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

Paper Overview

Field: Machine Learning Authors: Zhiyuan Zhai, Xinkai You, Wenjing Yan 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 Findings

• Formalizing redundancy: The redundancy of a correct trace is the largest fraction of its trailing segmented steps that can be truncated while the model (π), forced to terminate thinking and emit a final answer, still produces the correct answer.
• 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.
• Minimal critical prefix: In six of the eight conditions, the median critical prefix equals a single segmented step.
• Robustness: The finding is robust to the choice of judge family. Although redundancy ρ decreases with problem difficulty on MATH-500, all four models remain substantially redundant (ρ ∈ [46%, 85%]) even on the hardest Level-5 problems.

Theoretical Result

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
• Whether the policy is obtained via RL or distillation

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: available via the arXiv page.