MUR: Momentum Uncertainty guided Reasoning for Large Language Models

• URL: http://arxiv.org/abs/2507.14958v1
• Date: Sun, 20 Jul 2025 13:36:19 GMT
• Title: MUR: Momentum Uncertainty guided Reasoning for Large Language Models
• Authors: Hang Yan, Fangzhi Xu, Rongman Xu, Yifei Li, Jian Zhang, Haoran Luo, Xiaobao Wu, Luu Anh Tuan, Haiteng Zhao, Qika Lin, Jun Liu,
• Abstract summary: Large Language Models (LLMs) have achieved impressive performance on reasoning-intensive tasks.<n>Momentum Uncertainty-guided Reasoning (MUR) allocates thinking budgets to critical reasoning steps by tracking and aggregating stepwise uncertainty over time.<n>Results demonstrate that MUR reduces by over 50% on average while improving accuracy by 0.62-3.37%.
• Score: 23.766037094142117
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Large Language Models (LLMs) 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 LLM 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 over 50% on average while improving accuracy by 0.62-3.37%.

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