MUR: Momentum Uncertainty guided Reasoning for Large Language Models
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%.
688332d5846d2e78b7548b6f
Hang Yan
688332d5846d2e78b7548b70
Fangzhi Xu
688332d5846d2e78b7548b71
Rongman Xu
688332d5846d2e78b7548b72
Yifei Li
688332d5846d2e78b7548b73
Jian Zhang
688332d5846d2e78b7548b74
Haoran Luo
claimed_verified
2025-08-18T06:59:58.105Z
640ed7e2c025ddf61895269d
https://cdn-avatars.huggingface.co/v1/production/uploads/640ed7e2c025ddf61895269d/4XJ4eAB6dQsu5AQxsGcfF.png
Haoran Luo
user
LHRLAB
688332d5846d2e78b7548b75
Xiaobao Wu
688332d5846d2e78b7548b76
Luu Anh Tuan
688332d5846d2e78b7548b77
Haiteng Zhao
688332d5846d2e78b7548b78
Qika Lin
688332d5846d2e78b7548b79
Jun Liu
MUR: Momentum Uncertainty guided Reasoning for Large Language Models
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%.
Momentum Uncertainty-guided Reasoning (MUR) dynamically allocates computational resources to improve reasoning efficiency and accuracy in Large Language Models without additional training.
Large Language Models Test-Time Scaling Momentum Uncertainty-guided Reasoning gamma-control MATH-500 AIME24 AIME25 GPQA-diamond Qwen3