用动态不确定度分配思考预算，让大模型少算却更准。
MUR: Momentum Uncertainty guided Reasoning for Large Language Models
- 根据每步推理的不确定性动态调整思考资源
- 平均减少45%计算量，准确率提升0.33至3.46个百分点
- 无需额外训练，适合想优化推理效率的研究者
大语言模型在复杂推理任务中表现优异，但如何高效优化推理过程仍是挑战。测试时缩放（TTS）虽能提升质量，却常导致过度思考，浪费计算资源。本文提出动量不确定性引导推理（MUR），借鉴物理中的动量概念，通过追踪和累积各步推理的不确定性，动态分配关键步骤的思考预算。为实现灵活控制，引入伽马调节机制，仅用一个超参数即可调控推理开销。理论分析证明了MUR在稳定性和偏差上的优势。在四个挑战性基准（MATH-500、AIME24、AIME25、GPQA-diamond）上，使用不同规模的Qwen3模型（1.7B、4B、8B）进行评估，结果表明，MUR平均减少45%以上计算量，同时将准确率从0.33提升至3.46%。
原文摘要 · Abstract (English)
Large Language Models have achieved impressive performance on reasoning-intensive tasks, yet optimizing their reasoning efficiency remains an open challenge. While Test-Time Scaling (TTS) improves reasoning quality, it often leads to overthinking, wasting tokens on redundant computations. This work investigates how to efficiently and adaptively guide current model' test-time scaling without additional training. Inspired by the concept of momentum in physics, we propose Momentum Uncertainty-guided Reasoning (MUR), which dynamically allocates thinking budgets to critical reasoning steps by tracking and aggregating stepwise uncertainty over time. To support flexible inference-time control, we introduce gamma-control, a simple mechanism that tunes the reasoning budget via a single hyperparameter. We provide in-depth theoretical proof to support the superiority of MUR in terms of stability and biases. MUR is comprehensively evaluated against various TTS methods across four challenging benchmarks (MATH-500, AIME24, AIME25, and GPQA-diamond) using different sizes of recent Qwen3 models (1.7B, 4B, and 8B). Results demonstrate that MUR reduces computation by by over 45% on average while improving accuracy from 0.33 to 3.46%.
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