2026-05-26原文

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

This paper quantifies redundancy in reasoning LLMs, finding that 61-93% of chain-of-thought steps can be truncated without affecting correctness, and proves this redundancy is a structural consequence of length-agnostic outcome rewards.

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Key points

Formal definition of reasoning redundancy: fraction of trailing steps that can be truncated while still yielding correct answer
Measured redundancy of 61-93% across four frontier models and two math benchmarks
Proven that redundancy is structural due to length-agnostic outcome rewards, not a model bug
Redundancy persists even on hardest problems: 46-85% on Level-5

Why it matters

This matters because formal definition of reasoning redundancy: fraction of trailing steps that can be truncated while still yielding correct answer.

Technical impact

May affect model selection, inference cost, product capability, and evaluation benchmarks.

[2605.23926] How Much Thinking is Enough? Quantifying and Understanding Redundancy in LLM Reasoning

[Submitted on 21 Apr 2026]

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

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Abstract: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.

We formalise reasoning redundancy directly in terms of the reasoning model itself: the redundancy of a correct trace is the largest fraction of its trailing segmented steps that can be truncated while $\pi$, forced to terminate thinking and emit a final answer, still produces the correct answer. A large-scale quantification across four frontier reasoning models and two mathematical benchmarks shows that step-level redundancy is consistently high -- between 61% and 93% across the 8 (model, benchmark) conditions we study, with the median critical prefix equal to a single segmented step in six of the eight conditions -- that the finding is robust to the choice of judge family, and that 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.

We then 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; 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: this https URL

Subjects:

Artificial Intelligence (cs.AI); Machine Learning (cs.LG)

Cite as: arXiv:2605.23926 [cs.AI]

(or arXiv:2605.23926v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2605.23926

arXiv-issued DOI via DataCite

Submission history

From: Zhiyuan Zhai [view email] [v1] Tue, 21 Apr 2026 05:32:02 UTC (217 KB)

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