{"ID":2892605,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.14958","arxiv_id":"2507.14958","title":"MUR: Momentum Uncertainty guided Reasoning for Large Language Models","abstract":"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%.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2507.14958","url_pdf":"https://arxiv.org/pdf/2507.14958v5","authors":"[\"Hang Yan\",\"Fangzhi Xu\",\"Rongman Xu\",\"Yifei Li\",\"Jian Zhang\",\"Haoran Luo\",\"Xiaobao Wu\",\"Luu Anh Tuan\",\"Haiteng Zhao\",\"Qika Lin\",\"Jun Liu\"]","published":"2025-07-20T13:36:19Z","proceeding":"cs.CL","tasks":"[\"cs.CL\"]","methods":"[\"Language Model\"]","has_code":false}