Reasoning models excel by generating long chain-of-thoughts, but decoding the resulting thousands of tokens is slow. Token-level speculative decoding (SD) helps, but its benefit is capped, because the chance that an entire γ-token guess is correct falls exponentially as γ grows.

Large language models are increasingly used to support high-stakes decisions, potentially influencing who is granted bail or receives a loan. Naive chain-ofthought sampling can improve average decision accuracy, but has also been shown to amplify unfair bias. To address this challenge and enable the trustworthy use of reasoning models in high-stakes decision-making, we propose a framework for training a generalizable Fairness Reward Model (FRM). Our model assigns a fairness score to LLM reasoning, enabling the system to down-weight biased trajectories and favor equitable ones when aggregating decisions across reasoning chains. We show that a single Fairness Reward Model, trained on weakly supervised, LLM-annotated examples of biased versus unbiased reasoning, transfers across tasks, domains, and model families without additional fine-tuning. When applied to real-world decision-making tasks including recidivism prediction and social media moderation, our approach consistently improves fairness while matching, or even surpassing, baseline accuracy.

As textual reasoning with large language models (LLMs) has advanced significantly, there has been growing interest in enhancing the multimodal reasoning capabilities of large vision-language models (LVLMs). However, existing methods primarily approach multimodal reasoning in a straightforward, text-centric manner, where both reasoning and answer derivation are conducted purely through text, with the only difference being the presence of multimodal input. As a result, these methods often encounter fundamental limitations in spatial reasoning tasks that demand precise geometric understanding and continuous spatial tracking--capabilities that humans achieve through mental visualization and manipulation. To address the limitations, we propose drawing to reason in space, a novel paradigm that enables LVLMs to reason through elementary drawing operations in the visual space. By equipping models with basic drawing operations, including annotating bounding boxes and drawing auxiliary lines, we empower them to express and analyze spatial relationships through direct visual manipulation, meanwhile avoiding the performance ceiling imposed by specialized perception tools in previous tool-integrated reasoning approaches. To cultivate this capability, we develop a three-stage training framework: cold-start training with synthetic data to establish basic drawing abilities, reflective rejection sampling to enhance self-reflection behaviors, and reinforcement learning to directly optimize for target rewards. Extensive experiments demonstrate that our model, named VILASR, consistently outperforms existing methods across diverse spatial reasoning benchmarks, involving maze navigation, static spatial reasoning, video-based reasoning, and multi-view-based reasoning tasks, with an average improvement of 18.4%. Ablation studies reveal the critical role of each training stage, where reflective rejection sampling strengthens the model's self-correction capabilities, and reinforcement learning effectively unlocks its reasoning potential.

Chain-of-Thought (CoT) prompting plays an indispensable role in endowing large language models (LLMs) with complex reasoning capabilities. However, CoT currently faces two fundamental challenges: (1) Sufficiency, which ensures that the generated intermediate inference steps comprehensively cover and substantiate the final conclusion; and (2) Necessity, which identifies the inference steps that are truly indispensable for the soundness of the resulting answer. We propose a causal framework that characterizes CoT reasoning through the dual lenses of sufficiency and necessity. Incorporating causal Probability of Sufficiency and Necessity allows us not only to determine which steps are logically sufficient or necessary to the prediction outcome, but also to quantify their actual influence on the final reasoning outcome under different intervention scenarios, thereby enabling the automated addition of missing steps and the pruning of redundant ones. Extensive experimental results on various mathematical and commonsense reasoning benchmarks confirm substantial improvements in reasoning efficiency and reduced token usage without sacrificing accuracy. Our work provides a promising direction for improving LLM reasoning performance and cost-effectiveness.

Chain of thought reasoning has demonstrated remarkable success in large language models, yet its adaptation to vision-language reasoning remains an open challenge with unclear best practices. Existing attempts typically employ reasoning chains at a coarse-grained level, which struggles to perform fine-grained structured reasoning and, more importantly, are difficult to evaluate the reward and quality of intermediate reasoning.

Emerging reasoning LLMs such as OpenAI-o1 and DeepSeek-R1 have achieved strong performance on complex reasoning tasks by generating long chain-ofthought (CoT) traces. However, these long CoTs result in increased token usage, leading to higher inference latency and memory consumption. As a result, balancing accuracy and reasoning efficiency has become essential for deploying reasoning LLMs in practical applications. Existing long-to-short (Long2Short) methods aim to reduce inference length but often sacrifice accuracy, revealing a need for an approach that maintains performance while lowering token costs. To address this efficiency-accuracy tradeoff, we propose TokenSqueeze, a novel Long2Short method that condenses reasoning paths while preserving performance and relying exclusively on self-generated data. First, to prevent performance degradation caused by excessive compression of reasoning depth, we propose to select self-generated samples whose reasoning depth is adaptively matched to the complexity of the problem. To further optimize the linguistic expression without altering the underlying reasoning paths, we introduce a distribution-aligned linguistic refinement method that enhances the clarity and conciseness of the reasoning path while preserving its logical integrity. Comprehensive experimental results demonstrated the effectiveness of TokenSqueeze in reducing token usage while maintaining accuracy. Notably, DeepSeek-R1-Distill-Qwen-7B fine-tuned by using our proposed method achieved a 50% average token reduction while preserving accuracy on the MATH500 benchmark.

Multi-modal large language models (MLLMs) have achieved remarkable capabilities by integrating visual perception with language understanding, enabling applications such as image-grounded dialogue, visual question answering, and scientific analysis. However, most MLLMs adopt a static inference paradigm, encoding the entire image into fixed visual tokens upfront, which limits their ability to iteratively refine understanding or adapt to context during inference. This contrasts sharply with human perception, which is dynamic, selective, and feedback-driven. In this work, we introduce a novel framework for inference-time visual token scaling that enables MLLMs to perform iterative, verifier-guided reasoning over visual content. We formulate the problem as a Markov Decision Process, involving a reasoner that proposes visual actions and a verifier--trained via multi-step Direct Preference Optimization (DPO)--that evaluates these actions and determines when reasoning should terminate. To support this, we present a new dataset, VTS, comprising supervised reasoning trajectories (VTS-SFT) and preference-labeled reasoning comparisons (VTS-DPO). Our method significantly outperforms existing approaches across diverse visual reasoning benchmarks, offering not only improved accuracy but also more interpretable and grounded reasoning processes. These results demonstrate the promise of dynamic inference mechanisms for enabling fine-grained, context-aware visual reasoning in next-generation MLLMs. Code and datasets are publicly released at https://vts-v.github.io/.

Large Language Models (LLMs) have achieved significant performance gains through test-time scaling methods. However, existing approaches often incur redundant computations due to the accumulation of historical dependency information during inference. To address this challenge, we leverage the memoryless property of Markov processes to minimize reliance on historical context and propose a Markovian reasoning process. This foundational Markov chain structure enables seamless integration with various test-time scaling methods, thereby improving their scaling efficiency. By further scaling up the Markovian reasoning chain through integration with techniques such as tree search and reflective refinement, we uncover an emergent atomic reasoning structure, where reasoning trajectories are decomposed into a series of self-contained, low-complexity atomic units. We name this design Atom of Thoughts (AOT). Extensive experiments demonstrate that AOT consistently outperforms existing baselines as computational budgets increase. Importantly, AOT integrates seamlessly with existing reasoning frameworks and different LLMs (both reasoning and non-reasoning), facilitating scalable, high-performance inference.We submit our code alongside this paper and will make it publicly available to facilitate reproducibility and future research.

The role of reinforcement learning (RL) in enhancing the reasoning of large language models (LLMs) is becoming increasingly significant. Despite the success of RL in many scenarios, there are still many challenges in improving the reasoning of LLMs. One key challenge is the sparse reward, which introduces more training variance in policy optimization and makes it difficult to obtain a good estimation for value function in Actor-Critic (AC) methods. To address these issues, we introduce Direct Advantage-Based Policy Optimization (DAPO), a novel step-level offline RL algorithm with theoretical guarantees for enhancing the reasoning abilities of LLMs. Unlike response-level methods (such as DPO and GRPO) that the update directions of all reasoning steps are governed by the outcome reward uniformly, DAPO employs a critic function to provide step-level dense signals for policy optimization. Additionally, the actor and critic in DAPO are trained independently, ensuring that critic is a good estimation of true state value function and avoiding the co-training instability observed in standard AC methods. We train DAPO on mathematical and code problems and then evaluate its performance on multiple benchmarks. Our results show that DAPO can effectively enhance the mathematical and code capabilities on both SFT models and RL models, demonstrating the effectiveness of DAPO.

Chain-of-Thought (CoT) has widely enhanced mathematical reasoning in Large Language Models (LLMs), but it still remains challenging for extending it to multimodal domains. Existing works either adopt a similar textual reasoning for image input, or seek to interleave visual signals into mathematical CoT. However, they face three key limitations for math problem-solving: reliance on coarsegrained box-shaped image regions, limited perception of vision encoders on math content, and dependence on external capabilities for visual modification. In this paper, we propose MINT-CoT, introducing Mathematical INterleaved Tokens for Chain-of-Thought visual reasoning. MINT-CoT adaptively interleaves relevant visual tokens into textual reasoning steps via an Interleave Token, which dynamically selects visual regions of any shapes within math figures. To empower this capability, we construct the MINT-CoT dataset, containing 54K mathematical problems aligning each reasoning step with visual regions at the token level, accompanied by a rigorous data generation pipeline. We further present a threestage MINT-CoT training strategy, progressively combining text-only CoTSFT, interleaved CoTSFT, and interleaved CoTRL, which derives our MINT-CoT-7B model. Extensive experiments demonstrate the effectiveness of our method for effective visual interleaved reasoning in mathematical domains, where MINTCoT-7B outperforms the baseline model by +34.08% on MathVista, +28.78% on GeoQA, and +23.2% on MMStar, respectively.