@inproceedings{yan-etal-2026-mur,
    title = "{MUR}: Momentum Uncertainty guided Reasoning for Large Language Models",
    author = "Yan, Hang  and
      Xu, Fangzhi  and
      Xu, Rongman  and
      Li, Yifei  and
      Zhang, Jian  and
      Luo, Haoran  and
      Wu, Xiaobao  and
      Luu, Anh Tuan  and
      Zhao, Haiteng  and
      Lin, Qika  and
      Liu, Jun",
    editor = "Liakata, Maria  and
      Moreira, Viviane P.  and
      Zhang, Jiajun  and
      Jurgens, David",
    booktitle = "Proceedings of the 64th Annual Meeting of the {A}ssociation for {C}omputational {L}inguistics (Volume 1: Long Papers)",
    month = jul,
    year = "2026",
    address = "San Diego, California, United States",
    publisher = "Association for Computational Linguistics",
    url = "https://preview.aclanthology.org/ingest-acl/2026.acl-long.1058/",
    pages = "23078--23103",
    ISBN = "979-8-89176-390-6",
    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 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{\%}."
}