MUR: Momentum Uncertainty guided Reasoning for Large Language Models
Hang Yan Xi'an Jiaotong University, Fangzhi Xu Xi'an Jiaotong University, Rongman Xu School of Computer Science and Technology and School of Mathmatics and Statistics, Yifei Li, Jian Zhang, Haoran Luo Nanyang Technological University, Xiaobao Wu Shanghai Jiaotong University, Anh Tuan Luu Nanyang Technological University 等 11 位作者
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 TTS 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 step-wise uncertainty over time. To support flexible inference-time control, we introduce -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 45% on average while improving accuracy by 0.33–3.46%.
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Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · 2026 · 正式发表