Despite their strengths, large language models (LLMs) often fail to communicate their confidence accurately, making it difficult to assess when they might be wrong and limiting their reliability. In this work, we demonstrate that reasoning models that engage in extended chain-of-thought (CoT) reasoning exhibit superior performance not only in problem-solving but also in accurately expressing their confidence. Specifically, we benchmark six reasoning models across six datasets and find that they achieve strictly better confidence calibration than their non-reasoning counterparts in 33 out of the 36 settings. Our detailed analysis reveals that these gains in calibration stem from the slow thinking behaviors of reasoning models (e.g., exploring alternative approaches and backtracking) which enable them to adjust their confidence dynamically throughout their CoT, making it progressively more accurate. In particular, we find that reasoning models become increasingly better calibrated as their CoT unfolds, a trend not observed in non-reasoning models. Moreover, removing slow thinking behaviors from the CoT leads to a significant drop in calibration. Lastly, we show that non-reasoning models also demonstrate enhanced calibration when simply guided to slow think via in-context learning, fully isolating slow thinking as the source of the calibration gains.2

Recent studies show that the reasoning capabilities of Large Language Models (LLMs) can be improved by applying Reinforcement Learning (RL) to questionanswering (QA) tasks in areas such as math and coding. With a long context length, LLMs may learn to perform search, as indicated by the self-correction behavior observed in DeepSeek R1. However, this search behavior is often imprecise and lacks confidence, resulting in long, redundant responses and highlighting deficiencies in intuition and verification. Inspired by the Dual Process Theory in psychology, we introduce a simple modification to the QA task that includes four stages: Fast Thinking, where the LLM must answer within a strict token budget; Verification, where the model evaluates its initial response; Slow Thinking, where it refines the initial response with more deliberation; and Summarization, where it distills the refinement from the previous stage into precise steps. Our proposed task improves average accuracy from 25.6% to 27.3% for Qwen2.5-1.5B, and from 45.9% to 51.0% for DeepSeek-R1-Qwen-1.5B. Notably, for Qwen2.5-1.5B, the Fast Thinking mode alone achieves 25.2% accuracy using fewer than 1000 tokens, demonstrating substantial inference efficiency gains. These findings suggest that intuition and deliberative reasoning are distinct, complementary systems benefiting from targeted training. Additionally, we have open-sourced both the trained models and the source code.

Despite their strengths, large language models (LLMs) often fail to communicate their confidence accurately, making it difficult to assess when they might be wrong and limiting their reliability. In this work, we demonstrate that reasoning models that engage in extended chain-of-thought (CoT) reasoning exhibit superior performance not only in problem-solving but also in accurately expressing their confidence. Specifically, we benchmark six reasoning models across six datasets and find that they achieve strictly better confidence calibration than their non-reasoning counterparts in 33 out of the 36 settings. Our detailed analysis reveals that these gains in calibration stem from the slow thinking behaviors of reasoning models (e.g., exploring alternative approaches and backtracking) which enable them to adjust their confidence dynamically throughout their CoT, making it progressively more accurate. In particular, we find that reasoning models become increasingly better calibrated as their CoT unfolds, a trend not observed in non-reasoning models. Moreover, removing slow thinking behaviors from the CoT leads to a significant drop in calibration. Lastly, we show that non-reasoning models also demonstrate enhanced calibration when simply guided to slow think via in-context learning, fully isolating slow thinking as the source of the calibration gains.

Recent studies show that the reasoning capabilities of Large Language Models (LLMs) can be improved by applying Reinforcement Learning (RL) to question-answering (QA) tasks in areas such as math and coding. With a long context length, LLMs may learn to perform search, as indicated by the self-correction behavior observed in DeepSeek R1. However, this search behavior is often imprecise and lacks confidence, resulting in long, redundant responses and highlighting deficiencies in intuition and verification. Inspired by the Dual Process Theory in psychology, we introduce a simple modification to the QA task that includes four stages: Fast Thinking, where the LLM must answer within a strict token budget; Verification, where the model evaluates its initial response; Slow Thinking, where it refines the initial response with more deliberation; and Summarization, where it distills the refinement from the previous stage into precise steps. Our proposed task improves average accuracy from 25.6% to 27.3% for Qwen2.5-1.5B, and from 45.9% to 51.0% for DeepSeek-R1-Qwen-1.5B. Notably, for Qwen2.5-1.5B, the Fast Thinking mode alone achieves 25.2% accuracy using fewer than 1000 tokens, demonstrating substantial inference efficiency gains. These findings suggest that intuition and deliberative reasoning are distinct, complementary systems benefiting from targeted training. Additionally, we have open-sourced both the trained models and the source code.

Chain-of-Thought reasoning has emerged as a pivotal methodology for enhancing model inference capabilities. Despite growing interest in Chain-of-Thought reasoning, its underlying mechanisms remain unclear. This paper explores the working mechanisms of Chain-of-Thought reasoning from the perspective of the dual relationship between in-context learning and pretrained priors. We first conduct a fine-grained lexical-level analysis of rationales to examine the model's reasoning behavior. Then, by incrementally introducing noisy exemplars, we examine how the model balances pretrained priors against erroneous in-context information. Finally, we investigate whether prompt engineering can induce slow thinking in large language models. Our extensive experiments reveal three key findings: (1) The model not only quickly learns the reasoning structure at the lexical level but also grasps deeper logical reasoning patterns, yet it heavily relies on pretrained priors.

While large language models (LLMs) leverage both knowledge and reasoning during inference, the capacity to distinguish between them plays a pivotal role in model analysis, interpretability, and development. Inspired by dual-system cognitive theory, we propose a cognition attribution framework to decouple the contribution of knowledge and reasoning. In particular, the cognition of LLMs is decomposed into two distinct yet complementary phases: knowledge retrieval (Phase 1) and reasoning adjustment (Phase 2). To separate these phases, LLMs are prompted to generate answers under two different cognitive modes, fast thinking and slow thinking, respectively. The performance under different cognitive modes is analyzed to quantify the contribution of knowledge and reasoning. This architecture is employed to 15 LLMs across 3 datasets. Results reveal: (1) reasoning adjustment is domain-specific, benefiting reasoning-intensive domains (e.g., mathematics, physics, and chemistry) and potentially imparing knowledge-intensive domains. (2) Parameter scaling improves both knowledge and reasoning, with knowledge improvements being more pronounced. Additionally, parameter scaling make LLMs reasoning significantly more prudent, while moderately more intelligent. (3) Knowledge primarily resides in lower network layers, while reasoning operates in higher layers. Our framework not only helps understand LLMs from a "decoupling" perspective, but also provides new insights into existing research, including scaling laws, hierarchical knowledge editing, and limitations of small-model reasoning.

This paper presents AlphaOne ($α$1), a universal framework for modulating reasoning progress in large reasoning models (LRMs) at test time. $α$1 first introduces $α$ moment, which represents the scaled thinking phase with a universal parameter $α$. Within this scaled pre-$α$ moment phase, it dynamically schedules slow thinking transitions by modeling the insertion of reasoning transition tokens as a Bernoulli stochastic process. After the $α$ moment, $α$1 deterministically terminates slow thinking with the end-of-thinking token, thereby fostering fast reasoning and efficient answer generation. This approach unifies and generalizes existing monotonic scaling methods by enabling flexible and dense slow-to-fast reasoning modulation. Extensive empirical studies on various challenging benchmarks across mathematical, coding, and scientific domains demonstrate $α$1's superior reasoning capability and efficiency. Project page: https://alphaone-project.github.io/

Large Language Model (LLM) reasoning for complex tasks inherently involves a trade-off between solution accuracy and computational efficiency. The subsequent step of verification, while intended to improve performance, further complicates this landscape by introducing its own challenging trade-off: sophisticated Generative Reward Models (GenRMs) can be computationally prohibitive if naively integrated with LLMs at test-time, while simpler, faster methods may lack reliability. To overcome these challenges, we introduce FlexiVe, a novel generative verifier that flexibly balances computational resources between rapid, reliable fast thinking and meticulous slow thinking using a Flexible Allocation of Verification Budget strategy. We further propose the Solve-Detect-Verify pipeline, an efficient inference-time scaling framework that intelligently integrates FlexiVe, proactively identifying solution completion points to trigger targeted verification and provide focused solver feedback. Experiments show FlexiVe achieves superior accuracy in pinpointing errors within reasoning traces on ProcessBench. Furthermore, on challenging mathematical reasoning benchmarks (AIME 2024, AIME 2025, and CNMO), our full approach outperforms baselines like self-consistency in reasoning accuracy and inference efficiency. Our system offers a scalable and effective solution to enhance LLM reasoning at test time.

Recent advancements in Large Vision-Language Models have showcased remarkable capabilities. However, they often falter when confronted with complex reasoning tasks that humans typically address through visual aids and deliberate, step-by-step thinking. While existing methods have explored text-based slow thinking or rudimentary visual assistance, they fall short of capturing the intricate, interleaved nature of human visual-verbal reasoning processes. To overcome these limitations and inspired by the mechanisms of slow thinking in human cognition, we introduce VisuoThink, a novel framework that seamlessly integrates visuospatial and linguistic domains. VisuoThink facilitates multimodal slow thinking by enabling progressive visual-textual reasoning and incorporates test-time scaling through look-ahead tree search. Extensive experiments demonstrate that VisuoThink significantly enhances reasoning capabilities via inference-time scaling, even without fine-tuning, achieving state-of-the-art performance in tasks involving geometry and spatial reasoning.

To provide flexibility and low-level interaction capabilities, the unsafe tag in Rust is essential in many projects, but undermines memory safety and introduces Undefined Behaviors (UBs) that reduce safety. Eliminating these UBs requires a deep understanding of Rust's safety rules and strong typing. Traditional methods require depth analysis of code, which is laborious and depends on knowledge design. The powerful semantic understanding capabilities of LLM offer new opportunities to solve this problem. Although existing large model debugging frameworks excel in semantic tasks, limited by fixed processes and lack adaptive and dynamic adjustment capabilities. Inspired by the dual process theory of decision-making (Fast and Slow Thinking), we present a LLM-based framework called RustBrain that automatically and flexibly minimizes UBs in Rust projects. Fast thinking extracts features to generate solutions, while slow thinking decomposes, verifies, and generalizes them abstractly. To apply verification and generalization results to solution generation, enabling dynamic adjustments and precise outputs, RustBrain integrates two thinking through a feedback mechanism. Experimental results on Miri dataset show a 94.3% pass rate and 80.4% execution rate, improving flexibility and Rust projects safety.