via special tokens -- ideal when the appropriate format is known for a batch of tasks. 2) Consensus-Guided Mode, which aggregates the outputs of the three efficient formats and resorts to Long CoT in case of disagreement, prioritizing performance with higher token usage.

Most of the existing Out-Of-Distribution (OOD) detection algorithms depend on single input source: the feature, the logit, or the softmax probability. However, the immense diversity of the OOD examples makes such methods fragile. There are OOD samples that are easy to identify in the feature space while hard to distinguish in the logit space and vice versa. Motivated by this observation, we propose a novel OOD scoring method named Virtual-logit Matching (ViM), which combines the class-agnostic score from feature space and the In-Distribution (ID) class-dependent logits. Specifically, an additional logit representing the virtual OOD class is generated from the residual of the feature against the principal space, and then matched with the original logits by a constant scaling. The probability of this virtual logit after softmax is the indicator of OOD-ness. To facilitate the evaluation of large-scale OOD detection in academia, we create a new OOD dataset for ImageNet-1K, which is human-annotated and is 8.8x the size of existing datasets. We conducted extensive experiments, including CNNs and vision transformers, to demonstrate the effectiveness of the proposed ViM score. In particular, using the BiT-S model, our method gets an average AUROC 90.91% on four difficult OOD benchmarks, which is 4% ahead of the best baseline. Code and dataset are available at https://github.com/haoqiwang/vim.

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.

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.

Knowledge distillation involves transferring soft labels from a teacher to a student using a shared temperature-based softmax function. However, the assumption of a shared temperature between teacher and student implies a mandatory exact match between their logits in terms of logit range and variance. This side-effect limits the performance of student, considering the capacity discrepancy between them and the finding that the innate logit relations of teacher are sufficient for student to learn. To address this issue, we propose setting the temperature as the weighted standard deviation of logit and performing a plug-and-play Z-score pre-process of logit standardization before applying softmax and Kullback-Leibler divergence. Our pre-process enables student to focus on essential logit relations from teacher rather than requiring a magnitude match, and can improve the performance of existing logit-based distillation methods. We also show a typical case where the conventional setting of sharing temperature between teacher and student cannot reliably yield the authentic distillation evaluation; nonetheless, this challenge is successfully alleviated by our Z-score. We extensively evaluate our method for various student and teacher models on CIFAR-100 and ImageNet, showing its significant superiority. The vanilla knowledge distillation powered by our pre-process can achieve favorable performance against state-of-the-art methods, and other distillation variants can obtain considerable gain with the assistance of our pre-process.

In-Context Learning (ICL) emerges as a key feature for Large Language Models (LLMs), allowing them to adapt to new tasks by leveraging task-specific examples without updating model parameters. However, ICL faces challenges with increasing numbers of examples due to performance degradation and quadratic computational costs. In this paper, we propose Logit Arithmetic Reweighting Approach (LARA), a novel framework that enhances ICL by using logit-based ensembling of multiple demonstrations. Our approach divides long input demonstrations into parallelizable shorter inputs to significantly reduce memory requirements, and then effectively aggregate the information by reweighting logits of each group via a non-gradient optimization approach. We further introduce Binary LARA (B-LARA), a variant that constrains weights to binary values to simplify the search space and reduces memory usage by filtering out less informative demonstration groups. Experiments on BBH and MMLU demonstrate that LARA and B-LARA outperform all baseline methods in both accuracy and memory efficiency. We also conduct extensive analysis to show that LARA generalizes well to scenarios of varying numbers of examples from limited to many-shot demonstrations.

Users of music streaming, video streaming, news recommendation, and e-commerce services often engage with content in a sequential manner. Providing and evaluating good sequences of recommendations is therefore a central problem for these services. Prior reweighting-based counterfactual evaluation methods either suffer from high variance or make strong independence assumptions about rewards. We propose a new counterfactual estimator that allows for sequential interactions in the rewards with lower variance in an asymptotically unbiased manner. Our method uses graphical assumptions about the causal relationships of the slate to reweight the rewards in the logging policy in a way that approximates the expected sum of rewards under the target policy. Extensive experiments in simulation and on a live recommender system show that our approach outperforms existing methods in terms of bias and data efficiency for the sequential track recommendations problem.

Large reasoning models (LRMs) achieve higher performance on challenging reasoning tasks by generating more tokens at inference time, but this verbosity often wastes computation on easy problems. Existing solutions, including supervised finetuning on shorter traces, user-controlled budgets, or RL with uniform penalties, either require data curation, manual configuration, or treat all problems alike regardless of difficulty. We introduce Adaptive Length Penalty (ALP), a reinforcement learning objective tailoring generation length to per-prompt solve rate. During training, ALP monitors each prompt's online solve rate through multiple rollouts and adds a differentiable penalty whose magnitude scales inversely with that rate, so confident (easy) prompts incur a high cost for extra tokens while hard prompts remain unhindered. Posttraining DeepScaleR-1.5B with ALP cuts average token usage by 50\% without significantly dropping performance. Relative to fixed-budget and uniform penalty baselines, ALP redistributes its reduced budget more intelligently by cutting compute on easy prompts and reallocating saved tokens to difficult ones, delivering higher accuracy on the hardest problems with higher cost.

Over-parameterized deep networks trained using gradient-based optimizers are a popular choice for solving classification and ranking problems. Without appropriately tuned ell_2 regularization or weight decay, such networks have the tendency to make output scores (logits) and network weights large, causing training loss to become too small and the network to lose its adaptivity (ability to move around) in the parameter space. Although regularization is typically understood from an overfitting perspective, we highlight its role in making the network more adaptive and enabling it to escape more easily from weights that generalize poorly. To provide such a capability, we propose a method called Logit Attenuating Weight Normalization (LAWN), that can be stacked onto any gradient-based optimizer. LAWN controls the logits by constraining the weight norms of layers in the final homogeneous sub-network. Empirically, we show that the resulting LAWN variant of the optimizer makes a deep network more adaptive to finding minimas with superior generalization performance on large-scale image classification and recommender systems. While LAWN is particularly impressive in improving Adam, it greatly improves all optimizers when used with large batch sizes

The recent advancements in large language models (LLMs) have been extraordinary, yet the escalating inference costs associated with them present challenges in real-world applications. To address these challenges, we propose a novel approach called Early-exiting Speculative Decoding (EESD) with lossless acceleration. Specifically, EESD utilizes a segment of the LLM to generate draft tokens, incorporating Early-exiting structures after the first N layers. To enhance the quality of draft tokens, a self-distillation method is integrated. This early-exiting design not only reduces deployment and training costs but also significantly accelerates the token generation speed. Moreover, we introduce a novel sampling mechanism that leverages Thompson Sampling to regulate the generation processes, automatically determining the quantity of draft tokens in each round. The original LLM is then employed to validate these draft tokens through a single forward pass, and thus guarantees that the final output text maintains a distribution consistent with vanilla auto-regressive decoding. The experimental results on both 13B and 70B models demonstrate that our approach decodes tokens at a markedly accelerated rate compared to prior methods, showing the effectiveness of our approach.

Since the introduction of the transformer model by Vaswani et al. (2017), a fundamental question has yet to be answered: how does a model achieve extrapolation at inference time for sequences that are longer than it saw during training? We first show that extrapolation can be enabled by simply changing the position representation method, though we find that current methods do not allow for efficient extrapolation. We therefore introduce a simpler and more efficient position method, Attention with Linear Biases (ALiBi). ALiBi does not add positional embeddings to word embeddings; instead, it biases query-key attention scores with a penalty that is proportional to their distance. We show that this method trains a 1.3 billion parameter model on input sequences of length 1024 that extrapolates to input sequences of length 2048, achieving the same perplexity as a sinusoidal position embedding model trained on inputs of length 2048 but training 11% faster and using 11% less memory. ALiBi's inductive bias towards recency also leads it to outperform multiple strong position methods on the WikiText-103 benchmark.

Training modern large language models (LLMs) has become a veritable smorgasbord of algorithms and datasets designed to elicit particular behaviors, making it critical to develop techniques to understand the effects of datasets on the model's properties. This is exacerbated by recent experiments that show datasets can transmit signals that are not directly observable from individual datapoints, posing a conceptual challenge for dataset-centric understandings of LLM training and suggesting a missing fundamental account of such phenomena. Towards understanding such effects, inspired by recent work on the linear structure of LLMs, we uncover a general mechanism through which hidden subtexts can arise in generic datasets. We introduce Logit-Linear-Selection (LLS), a method that prescribes how to select subsets of a generic preference dataset to elicit a wide range of hidden effects. We apply LLS to discover subsets of real-world datasets so that models trained on them exhibit behaviors ranging from having specific preferences, to responding to prompts in a different language not present in the dataset, to taking on a different persona. Crucially, the effect persists for the selected subset, across models with varying architectures, supporting its generality and universality.

Recent advances in large language models (LLMs) have intensified efforts to fuse heterogeneous open-source models into a unified system that inherits their complementary strengths. Existing logit-based fusion methods maintain inference efficiency but treat vocabulary dimensions independently, overlooking semantic dependencies encoded by cross-dimension interactions. These dependencies reflect how token types interact under a model's internal reasoning and are essential for aligning models with diverse generation behaviors. To explicitly model these dependencies, we propose InfiGFusion, the first structure-aware fusion framework with a novel Graph-on-Logits Distillation (GLD) loss. Specifically, we retain the top-k logits per output and aggregate their outer products across sequence positions to form a global co-activation graph, where nodes represent vocabulary channels and edges quantify their joint activations. To ensure scalability and efficiency, we design a sorting-based closed-form approximation that reduces the original O(n^4) cost of Gromov-Wasserstein distance to O(n log n), with provable approximation guarantees. Experiments across multiple fusion settings show that GLD consistently improves fusion quality and stability. InfiGFusion outperforms SOTA models and fusion baselines across 11 benchmarks spanning reasoning, coding, and mathematics. It shows particular strength in complex reasoning tasks, with +35.6 improvement on Multistep Arithmetic and +37.06 on Causal Judgement over SFT, demonstrating superior multi-step and relational inference.

We characterize the statistical efficiency of knowledge transfer through n samples from a teacher to a probabilistic student classifier with input space mathcal S over labels mathcal A. We show that privileged information at three progressive levels accelerates the transfer. At the first level, only samples with hard labels are known, via which the maximum likelihood estimator attains the minimax rate {|{mathcal S||{mathcal A}|}/{n}}. The second level has the teacher probabilities of sampled labels available in addition, which turns out to boost the convergence rate lower bound to {{|{mathcal S}||{mathcal A}|}/{n}}. However, under this second data acquisition protocol, minimizing a naive adaptation of the cross-entropy loss results in an asymptotically biased student. We overcome this limitation and achieve the fundamental limit by using a novel empirical variant of the squared error logit loss. The third level further equips the student with the soft labels (complete logits) on {mathcal A} given every sampled input, thereby provably enables the student to enjoy a rate {|{mathcal S}|}/{n} free of |{mathcal A}|. We find any Kullback-Leibler divergence minimizer to be optimal in the last case. Numerical simulations distinguish the four learners and corroborate our theory.

Large Language Diffusion Models, or diffusion LLMs, have emerged as a significant focus in NLP research, with substantial effort directed toward understanding their scalability and downstream task performance. However, their long-context capabilities remain unexplored, lacking systematic analysis or methods for context extension. In this work, we present the first systematic investigation comparing the long-context performance of diffusion LLMs and traditional auto-regressive LLMs. We first identify a unique characteristic of diffusion LLMs, unlike auto-regressive LLMs, they maintain remarkably \textit{stable perplexity} during direct context extrapolation. Furthermore, where auto-regressive models fail outright during the Needle-In-A-Haystack task with context exceeding their pretrained length, we discover diffusion LLMs exhibit a distinct \textit{local perception} phenomenon, enabling successful retrieval from recent context segments. We explain both phenomena through the lens of Rotary Position Embedding (RoPE) scaling theory. Building on these observations, we propose LongLLaDA, a training-free method that integrates LLaDA with the NTK-based RoPE extrapolation. Our results validate that established extrapolation scaling laws remain effective for extending the context windows of diffusion LLMs. Furthermore, we identify long-context tasks where diffusion LLMs outperform auto-regressive LLMs and others where they fall short. Consequently, this study establishes the first context extrapolation method for diffusion LLMs while providing essential theoretical insights and empirical benchmarks critical for advancing future research on long-context diffusion LLMs.

Large language models (LLMs) are typically personalized via prompt engineering or parameter-efficient fine-tuning such as LoRA. However, writing style can be difficult to distill into a single prompt, and LoRA fine-tuning requires computationally intensive training and infrastructure. We investigate a possible lightweight alternative: steering a frozen LLM with n-gram style priors injected in logit space at decoding time. We train an n-gram model on stylistically distinct corpora -- including Don Quixote, CNN/DailyMail news headlines, and arXiv abstracts -- constructing an interpolated 1-to-3-gram prior over next-token probabilities. During generation we modify the LLM's logits by adding a weighted sum of style log-probabilities from each n-gram order that matches the current context, scaled by a control parameter lambda in [0, 1]. We sweep lambda and style corpora and report style perplexity under the n-gram model, base-model perplexity as a proxy for fluency, Jensen-Shannon (JS) divergence between the original and steered token distributions, and token-overlap statistics. On TinyLlama-1.1B we identify a single narrow regime (for the Don Quixote corpus at lambda=0.1) where style perplexity improves by 24.7% and base-model perplexity improves by 51.4% relative to the frozen model. Outside this regime, and for multi-author corpora such as CNN/DailyMail and arXiv abstracts, even small nonzero lambda values generally result in worse style and fluency, and larger lambda values lead to collapse with extreme perplexities and incoherent text. Logit-space injection of n-gram style priors provides lightweight, tunable style control, but it is fragile: it operates effectively only within a narrow range of low lambda values and is consistently outperformed by prompting and LoRA.

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

Length extrapolation has attracted considerable attention recently since it allows transformers to be tested on longer sequences than those used in training. Previous research has shown that this property can be attained by using carefully designed Relative Positional Encodings (RPEs). While these methods perform well on a variety of corpora, the conditions for length extrapolation have yet to be investigated. This paper attempts to determine what types of RPEs allow for length extrapolation through a thorough mathematical and empirical analysis. We discover that a transformer is certain to possess this property as long as the series that corresponds to the RPE's exponential converges. Two practices are derived from the conditions and examined in language modeling tasks on a variety of corpora. As a bonus from the conditions, we derive a new Theoretical Receptive Field (TRF) to measure the receptive field of RPEs without taking any training steps. Extensive experiments are conducted on the Wikitext-103, Books, Github, and WikiBook datasets to demonstrate the viability of our discovered conditions. We also compare TRF to Empirical Receptive Field (ERF) across different models, showing consistently matched trends on the aforementioned datasets. The code is available at https://github.com/OpenNLPLab/Rpe.

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.

Modern large language models (LLMs) that rely on attention mechanisms are typically trained with fixed context lengths which enforce upper limits on the length of input sequences that they can handle at evaluation time. To use these models on sequences longer than the train-time context length, one might employ techniques from the growing family of context length extrapolation methods -- most of which focus on modifying the system of positional encodings used in the attention mechanism to indicate where tokens or activations are located in the input sequence. We conduct a wide survey of existing methods of context length extrapolation on a base LLaMA or LLaMA 2 model, and introduce some of our own design as well -- in particular, a new truncation strategy for modifying the basis for the position encoding. We test these methods using three new evaluation tasks (FreeFormQA, AlteredNumericQA, and LongChat-Lines) as well as perplexity, which we find to be less fine-grained as a measure of long context performance of LLMs. We release the three tasks publicly as datasets on HuggingFace. We discover that linear scaling is the best method for extending context length, and show that further gains can be achieved by using longer scales at evaluation time. We also discover promising extrapolation capabilities in the truncated basis. To support further research in this area, we release three new 13B parameter long-context models which we call Giraffe: 4k and 16k context models trained from base LLaMA-13B, and a 32k context model trained from base LLaMA2-13B. We also release the code to replicate our results.

Position modeling plays a critical role in Transformers. In this paper, we focus on length extrapolation, i.e., training on short texts while evaluating longer sequences. We define attention resolution as an indicator of extrapolation. Then we propose two designs to improve the above metric of Transformers. Specifically, we introduce a relative position embedding to explicitly maximize attention resolution. Moreover, we use blockwise causal attention during inference for better resolution. We evaluate different Transformer variants with language modeling. Experimental results show that our model achieves strong performance in both interpolation and extrapolation settings. The code will be available at https://aka.ms/LeX-Transformer.

This paper proposes a new loss function for adversarial training. Since adversarial training has difficulties, e.g., necessity of high model capacity, focusing on important data points by weighting cross-entropy loss has attracted much attention. However, they are vulnerable to sophisticated attacks, e.g., Auto-Attack. This paper experimentally reveals that the cause of their vulnerability is their small margins between logits for the true label and the other labels. Since neural networks classify the data points based on the logits, logit margins should be large enough to avoid flipping the largest logit by the attacks. Importance-aware methods do not increase logit margins of important samples but decrease those of less-important samples compared with cross-entropy loss. To increase logit margins of important samples, we propose switching one-vs-the-rest loss (SOVR), which switches from cross-entropy to one-vs-the-rest loss for important samples that have small logit margins. We prove that one-vs-the-rest loss increases logit margins two times larger than the weighted cross-entropy loss for a simple problem. We experimentally confirm that SOVR increases logit margins of important samples unlike existing methods and achieves better robustness against Auto-Attack than importance-aware methods.

Large language models increasingly rely on long chains of thought to improve accuracy, yet such gains come with substantial inference-time costs. We revisit token-efficient post-training and argue that existing sequence-level reward-shaping methods offer limited control over how reasoning effort is allocated across tokens. To bridge the gap, we propose IAPO, an information-theoretic post-training framework that assigns token-wise advantages based on each token's conditional mutual information (MI) with the final answer. This yields an explicit, principled mechanism for identifying informative reasoning steps and suppressing low-utility exploration. We provide a theoretical analysis showing that our IAPO can induce monotonic reductions in reasoning verbosity without harming correctness. Empirically, IAPO consistently improves reasoning accuracy while reducing reasoning length by up to 36%, outperforming existing token-efficient RL methods across various reasoning datasets. Extensive empirical evaluations demonstrate that information-aware advantage shaping is a powerful and general direction for token-efficient post-training. The code is available at https://github.com/YinhanHe123/IAPO.

Current critic-free RL methods for large reasoning models suffer from severe inefficiency when training on positive homogeneous prompts (where all rollouts are correct), resulting in waste of rollouts due to zero advantage estimates. We introduce a radically simple yet powerful solution to Mine intrinsic mastery (Miner), that repurposes the policy's intrinsic uncertainty as a self-supervised reward signal, with no external supervision, auxiliary models, or additional inference cost. Our method pioneers two key innovations: (1) a token-level focal credit assignment mechanism that dynamically amplifies gradients on critical uncertain tokens while suppressing overconfident ones, and (2) adaptive advantage calibration to seamlessly integrate intrinsic and verifiable rewards. Evaluated across six reasoning benchmarks on Qwen3-4B and Qwen3-8B base models, Miner achieves state-of-the-art performance among the other four algorithms, yielding up to 4.58 absolute gains in Pass@1 and 6.66 gains in Pass@K compared to GRPO. Comparison with other methods targeted at exploration enhancement further discloses the superiority of the two newly proposed innovations. This demonstrates that latent uncertainty exploitation is both necessary and sufficient for efficient and scalable RL training of reasoning models.

Generative Language Models (GLMs) have shown impressive performance in tasks such as text generation, understanding, and reasoning. However, the large model size poses challenges for practical deployment. To solve this problem, Quantization-Aware Training (QAT) has become increasingly popular. However, current QAT methods for generative models have resulted in a noticeable loss of accuracy. To counteract this issue, we propose a novel knowledge distillation method specifically designed for GLMs. Our method, called token-scaled logit distillation, prevents overfitting and provides superior learning from the teacher model and ground truth. This research marks the first evaluation of ternary weight quantization-aware training of large-scale GLMs with less than 1.0 degradation in perplexity and no loss of accuracy in a reasoning task.

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.

Transformer has taken the field of natural language processing (NLP) by storm since its birth. Further, Large language models (LLMs) built upon it have captured worldwide attention due to its superior abilities. Nevertheless, all Transformer-based models including these powerful LLMs suffer from a preset length limit and can hardly generalize from short training sequences to longer inference ones, namely, they can not perform length extrapolation. Hence, a plethora of methods have been proposed to enhance length extrapolation of Transformer, in which the positional encoding (PE) is recognized as the major factor. In this survey, we present these advances towards length extrapolation in a unified notation from the perspective of PE. Specifically, we first introduce extrapolatable PEs, including absolute and relative PEs. Then, we dive into extrapolation methods based on them, covering position interpolation and randomized position methods. Finally, several challenges and future directions in this area are highlighted. Through this survey, We aim to enable the reader to gain a deep understanding of existing methods and provide stimuli for future research.

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.

Large reasoning models (LRMs) boosted by Reinforcement Learning from Verifier Reward (RLVR) have shown great power in problem solving, yet they often cause overthinking: excessive, meandering reasoning that inflates computational cost. Prior designs of penalization in RLVR manage to reduce token consumption while often harming model performance, which arises from the oversimplicity of token-level supervision. In this paper, we argue that the granularity of supervision plays a crucial role in balancing efficiency and accuracy, and propose Group Relative Segment Penalization (GRSP), a step-level method to regularize reasoning. Since preliminary analyses show that reasoning segments are strongly correlated with token consumption and model performance, we design a length-aware weighting mechanism across segment clusters. Extensive experiments demonstrate that GRSP achieves superior token efficiency without heavily compromising accuracy, especially the advantages with harder problems. Moreover, GRSP stabilizes RL training and scales effectively across model sizes.

In recent years, developing compact and efficient large language models (LLMs) has emerged as a thriving area of research. Traditional Supervised Fine-Tuning (SFT), which relies on singular ground truth labels, often fails to capture token-level dependencies and linguistic diversity. To address these limitations, we propose a logits-based fine-tuning framework that integrates the strengths of supervised learning and knowledge distillation. Our approach constructs enriched training targets by combining teacher logits with ground truth labels, preserving both correctness and linguistic diversity. This ensures more reliable and effective training. We constructed a large-scale 1.2M logits dataset and trained a series of science-focused models. Experimental results demonstrate that our method achieves significant improvements, with accuracy gains of 18% on Mawps and 22.7% on TabMWP. Across nine widely used mathematical benchmarks, our method consistently outperforms prior SFT models, achieving an average improvement of 7.28%. Codes are available at https://github.com/dvlab-research/Logits-Based-Finetuning.

Speculative decoding is a powerful way to accelerate autoregressive large language models (LLMs), but directly porting it to vision-language models (VLMs) faces unique systems constraints: the prefill stage is dominated by visual tokens whose count scales with image resolution and video length, inflating both compute and memory, especially the key-value (KV) cache. We study speculative decoding for VLMs and introduce SpecVLM, a practical system that (1) establishes a strong EAGLE-2-style baseline, EagleVLM, delivering 1.5--2.3x end-to-end speedups over full autoregressive inference, and (2) further accelerates VLM inference with an elastic visual compressor that adaptively selects among pruning, pooling, convolution, and resampler primitives to balance FLOPs/parameters and accuracy per input. To avoid costly offline distillation corpora, we propose an online-logit distillation protocol that trains the draft model with on-the-fly teacher logits and penultimate features using a combined cross-entropy and Smooth L1 objective, eliminating storage and preprocessing while remaining compute-efficient. This protocol reveals a training-time scaling effect: longer online training monotonically increases the draft model's average accepted length, improving speculative efficiency. Empirically, SpecVLM achieves additional acceleration, culminating in 2.5--2.9x end-to-end speedups within 5 epochs across LLaVA and MMMU, consistently over resolutions and task difficulties, while preserving the target model's output distribution (lossless decoding). Our code is available at https://github.com/haiduo/SpecVLM.

Large reasoning models improve with more test-time computation, but often overthink, producing unnecessarily long chains-of-thought that raise cost without improving accuracy. Prior reinforcement learning approaches typically rely on a single outcome reward with trajectory-level length penalties, which cannot distinguish essential from redundant reasoning steps and therefore yield blunt compression. Although recent work incorporates step-level signals, such as offline pruning, supervised data construction, or verifier-based intermediate rewards, reasoning length is rarely treated as an explicit step-level optimization objective during RL. We propose Step-wise Adaptive Penalization (SWAP), a fine-grained framework that allocates length reduction across steps based on intrinsic contribution. We estimate step importance from the model's on-policy log-probability improvement toward the correct answer, then treat excess length as a penalty mass redistributed to penalize low-importance steps more heavily while preserving high-importance reasoning. We optimize with a unified outcome-process advantage within group-relative policy optimization. Extensive experiments demonstrate that SWAP reduces reasoning length by 64.3% on average while improving accuracy by 5.7% relative to the base model.

Autoregressive language models demonstrate excellent performance in various scenarios. However, the inference efficiency is limited by its one-step-one-word generation mode, which has become a pressing problem recently as the models become increasingly larger. Speculative decoding employs a "draft and then verify" mechanism to allow multiple tokens to be generated in one step, realizing lossless acceleration. Existing methods mainly adopt fixed heuristic draft structures, which fail to adapt to different situations to maximize the acceptance length during verification. To alleviate this dilemma, we proposed OPT-Tree, an algorithm to construct adaptive and scalable draft trees. It searches the optimal tree structure that maximizes the mathematical expectation of the acceptance length in each decoding step. Experimental results reveal that OPT-Tree outperforms the existing draft structures and achieves a speed-up ratio of up to 3.2 compared with autoregressive decoding. If the draft model is powerful enough and the node budget is sufficient, it can generate more than ten tokens in a single step. Our code is available at https://github.com/Jikai0Wang/OPT-Tree.

Recently, scaling reinforcement learning with verifiable rewards (RLVR) for large language models (LLMs) has emerged as an effective training paradigm for significantly improving model capabilities, which requires guiding the model to perform extensive exploration and learning, leading to substantial computational overhead and becoming a key challenge. To reduce the number of training steps, Prior work performs linear extrapolation of model parameters. However, the dynamics of model parameter updates during RLVR training remain insufficiently understood. To further investigate the evolution of LLMs during RLVR training, we conduct empirical experiments and find that the rank-1 subspace of the model does not evolve linearly, and its dominance over the original parameters is further amplified during LoRA training. Based on the above insights, we propose the Nonlinear Extrapolation of low-rank trajectories (NExt), a novel framework that models and extrapolates low-rank parameter trajectories in a nonlinear manner. Concretely, we first train the model using LoRA and extract the rank-1 subspace of parameter differences at multiple training steps, which is then used for the subsequent nonlinear extrapolation. Afterward, we utilized the extracted rank-1 subspace to train a predictor, which can model the trajectory of parameter updates during RLVR, and then perform the predict-extend process to extrapolate model parameters, achieving the acceleration of RLVR. To further study and understand NExt, we conduct comprehensive experiments that demonstrate the effectiveness and robustness of the method. Our method reduces computational overhead by approximately 37.5\% while remaining compatible with a wide range of RLVR algorithms and tasks. We release our code in https://github.com/RUCAIBox/NExt.

Knowledge distillation is a model compression technique in which a compact "student" network is trained to replicate the predictive behavior of a larger "teacher" network. In logit-based knowledge distillation, it has become the de facto approach to augment cross-entropy with a distillation term. Typically, this term is either a KL divergence that matches marginal probabilities or a correlation-based loss that captures intra- and inter-class relationships. In every case, it acts as an additional term to cross-entropy. This term has its own weight, which must be carefully tuned. In this paper, we adopt a choice-theoretic perspective and recast knowledge distillation under the Plackett-Luce model by interpreting teacher logits as "worth" scores. We introduce "Plackett-Luce Distillation (PLD)", a weighted list-wise ranking loss. In PLD, the teacher model transfers knowledge of its full ranking of classes, weighting each ranked choice by its own confidence. PLD directly optimizes a single "teacher-optimal" ranking. The true label is placed first, followed by the remaining classes in descending teacher confidence. This process yields a convex and translation-invariant surrogate that subsumes weighted cross-entropy. Empirically, across CIFAR-100, ImageNet-1K, and MS-COCO, PLD achieves consistent gains across diverse architectures and distillation objectives, including divergence-based, correlation-based, and feature-based methods, in both homogeneous and heterogeneous teacher-student pairs.

We introduce AutoJudge, a framework that accelerates large language model (LLM) inference with task-specific lossy speculative decoding. Instead of matching the original model output distribution token-by-token, we identify which of the generated tokens affect the downstream quality of the generated response, relaxing the guarantee so that the "unimportant" tokens can be generated faster. Our approach relies on a semi-greedy search algorithm to test which of the mismatches between target and draft model should be corrected to preserve quality, and which ones may be skipped. We then train a lightweight classifier based on existing LLM embeddings to predict, at inference time, which mismatching tokens can be safely accepted without compromising the final answer quality. We test our approach with Llama 3.2 1B (draft) and Llama 3.1 8B (target) models on zero-shot GSM8K reasoning, where it achieves up to 1.5x more accepted tokens per verification cycle with under 1% degradation in answer accuracy compared to standard speculative decoding and over 2x with small loss in accuracy. When applied to the LiveCodeBench benchmark, our approach automatically detects other, programming-specific important tokens and shows similar speedups, demonstrating its ability to generalize across tasks.

Personalizing large language models (LLMs) for individual users has become increasingly important as they are progressively integrated into real-world applications to support users' daily lives. However, existing personalization approaches often fail to distinguish which components of model predictions and training data truly reflect user preferences, leading to superficial personalization alignment. In this paper, we introduce NextQuill, a novel LLM personalization alignment framework grounded in causal preference modeling. We approach personalization from a causal perspective, treating both model predictions and ground-truth data generation as outcomes influenced by user preferences, along with other factors. We define the true preference effect as the causal impact of user history (which reflects preferences) on each token prediction or data generation instance, estimated through causal intervention techniques. Building on this insight, NextQuill introduces two complementary alignment strategies: (1) aligning model-internal causal preference effects on predictions with those reflected in ground-truth data, rather than indiscriminately fitting predictions, and (2) focusing on fitting preference-bearing tokens identified via ground-truth data preference effects, rather than treating all tokens uniformly. By integrating these strategies, NextQuill shifts the alignment process toward learning from causal preference effects, facilitating more effective and personalized adaptation. Experiments across multiple personalization benchmarks demonstrate that NextQuill significantly improves personalization quality, offering a principled, causal foundation for LLM personalization. Our codes are available on https://github.com/juntaoyou/NextQuill.

The number of large language models (LLMs) with varying parameter scales and vocabularies is increasing. While they deliver powerful performance, they also face a set of common optimization needs to meet specific requirements or standards, such as instruction following or avoiding the output of sensitive information from the real world. However, how to reuse the fine-tuning outcomes of one model to other models to reduce training costs remains a challenge. To bridge this gap, we introduce Cross-model Control (CMC), a method that improves multiple LLMs in one-time training with a portable tiny language model. Specifically, we have observed that the logit shift before and after fine-tuning is remarkably similar across different models. Based on this insight, we incorporate a tiny language model with a minimal number of parameters. By training alongside a frozen template LLM, the tiny model gains the capability to alter the logits output by the LLMs. To make this tiny language model applicable to models with different vocabularies, we propose a novel token mapping strategy named PM-MinED. We have conducted extensive experiments on instruction tuning and unlearning tasks, demonstrating the effectiveness of CMC. Our code is available at https://github.com/wujwyi/CMC.

In the presence of noisy labels, designing robust loss functions is critical for securing the generalization performance of deep neural networks. Cross Entropy (CE) loss has been shown to be not robust to noisy labels due to its unboundedness. To alleviate this issue, existing works typically design specialized robust losses with the symmetric condition, which usually lead to the underfitting issue. In this paper, our key idea is to induce a loss bound at the logit level, thus universally enhancing the noise robustness of existing losses. Specifically, we propose logit clipping (LogitClip), which clamps the norm of the logit vector to ensure that it is upper bounded by a constant. In this manner, CE loss equipped with our LogitClip method is effectively bounded, mitigating the overfitting to examples with noisy labels. Moreover, we present theoretical analyses to certify the noise-tolerant ability of LogitClip. Extensive experiments show that LogitClip not only significantly improves the noise robustness of CE loss, but also broadly enhances the generalization performance of popular robust losses.

Large reasoning models (LRMs) are typically trained using reinforcement learning with verifiable reward (RLVR) to enhance their reasoning abilities. In this paradigm, policies are updated using both positive and negative self-generated rollouts, which correspond to distinct sample polarities. In this paper, we provide a systematic investigation into how these sample polarities affect RLVR training dynamics and behaviors. We find that positive samples sharpen existing correct reasoning patterns, while negative samples encourage exploration of new reasoning paths. We further explore how adjusting the advantage values of positive and negative samples at both the sample level and the token level affects RLVR training. Based on these insights, we propose an Adaptive and Asymmetric token-level Advantage shaping method for Policy Optimization, namely A3PO, that more precisely allocates advantage signals to key tokens across different polarities. Experiments across five reasoning benchmarks demonstrate the effectiveness of our approach.

Large language models (LLMs) have demonstrated strong reasoning abilities in mathematical tasks, often enhanced through reinforcement learning (RL). However, RL-trained models frequently produce unnecessarily long reasoning traces -- even for simple queries -- leading to increased inference costs and latency. While recent approaches attempt to control verbosity by adding length penalties to the reward function, these methods rely on fixed penalty terms that are hard to tune and cannot adapt as the model's reasoning capability evolves, limiting their effectiveness. In this work, we propose an adaptive reward-shaping method that enables LLMs to "think fast and right" -- producing concise outputs without sacrificing correctness. Our method dynamically adjusts the reward trade-off between accuracy and response length based on model performance: when accuracy is high, the length penalty increases to encourage faster length reduction; when accuracy drops, the penalty is relaxed to preserve correctness. This adaptive reward accelerates early-stage length reduction while avoiding over-compression in later stages. Experiments across multiple datasets show that our approach consistently and dramatically reduces reasoning length while largely maintaining accuracy, offering a new direction for cost-efficient adaptive reasoning in large-scale language models.

Diffusion Large Language Models (dLLMs) represent a new paradigm beyond autoregressive modeling, offering competitive performance while naturally enabling a flexible decoding process. Specifically, dLLMs can generate tokens at arbitrary positions in parallel, endowing them with significant potential for parallel test-time scaling, which was previously constrained by severe inefficiency in autoregressive modeling. In this work, we introduce dVoting, a fast voting technique that boosts reasoning capability without training, with only an acceptable extra computational overhead. dVoting is motivated by the observation that, across multiple samples for the same prompt, token predictions remain largely consistent, whereas performance is determined by a small subset of tokens exhibiting cross-sample variability. Leveraging the arbitrary-position generation capability of dLLMs, dVoting performs iterative refinement by sampling, identifying uncertain tokens via consistency analysis, regenerating them through voting, and repeating this process until convergence. Extensive evaluations demonstrate that dVoting consistently improves performance across various benchmarks. It achieves gains of 6.22%-7.66% on GSM8K, 4.40%-7.20% on MATH500, 3.16%-14.84% on ARC-C, and 4.83%-5.74% on MMLU. Our code is available at https://github.com/fscdc/dVoting

Linear position interpolation helps pre-trained models using rotary position embeddings (RoPE) to extrapolate to longer sequence lengths. We propose using linear position interpolation to extend the extrapolation range of models using Attention with Linear Biases (ALiBi). We find position interpolation significantly improves extrapolation capability on upstream language modelling and downstream summarization and retrieval tasks.

This paper proposes a simple method for controllable text generation based on weighting logits with a free-form classifier, namely CAIF sampling. Using an arbitrary text classifier, we adjust a small part of a language model's logits and guide text generation towards or away from classifier prediction. We experimented with toxicity avoidance and sentiment control tasks and showed that the proposed method significantly outperforms recent PPLM, GeDi, and DExperts on PPL and task accuracy metrics based on the external classifier of generated texts. In addition, compared to other approaches, it is easier to implement and tune and has significantly fewer restrictions and requirements.

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.

Multi-choice questions (MCQs) serve as a common yet important task format in the research of large language models (LLMs). Our work shows that LLMs exhibit an inherent "selection bias" in MCQs, which refers to LLMs' preferences to select options located at specific positions (like "Option C"). This bias is prevalent across various LLMs, making their performance vulnerable to option position changes in MCQs. We identify that one primary cause resulting in selection bias is option numbering, i.e., the ID symbols A/B/C/D associated with the options. To mitigate selection bias, we propose a new method called PriDe. PriDe first decomposes the observed model prediction distribution into an intrinsic prediction over option contents and a prior distribution over option IDs. It then estimates the prior by permutating option contents on a small number of test samples, which is used to debias the subsequent test samples. We demonstrate that, as a label-free, inference-time method, PriDe achieves a more effective and computation-efficient debiasing than strong baselines. We further show that the priors estimated by PriDe generalize well across different domains, highlighting its practical potential in broader scenarios.

Large reasoning models (LRMs), such as OpenAI's o1 and DeepSeek-R1, harness test-time scaling to perform multi-step reasoning for complex problem-solving. This reasoning process, executed before producing final answers, is often guided by special juncture tokens or textual segments that prompt self-evaluative reflection. We refer to these transition markers and reflective cues as "reflection tokens" (e.g., "wait", "but", "alternatively"). In this work, we treat reflection tokens as a "resource" and introduce the problem of resource allocation, aimed at improving the test-time compute performance of LRMs by adaptively regulating the frequency and placement of reflection tokens. Through empirical analysis, we show that both excessive and insufficient use of reflection tokens, referred to as over-reflection and under-reflection, can degrade model performance. To better understand and manage this trade-off, we draw an analogy between reflection token usage and learning rate scheduling in optimization. Building on this insight, we propose cyclical reflection token scheduling (termed CyclicReflex), a decoding strategy that dynamically modulates reflection token logits using a position-dependent triangular waveform. Experiments on MATH500, AIME2024/2025, and AMC2023 demonstrate that CyclicReflex consistently improves performance across model sizes (1.5B-8B), outperforming standard decoding and more recent approaches such as TIP (thought switching penalty) and S1. Codes are available at https://github.com/OPTML-Group/CyclicReflex.

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.

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).

Large language models have demonstrated impressive reasoning capabilities, yet they often suffer from inefficiencies due to unnecessarily verbose or redundant outputs. While many works have explored reinforcement learning (RL) to enhance reasoning abilities, most primarily focus on improving accuracy, with limited attention to reasoning efficiency. Some existing approaches introduce direct length-based rewards to encourage brevity, but this often leads to noticeable drops in accuracy. In this paper, we propose Bingo, an RL framework that advances length-based reward design to boost efficient reasoning. Bingo incorporates two key mechanisms: a significance-aware length reward, which gradually guides the model to reduce only insignificant tokens, and a dynamic length reward, which initially encourages elaborate reasoning for hard questions but decays over time to improve overall efficiency. Experiments across multiple reasoning benchmarks show that Bingo improves both accuracy and efficiency. It outperforms the vanilla reward and several other length-based reward baselines in RL, achieving a favorable trade-off between accuracy and efficiency. These results underscore the potential of training LLMs explicitly for efficient reasoning.

In knowledge distillation literature, feature-based methods have dominated due to their ability to effectively tap into extensive teacher models. In contrast, logit-based approaches, which aim to distill `dark knowledge' from teachers, typically exhibit inferior performance compared to feature-based methods. To bridge this gap, we present LumiNet, a novel knowledge distillation algorithm designed to enhance logit-based distillation. We introduce the concept of 'perception', aiming to calibrate logits based on the model's representation capability. This concept addresses overconfidence issues in logit-based distillation method while also introducing a novel method to distill knowledge from the teacher. It reconstructs the logits of a sample/instances by considering relationships with other samples in the batch. LumiNet excels on benchmarks like CIFAR-100, ImageNet, and MSCOCO, outperforming leading feature-based methods, e.g., compared to KD with ResNet18 and MobileNetV2 on ImageNet, it shows improvements of 1.5% and 2.05%, respectively.

Speculative decoding accelerates large language model inference by proposing tokens with a lightweight draft model and selectively accepting them using a target model. This work introduces DropMatch, a novel approach that matches draft tokens to the predictive distribution of the target model via Monte Carlo dropout applied exclusively to the LM head, enabling sampling-based acceptance decisions. By generating multiple decoding paths, our method forms an empirical token distribution against which draft tokens are evaluated for consistency. This acceptance mechanism enables the model to adaptively control the size of decoding paths under an appropriate dropout probability, preventing substantial distortion of the target model predictive distribution. The proposed method operates in a training-free, data-free, and calibration-free manner, requires no architectural modification to pretrained models, and can be orthogonally integrated with a wide range of existing speculative decoding and inference acceleration techniques. Experiments across multiple benchmarks demonstrate that our approach increases acceptance length while maintaining competitive task performance, yielding inference speedups ranging from 1.09x to 1.33x over the standard baseline, and up to an additional 1.09x speedup when applied on top of EAGLE3.

Large reasoning models enhanced by reinforcement learning with verifiable rewards have achieved significant performance gains by extending their chain-of-thought. However, this paradigm incurs substantial deployment costs as models often exhibit excessive verbosity on simple queries. Existing efficient reasoning methods relying on explicit length penalties often introduce optimization conflicts and leave the generative mechanisms driving overthinking largely unexamined. In this paper, we identify a phenomenon termed length shift where models increasingly generate unnecessary reasoning on trivial inputs during training. To address this, we introduce Dynamic Outlier Truncation (DOT), a training-time intervention that selectively suppresses redundant tokens. This method targets only the extreme tail of response lengths within fully correct rollout groups while preserving long-horizon reasoning capabilities for complex problems. To complement this intervention and ensure stable convergence, we further incorporate auxiliary KL regularization and predictive dynamic sampling. Experimental results across multiple model scales demonstrate that our approach significantly pushes the efficiency-performance Pareto frontier outward. Notably, on the AIME-24, our method reduces inference token usage by 78% while simultaneously increasing accuracy compared to the initial policy and surpassing state-of-the-art efficient reasoning methods.

Transformer-based Large Language Models (LLMs) are pioneering advances in many natural language processing tasks, however, their exceptional capabilities are restricted within the preset context window of Transformer. Position Embedding (PE) scaling methods, while effective in extending the context window to a specific length, demonstrate either notable limitations in their extrapolation abilities or sacrificing partial performance within the context window. Length extrapolation methods, although theoretically capable of extending the context window beyond the training sequence length, often underperform in practical long-context applications. To address these challenges, we propose Continuous Length EXtrapolation (CLEX) for LLMs. We generalise the PE scaling approaches to model the continuous dynamics by ordinary differential equations over the length scaling factor, thereby overcoming the constraints of current PE scaling methods designed for specific lengths. Moreover, by extending the dynamics to desired context lengths beyond the training sequence length, CLEX facilitates the length extrapolation with impressive performance in practical tasks. We demonstrate that CLEX can be seamlessly incorporated into LLMs equipped with Rotary Position Embedding, such as LLaMA and GPT-NeoX, with negligible impact on training and inference latency. Experimental results reveal that CLEX can effectively extend the context window to over 4x or almost 8x training length, with no deterioration in performance. Furthermore, when evaluated on the practical LongBench benchmark, our model trained on a 4k length exhibits competitive performance against state-of-the-art open-source models trained on context lengths up to 32k.

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

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

We introduce Leap+Verify, a framework that applies speculative execution -- predicting future model weights and validating predictions before acceptance -- to accelerate neural network training. Inspired by speculative decoding in language model inference and by the Automatically Scalable Computation (ASC) architecture for program execution, Leap+Verify decomposes training into three dynamically detected regimes (chaotic, transition, stable) using activation-space cosine similarity as a real-time Lyapunov proxy signal. Within each regime, analytic weight predictors (momentum, linear, quadratic extrapolation) attempt to forecast model parameters K training steps ahead; predictions are accepted only when validated against a held-out loss criterion. We evaluate Leap+Verify on GPT-2 124M and Qwen 2.5-1.5B trained on WikiText-103 across five random seeds, sweeping prediction depth K in {5, 10, 25, 50, 75, 100}. Momentum-based prediction (Adam moment extrapolation) fails catastrophically at both scales, with predicted losses exceeding actuals by 100-10,000x -- a universal norm explosion in optimizer-state extrapolation. Finite-difference predictors (linear, quadratic) succeed where momentum fails: at 124M, they achieve 24% strict acceptance at K=5 in stable regimes; at 1.5B, they achieve 37% strict acceptance in transition regimes. The scale-dependent finding is in regime distribution: GPT-2 124M spends 34% of training in stable regime, while Qwen 1.5B spends 64% in chaotic regime and reaches stable in only 0-2 of 40 checkpoints. Larger models are more predictable when predictable, but less often predictable -- the practical bottleneck shifts from predictor accuracy to regime availability. Cross-seed results are highly consistent (less than 1% validation loss variance), and the three-regime framework produces identical phase boundaries (plus or minus 50 steps) across seeds.

Large language models trained with reinforcement learning with verifiable rewards tend to trade accuracy for length--inflating response lengths to achieve gains in accuracy. While longer answers may be warranted for harder problems, many tokens are merely "filler": repetitive, verbose text that makes no real progress. We introduce GFPO (Group Filtered Policy Optimization), which curbs this length explosion by sampling larger groups per problem during training and filtering responses to train on based on two key metrics: (1) response length and (2) token efficiency: reward per token ratio. By sampling more at training time, we teach models to think less at inference time. On the Phi-4-reasoning model, GFPO cuts GRPO's length inflation by 46-71% across challenging STEM and coding benchmarks (AIME 24/25, GPQA, Omni-MATH, LiveCodeBench) while maintaining accuracy. Optimizing for reward per token further increases reductions in length inflation to 71-85%. We also propose Adaptive Difficulty GFPO, which dynamically allocates more training resources to harder problems based on real-time difficulty estimates, improving the balance between computational efficiency and accuracy especially on difficult questions. GFPO demonstrates that increased training-time compute directly translates to reduced test-time compute--a simple yet effective trade-off for efficient reasoning.

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.

We consider the task of evaluating policies of algorithmic resource allocation through randomized controlled trials (RCTs). Such policies are tasked with optimizing the utilization of limited intervention resources, with the goal of maximizing the benefits derived. Evaluation of such allocation policies through RCTs proves difficult, notwithstanding the scale of the trial, because the individuals' outcomes are inextricably interlinked through resource constraints controlling the policy decisions. Our key contribution is to present a new estimator leveraging our proposed novel concept, that involves retrospective reshuffling of participants across experimental arms at the end of an RCT. We identify conditions under which such reassignments are permissible and can be leveraged to construct counterfactual trials, whose outcomes can be accurately ascertained, for free. We prove theoretically that such an estimator is more accurate than common estimators based on sample means -- we show that it returns an unbiased estimate and simultaneously reduces variance. We demonstrate the value of our approach through empirical experiments on synthetic, semi-synthetic as well as real case study data and show improved estimation accuracy across the board.

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

Reasoning large language models (LLMs) excel in complex tasks, which has drawn significant attention to reinforcement learning (RL) for LLMs. However, existing approaches allocate an equal number of rollouts to all questions during the RL process, which is inefficient. This inefficiency stems from the fact that training on simple questions yields limited gains, whereas more rollouts are needed for challenging questions to sample correct answers. Furthermore, while RL improves response precision, it limits the model's exploration ability, potentially resulting in a performance cap below that of the base model prior to RL. To address these issues, we propose a mechanism for dynamically allocating rollout budgets based on the difficulty of the problems, enabling more efficient RL training. Additionally, we introduce an adaptive dynamic temperature adjustment strategy to maintain the entropy at a stable level, thereby encouraging sufficient exploration. This enables LLMs to improve response precision while preserving their exploratory ability to uncover potential correct pathways. The code and data is available on: https://github.com/LiaoMengqi/E3-RL4LLMs

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.

Current language models demonstrate remarkable proficiency in text generation. However, for many applications it is desirable to control attributes, such as sentiment, or toxicity, of the generated language -- ideally tailored towards each specific use case and target audience. For auto-regressive language models, existing guidance methods are prone to decoding errors that cascade during generation and degrade performance. In contrast, text diffusion models can easily be guided with, for example, a simple linear sentiment classifier -- however they do suffer from significantly higher perplexity than auto-regressive alternatives. In this paper we use a guided diffusion model to produce a latent proposal that steers an auto-regressive language model to generate text with desired properties. Our model inherits the unmatched fluency of the auto-regressive approach and the plug-and-play flexibility of diffusion. We show that it outperforms previous plug-and-play guidance methods across a wide range of benchmark data sets. Further, controlling a new attribute in our framework is reduced to training a single logistic regression classifier.

On-policy Reinforcement Learning (RL) with PPO-like clip objectives has become the standard choice for reward-based fine-tuning of large language models (LLMs). Although recent work has explored improved estimators of advantages and normalization, the clipping mechanism itself has remained untouched. Originally introduced as a proxy for principled KL-based trust regions, clipping is a crude approximation that often causes unstable updates and suboptimal performance. We replace the clip objective with a novel discrete differentiable trust region projection, which provides principled token-level KL constraints. The projection operates on a sparse subset of the model's most important token logits to balance computational cost and projection effectiveness. Our approach, Trust Region Optimization for Large Language Models (TROLL), serves as a direct replacement for PPO-like clipping during training and does not alter the model's inference behavior. Across datasets, model families, and advantage-estimation methods, TROLL consistently outperforms PPO-like clipping in terms of training speed, stability, and final success rates.

Speculative decoding reduces the inference latency of a target large language model via utilizing a smaller and faster draft model. Its performance depends on a hyperparameter K -- the candidate length, i.e., the number of candidate tokens for the target model to verify in each round. However, previous methods often use simple heuristics to choose K, which may result in sub-optimal performance. We study the choice of the candidate length K and formulate it as a Markov Decision Process. We theoretically show that the optimal policy of this Markov decision process takes the form of a threshold policy, i.e., the current speculation should stop and be verified when the probability of getting a rejection exceeds a threshold value. Motivated by this theory, we propose SpecDec++, an enhanced version of speculative decoding that adaptively determines the candidate length on the fly. We augment the draft model with a trained acceptance prediction head to predict the conditional acceptance probability of the candidate tokens. SpecDec++ will stop the current speculation when the predicted probability that at least one token gets rejected exceeds a threshold. We implement SpecDec++ and apply it to the llama-2-chat 7B & 70B model pair. Our adaptive method achieves a 2.04x speedup on the Alpaca dataset (an additional 7.2% improvement over the baseline speculative decoding). On the GSM8K and HumanEval datasets, our method achieves a 2.26x speedup (9.4% improvement) and 2.23x speedup (11.1% improvement), respectively.

Aligning Large Language Models (LLMs) to human preferences through preference optimization has been crucial but labor-intensive, necessitating for each prompt a comparison of both a chosen and a rejected text completion by evaluators. Recently, Kahneman-Tversky Optimization (KTO) has demonstrated that LLMs can be aligned using merely binary "thumbs-up" or "thumbs-down" signals on each prompt-completion pair. In this paper, we present theoretical foundations to explain the successful alignment achieved through these binary signals. Our analysis uncovers a new perspective: optimizing a binary classifier, whose logit is a reward, implicitly induces minimizing the Direct Preference Optimization (DPO) loss. In the process of this discovery, we identified two techniques for effective alignment: reward shift and underlying distribution matching. Consequently, we propose a new algorithm, Binary Classifier Optimization, that integrates the techniques. We validate our methodology in two settings: first, on a paired preference dataset, where our method performs on par with DPO and KTO; and second, on binary signal datasets simulating real-world conditions with divergent underlying distributions between thumbs-up and thumbs-down data. Our model consistently demonstrates effective and robust alignment across two base LLMs and three different binary signal datasets, showcasing the strength of our approach to learning from binary feedback.

Recommendation systems (RS) aim to provide personalized content, but they face a challenge in unbiased learning due to selection bias, where users only interact with items they prefer. This bias leads to a distorted representation of user preferences, which hinders the accuracy and fairness of recommendations. To address the issue, various methods such as error imputation based, inverse propensity scoring, and doubly robust techniques have been developed. Despite the progress, from the structural causal model perspective, previous debiasing methods in RS assume the independence of the exogenous variables. In this paper, we release this assumption and propose a learning algorithm based on likelihood maximization to learn a prediction model. We first discuss the correlation and difference between unmeasured confounding and our scenario, then we propose a unified method that effectively handles latent exogenous variables. Specifically, our method models the data generation process with latent exogenous variables under mild normality assumptions. We then develop a Monte Carlo algorithm to numerically estimate the likelihood function. Extensive experiments on synthetic datasets and three real-world datasets demonstrate the effectiveness of our proposed method. The code is at https://github.com/WallaceSUI/kdd25-background-variable.

We present Future-KL Influenced Policy Optimization (FIPO), a reinforcement learning algorithm designed to overcome reasoning bottlenecks in large language models. While GRPO style training scales effectively, it typically relies on outcome-based rewards (ORM) that distribute a global advantage uniformly across every token in a trajectory. We argue that this coarse-grained credit assignment imposes a performance ceiling by failing to distinguish critical logical pivots from trivial tokens. FIPO addresses this by incorporating discounted future-KL divergence into the policy update, creating a dense advantage formulation that re-weights tokens based on their influence on subsequent trajectory behavior. Empirically, FIPO enables models to break through the length stagnation seen in standard baselines. Evaluated on Qwen2.5-32B, FIPO extends the average chain-of-thought length from roughly 4,000 to over 10,000 tokens and increases AIME 2024 Pass@1 accuracy from 50.0% to a peak of 58.0% (converging at approximately 56.0\%). This outperforms both DeepSeek-R1-Zero-Math-32B (around 47.0%) and o1-mini (approximately 56.0%). Our results suggest that establishing dense advantage formulations is a vital path for evolving ORM-based algorithms to unlock the full reasoning potential of base models. We open-source our training system, built on the verl framework.

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

Although the capabilities of large language models (LLMs) ideally scale up with increasing data and compute, they are inevitably constrained by limited resources in reality. Suppose we have a moderately trained LLM (e.g., trained to align with human preference) in hand, can we further exploit its potential and cheaply acquire a stronger model? In this paper, we propose a simple method called ExPO to boost LLMs' alignment with human preference. ExPO assumes that a medium-aligned model can be interpolated between a less-aligned (weaker) model, e.g., the initial SFT model, and a better-aligned (stronger) one, thereby directly obtaining this stronger model by extrapolating from the weights of the former two relatively weaker models. On the AlpacaEval 2.0 benchmark, we show that ExPO pushes models trained with less preference data (e.g., 10% or 20%) to reach and even surpass the fully-trained one, without any additional training. Furthermore, ExPO also significantly improves off-the-shelf DPO/RLHF models and exhibits decent scalability across model sizes from 7B to 70B. Our work demonstrates the efficacy of model extrapolation in exploiting LLMs' capabilities, suggesting a promising direction that deserves future exploration.

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.

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.

Reinforcement Learning with Verifiable Rewards (RLVR) for large language models (LLMs) has achieved remarkable progress in enhancing LLMs' reasoning capabilities on tasks with clear correctness criteria, such as mathematical reasoning tasks. Several training metrics, such as entropy or response length, have been observed to correlate with different reasoning behaviors in reinforcement learning. Prior approaches incorporate such priors through reward or advantage shaping, which often relies on hand-crafted penalties and preferences (e.g., higher-is-better or lower-is-better). However, without careful hyperparameter tuning, these directional priors can be overly biased and may lead to failure. To this end, we introduce Conditional advANtage estimatiON (CANON), amplifying the impact of the target metric without presuming its direction. Specifically, CANON regroups the sampled responses into two groups based on the higher or lower value of a target metric, measures which metric trend contributes to better performance through inter-group comparison, and identifies the better response within the same group. In summary, CANON based on entropy consistently outperforms prior methods across three LLMs on both math reasoning and high-complexity logic tasks. When applied to response length, CANON further improves token efficiency, yielding a more favorable Pareto frontier in the performance-cost trade-off.

Deploying large language models (LLMs) of several billion parameters can be impractical in most industrial use cases due to constraints such as cost, latency limitations, and hardware accessibility. Knowledge distillation (KD) offers a solution by compressing knowledge from resource-intensive large models to smaller ones. Various strategies exist, some relying on the text generated by the teacher model and optionally utilizing his logits to enhance learning. However, these methods based on logits often require both teacher and student models to share the same tokenizer, limiting their applicability across different LLM families. In this paper, we introduce Universal Logit Distillation (ULD) loss, grounded in optimal transport, to address this limitation. Our experimental results demonstrate the effectiveness of ULD loss in enabling distillation across models with different architectures and tokenizers, paving the way to a more widespread use of distillation techniques.

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.

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

Reinforcement learning algorithms such as GRPO have driven recent advances in large language model (LLM) reasoning. While scaling the number of rollouts stabilizes training, existing approaches suffer from limited exploration on challenging prompts and leave informative feedback signals underexploited, due to context-independent rollout allocation across prompts (e.g., generating 16 rollouts per prompt) and relying heavily on sparse rewards. This paper presents XRPO(eXplore - eXploit GRPO), a unified framework that recasts policy optimization through the principled lens of rollout exploration-exploitation. To enhance exploration, XRPO introduces a mathematically grounded rollout allocator that adaptively prioritizes prompts with higher potential for uncertainty reduction. It further addresses stagnation on zero-reward prompts through an in-context seeding strategy that injects curated exemplars, steering the model into more difficult reasoning trajectories. To strengthen exploitation, XRPO develops a group-relative, novelty-aware advantage sharpening mechanism that leverages sequence likelihoods to amplify low-probability yet correct responses, thereby extending the policy's reach beyond sparse rewards. Experiments across diverse math and coding benchmarks on both reasoning and non-reasoning models demonstrate that XRPO outperforms existing advances (e.g., GRPO and GSPO) up to 4% pass@1 and 6% cons@32, while accelerating training convergence by up to 2.7X.

We present Position Interpolation (PI) that extends the context window sizes of RoPE-based pretrained LLMs such as LLaMA models to up to 32768 with minimal fine-tuning (within 1000 steps), while demonstrating strong empirical results on various tasks that require long context, including passkey retrieval, language modeling, and long document summarization from LLaMA 7B to 65B. Meanwhile, the extended model by Position Interpolation preserve quality relatively well on tasks within its original context window. To achieve this goal, Position Interpolation linearly down-scales the input position indices to match the original context window size, rather than extrapolating beyond the trained context length which may lead to catastrophically high attention scores that completely ruin the self-attention mechanism. Our theoretical study shows that the upper bound of interpolation is at least sim 600 times smaller than that of extrapolation, further demonstrating its stability. Models extended via Position Interpolation retain its original architecture and can reuse most pre-existing optimization and infrastructure.

Reinforcement learning with verifiable rewards (RLVR) has been shown to enhance the reasoning capabilities of large language models (LLMs), enabling the development of large reasoning models (LRMs). However, LRMs such as DeepSeek-R1 and OpenAI o1 often generate verbose responses containing redundant or irrelevant reasoning step-a phenomenon known as overthinking-which substantially increases computational costs. Prior efforts to mitigate this issue commonly incorporate length penalties into the reward function, but we find they frequently suffer from two critical issues: length collapse and training collapse, resulting in sub-optimal performance. To address them, we propose a pipeline for training a Conciseness Reward Model (CRM) that scores the conciseness of reasoning path. Additionally, we introduce a novel reward formulation named Conciseness Reward Function (CRF) with explicit dependency between the outcome reward and conciseness score, thereby fostering both more effective and more efficient reasoning. From a theoretical standpoint, we demonstrate the superiority of the new reward from the perspective of variance reduction and improved convergence properties. Besides, on the practical side, extensive experiments on five mathematical benchmark datasets demonstrate the method's effectiveness and token efficiency, which achieves an 8.1% accuracy improvement and a 19.9% reduction in response token length on Qwen2.5-7B. Furthermore, the method generalizes well to other LLMs including Llama and Mistral. The implementation code and datasets are publicly available for reproduction: https://anonymous.4open.science/r/CRM.

In the field of computational advertising, the integration of ads into the outputs of large language models (LLMs) presents an opportunity to support these services without compromising content integrity. This paper introduces novel auction mechanisms for ad allocation and pricing within the textual outputs of LLMs, leveraging retrieval-augmented generation (RAG). We propose a segment auction where an ad is probabilistically retrieved for each discourse segment (paragraph, section, or entire output) according to its bid and relevance, following the RAG framework, and priced according to competing bids. We show that our auction maximizes logarithmic social welfare, a new notion of welfare that balances allocation efficiency and fairness, and we characterize the associated incentive-compatible pricing rule. These results are extended to multi-ad allocation per segment. An empirical evaluation validates the feasibility and effectiveness of our approach over several ad auction scenarios, and exhibits inherent tradeoffs in metrics as we allow the LLM more flexibility to allocate ads.

Reinforcement learning (RL) has become a key driver of progress in large language models, but scaling RL to long chain-of-thought (CoT) trajectories is increasingly constrained by backpropagation over every generated token. Even with optimized rollout engines, full-token updates can consume a large fraction of total training cost, turning token length into a hidden tax on RL. We introduce Not All Tokens Are Needed (NAT), a unified framework that makes the token budget a first-class optimization primitive. NAT updates the policy using only a selected subset of generated tokens while preserving the learning signal of full-sequence RL. The core idea is an unbiased partial-token policy-gradient estimator via Horvitz-Thompson reweighting, which ensures statistically correct gradients despite subsampling. We instantiate NAT with two simple, plug-and-play token selection schemes: Uniform Random Sampling (URS) and Random Prefix Cutting (RPC), both of which reduce forward and backward compute and memory without modifying the reward computation or rollout pipeline. Across mathematical reasoning benchmarks, NAT matches full-token GRPO performance while using as few as 50% of tokens, providing an efficient and orthogonal pathway to scaling RL beyond the limits imposed by long trajectories. In our experiments, RPC saves 18% peak GPU memory and 29% forward and backward RL training time for Qwen3-8B.

The mathematical problem-solving capabilities of large language models have become a focal point of research, with growing interests in leveraging self-generated reasoning paths as a promising way to refine and enhance these models. These paths capture step-by-step logical processes while requiring only the correct answer for supervision. The self-training method has been shown to be effective in reasoning tasks while eliminating the need for external models and manual annotations. However, optimizing the use of self-generated data for model training remains an open challenge. In this work, we propose Entropy-Based Adaptive Weighting for Self-Training (EAST), an adaptive weighting strategy designed to prioritize uncertain data during self-training. Specifically, EAST employs a mapping function with a tunable parameter that controls the sharpness of the weighting, assigning higher weights to data where the model exhibits greater uncertainty. This approach guides the model to focus on more informative and challenging examples, thereby enhancing its reasoning ability. We evaluate our approach on GSM8K and MATH benchmarks. Empirical results show that, while the vanilla method yields virtually no improvement (0%) on MATH, EAST achieves around a 1% gain over backbone model. On GSM8K, EAST attains a further 1-2% performance boost compared to the vanilla method.

Training Large Language Models (LLMs) for chain-of-thought reasoning presents a significant challenge: supervised fine-tuning on a single "golden" rationale hurts generalization as it penalizes equally valid alternatives, whereas reinforcement learning with verifiable rewards struggles with credit assignment and prohibitive computational cost. To tackle these limitations, we introduce InTRO (In-Token Rationality Optimization), a new framework that enables both token-level exploration and self-feedback for accurate and concise reasoning. Instead of directly optimizing an intractable objective over all valid reasoning paths, InTRO leverages correction factors-token-wise importance weights estimated by the information discrepancy between the generative policy and its answer-conditioned counterpart, for informative next token selection. This approach allows the model to perform token-level exploration and receive self-generated feedback within a single forward pass, ultimately encouraging accurate and concise rationales. Across six math-reasoning benchmarks, InTRO consistently outperforms other baselines, raising solution accuracy by up to 20% relative to the base model. Its chains of thought are also notably more concise, exhibiting reduced verbosity. Beyond this, InTRO enables cross-domain transfer, successfully adapting to out-of-domain reasoning tasks that extend beyond the realm of mathematics, demonstrating robust generalization.

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

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

Large language models (LLMs) are in need of sufficient contexts to handle many critical applications, such as retrieval augmented generation and few-shot learning. However, due to the constrained window size, the LLMs can only access to the information within a limited context. Although the size of context window can be extended by fine-tuning, it will result in a substantial cost in both training and inference stage. In this paper, we present Extensible Tokenization as an alternative method which realizes the flexible scaling of LLMs' context. Extensible Tokenization stands as a midware in between of the tokenized context and the LLM, which transforms the raw token embeddings into the extensible embeddings. Such embeddings provide a more compact representation for the long context, on top of which the LLM is able to perceive more information with the same context window. Extensible Tokenization is also featured by its flexibility: the scaling factor can be flexibly determined within a feasible scope, leading to the extension of an arbitrary context length at the inference time. Besides, Extensible Tokenization is introduced as a drop-in component, which can be seamlessly plugged into not only the LLM itself and but also its fine-tuned derivatives, bringing in the extended contextual information while fully preserving the LLM's existing capabilities. We perform comprehensive experiments on long-context language modeling and understanding tasks, which verify Extensible Tokenization as an effective, efficient, flexible, and compatible method to extend LLM's context. Our model and source code will be made publicly available.

Reinforcement learning from human feedback (RLHF) has been crucial in aligning large language models (LLMs) with human values. Traditionally, RLHF involves generating responses to a query and using a reward model to assign a reward to the entire response. However, this approach faces challenges due to its reliance on a single, sparse reward, which makes it challenging for the model to identify which parts of the sequence contribute most significantly to the final reward. Recent methods have attempted to address this limitation by introducing token-level rewards. However, these methods often rely on either a trained credit assignment model or AI annotators, raising concerns about the quality and reliability of the rewards. In this paper, we propose token-level reward regularization (T-REG), a novel approach that leverages both sequence-level and token-level rewards for preference optimization. Harnessing the self-refinement capabilities of LLMs, our method uses contrastive prompting to enable LLMs to self-generate token-level rewards. These self-generated rewards then act as reward regularization, guiding the model to more effectively distribute sequence-level rewards across tokens. This facilitates better token-level credit assignment and enhances alignment performance. Experiments on the instruction following benchmarks, including Alpaca Eval 2 and Arena-Hard, show that our method consistently outperforms baseline methods by up to 3.8% and 4.4%, respectively. We will release the code and models at https://github.com/wzhouad/T-REG.

Reinforcement Learning with Verifiable Rewards (RLVR) has shown significant promise for enhancing the reasoning capabilities of large language models (LLMs). However, prevailing algorithms like GRPO broadcast a uniform advantage signal across all tokens in a sequence. This coarse-grained approach overlooks the pivotal role of uncertain, high-stakes decisions during reasoning, leading to inefficient exploration and the well-documented problem of entropy collapse. To address this, we introduce UnCertainty-aware Advantage Shaping (UCAS), a model-free method that refines credit assignment by leveraging the model's internal uncertainty signals. UCAS operates in two stages: it first modulates the response-level advantage using the model's overall self-confidence, and then applies a token-level penalty based on raw logit certainty. This dual mechanism encourages exploration of high-uncertainty paths that yield correct answers while penalizing overconfident yet erroneous reasoning, effectively balancing the exploration-exploitation trade-off. Extensive experiments on five mathematical reasoning benchmarks show that UCAS significantly outperforms strong RLVR baselines across multiple model scales, including 1.5B and 7B. Our analysis confirms that UCAS not only achieves higher rewards but also promotes greater reasoning diversity and successfully mitigates entropy collapse.

Speculative Decoding (SD) has become an important technique in accelerating the inference speed of large language models. Conventional SD methods employ a fixed draft length, which ignores the token generation difficulty across tasks. Consequently, in this paper, we address such an issue and introduce SVIP - a difficulty-aware dynamic draft length policy for speculative decoding systems. Based on a theoretical lower bound of draft token acceptance rate and its inference-time approximation, SVIP adaptively determines the lengths of draft sequences based on the entropy of each draft token distribution. Experimental results on mainstream SD benchmarks and frameworks demonstrate the superior performance of SVIP, achieving up to 20\% walltime speedup on SpecBench over baseline SD methods and 60\% speedup on MT-Bench for long-form generation of up to 8K tokens. Moreover, SVIP is totally training-free and compatible with any existing SD methods that generate draft tokens autoregressively. Experimental results also show that SVIP yields consistent walltime improvement on top of GliDe & CaPE and EAGLE-2.

The premise of identifiable and causal representation learning is to improve the current representation learning paradigm in terms of generalizability or robustness. Despite recent progress in questions of identifiability, more theoretical results demonstrating concrete advantages of these methods for downstream tasks are needed. In this paper, we consider the task of intervention extrapolation: predicting how interventions affect an outcome, even when those interventions are not observed at training time, and show that identifiable representations can provide an effective solution to this task even if the interventions affect the outcome non-linearly. Our setup includes an outcome Y, observed features X, which are generated as a non-linear transformation of latent features Z, and exogenous action variables A, which influence Z. The objective of intervention extrapolation is to predict how interventions on A that lie outside the training support of A affect Y. Here, extrapolation becomes possible if the effect of A on Z is linear and the residual when regressing Z on A has full support. As Z is latent, we combine the task of intervention extrapolation with identifiable representation learning, which we call Rep4Ex: we aim to map the observed features X into a subspace that allows for non-linear extrapolation in A. We show that the hidden representation is identifiable up to an affine transformation in Z-space, which is sufficient for intervention extrapolation. The identifiability is characterized by a novel constraint describing the linearity assumption of A on Z. Based on this insight, we propose a method that enforces the linear invariance constraint and can be combined with any type of autoencoder. We validate our theoretical findings through synthetic experiments and show that our approach succeeds in predicting the effects of unseen interventions.