@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://aclanthology.org/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{\%}."
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<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%.</abstract>
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%0 Conference Proceedings
%T MUR: Momentum Uncertainty guided Reasoning for Large Language Models
%A Yan, Hang
%A Xu, Fangzhi
%A Xu, Rongman
%A Li, Yifei
%A Zhang, Jian
%A Luo, Haoran
%A Wu, Xiaobao
%A Luu, Anh Tuan
%A Zhao, Haiteng
%A Lin, Qika
%A Liu, Jun
%Y Liakata, Maria
%Y Moreira, Viviane P.
%Y Zhang, Jiajun
%Y Jurgens, David
%S Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)
%D 2026
%8 July
%I Association for Computational Linguistics
%C San Diego, California, United States
%@ 979-8-89176-390-6
%F yan-etal-2026-mur
%X 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%.
%U https://aclanthology.org/2026.acl-long.1058/
%P 23078-23103
Markdown (Informal)
[MUR: Momentum Uncertainty guided Reasoning for Large Language Models](https://aclanthology.org/2026.acl-long.1058/) (Yan et al., ACL 2026)
ACL
- Hang Yan, Fangzhi Xu, Rongman Xu, Yifei Li, Jian Zhang, Haoran Luo, Xiaobao Wu, Anh Tuan Luu, Haiteng Zhao, Qika Lin, and Jun Liu. 2026. MUR: Momentum Uncertainty guided Reasoning for Large Language Models. In Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 23078–23103, San Diego, California, United States. Association for Computational Linguistics.