How Much Thinking is Enough? Quantifying and Understanding Redundancy in LLM Reasoning

Paper Overview

Field: Machine Learning Authors: Zhiyuan Zhai, Xinkai You, Wenjing Yan Published: 2026-05-26 arXiv: 2505.21642

Summary

Reasoning-capable large language models solve hard problems by emitting long chains of thought, paying heavily in latency, GPU time, and energy. Casual inspection of their traces reveals extensive reformulation, verification, and circular self-reflection, yet how much of this deliberation is actually necessary has never been measured at scale or explained from first principles. This paper closes both gaps.

Key Contributions

1. Formalizing reasoning redundancy: The redundancy of a correct trace is defined as the largest fraction of its trailing segmented steps that can be truncated while the model — forced to terminate thinking and emit a final answer — still produces the correct answer.

2. Large-scale quantification: Across four frontier reasoning models and two mathematical benchmarks:

• Step-level redundancy is consistently high: between 61% and 93% across the 8 (model, benchmark) conditions studied.
• The median critical prefix equals a single segmented step in six of the eight conditions.
• The finding is robust to the choice of judge family.
• Although rho decreases with problem difficulty on MATH-500, all four models remain substantially redundant (rho in [46%, 85%]) even on the hardest Level-5 problems.

3. Theoretical explanation: The authors prove that this redundancy is a structural consequence of length-agnostic outcome rewards, not a model-specific artefact. Under any such reward, no finite expected stopping time is optimal. The result holds regardless of RL algorithm, base model, data distribution, or whether the policy is obtained via RL or distillation.

Conclusion

Over-thinking is therefore not a bug to be patched in individual models but a structural property of how current reasoning models are trained.

Code: arXiv:2505.21642