# Reconsidering Overthinking: Penalizing Internal and External Redundancy in CoT Reasoning

arXiv: https://arxiv.org/abs/2508.02178 · HTML: https://mlsanity.com/paper/2508.02178/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 16 of its 31 references that are in the map.
- First posted on arXiv 4 Aug 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 16 of 16)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs](https://mlsanity.com/paper/2412.21187/) (2024)
- [Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models](https://mlsanity.com/paper/2503.16419/) (2025)
- [O1-Pruner: Length-Harmonizing Fine-Tuning for O1-Like Reasoning Pruning](https://mlsanity.com/paper/2501.12570/) (2025)
- [ThinkPrune: Pruning Long Chain-of-Thought of LLMs via Reinforcement Learning](https://mlsanity.com/paper/2504.01296/) (2025)
- [Thoughts Are All Over the Place: On the Underthinking of o1-Like LLMs](https://mlsanity.com/paper/2501.18585/) (2025)
- [Wait, We Don't Need to "Wait"! Removing Thinking Tokens Improves Reasoning Efficiency](https://mlsanity.com/paper/2506.08343/) (2025)
- [Think When You Need: Self-Adaptive Chain-of-Thought Learning](https://mlsanity.com/paper/2504.03234/) (2025)
- [Optimizing Length Compression in Large Reasoning Models](https://mlsanity.com/paper/2506.14755/) (2025)
- [Efficient Reasoning Through Suppression of Self-Affirmation Reflections in Large Reasoning Models](https://mlsanity.com/paper/2506.12353/) (2025)

## Built on by (most cited first, 13 of 13)

- [Implicit Reasoning in Large Language Models: A Comprehensive Survey](https://mlsanity.com/paper/2509.02350/) (2025)
- [Neural Chain-of-Thought Search: Searching the Optimal Reasoning Path to Enhance Large Language Models](https://mlsanity.com/paper/2601.11340/) (2026)
- [RADAR: Reasoning-Ability and Difficulty-Aware Routing for Reasoning LLMs](https://mlsanity.com/paper/2509.25426/) (2025)
- [Characterizing, Evaluating, and Optimizing Complex Reasoning](https://mlsanity.com/paper/2602.08498/) (2026)
- [Measuring Weak-to-Strong Legibility of Reasoning Models](https://mlsanity.com/paper/2603.20508/) (2026)
- [Explore Briefly, Then Decide: Mitigating LLM Overthinking via Cumulative Entropy Regulation](https://mlsanity.com/paper/2510.02249/) (2025)
- [Capabilities and Fundamental Limits of Latent Chain-of-Thought](https://mlsanity.com/paper/2602.01148/) (2026)
- [CoTJudger: A Graph-Driven Framework for Automatic Evaluation of Chain-of-Thought Efficiency and Redundancy in LRMs](https://mlsanity.com/paper/2603.07078/) (2026)
- [R-Capsule: Compressing High-Level Plans for Efficient Large Language Model Reasoning](https://mlsanity.com/paper/2509.22131/) (2025)
- [Thinking-Based Non-Thinking: Solving the Reward Hacking Problem in Training Hybrid Reasoning Models via Reinforcement Learning](https://mlsanity.com/paper/2601.04805/) (2026)
- [When Compression Helps and When It Hurts: Condition-Aware Analysis of Chain-of-Thought Distillation](https://mlsanity.com/paper/2606.21704/) (2026)
- [A First-Principles Theory of Slow Thinking and Active Perception](https://mlsanity.com/paper/2607.08196/) (2026)
- [QLPO: Quadrant-weighted Sampling for Length-aware Policy Optimization](https://mlsanity.com/paper/2607.21793/) (2026)

## Abstract (arXiv)

Large reasoning models (LRMs) often exhibit overthinking, producing verbose Chain-of-Thought (CoT) traces that increase inference cost and obscure the underlying reasoning process. Existing CoT compression methods mainly rely on global length rewards, which conflate necessary intermediate reasoning with redundant text and may therefore compromise reasoning fidelity. This paper revisits overthinking from a semantic-efficiency perspective and decomposes CoT redundancy into two distinct forms: internal redundancy, defined as informational stagnation before the first correct answer, and external redundancy, defined as superfluous continuation after the first correct answer. Based on this decomposition, we propose a dual-penalty reinforcement learning framework that separately optimizes reasoning progress and termination behavior. Specifically, a sliding-window semantic similarity metric penalizes low-progress reasoning segments, while a normalized external-redundancy metric discourages post-answer continuation. Experiments on GSM8K, MATH500, and AIME24 across different model scales show that our method reduces average reasoning length by 41.3% on the 1.5B model and 40.1% on the 7B model, while preserving competitive accuracy and achieving the best overall accuracy-efficiency score among evaluated baselines. The learned compression behavior further transfers to out-of-domain reasoning tasks, including GPQA and LiveCodeBench. More importantly, our analysis reveals a clear asymmetry between the two redundancy types: external redundancy can be largely removed with little performance loss, whereas internal redundancy compression follows a sensitive accuracy-efficiency trade-off. These results suggest that effective CoT compression should optimize semantic efficiency rather than sequence length alone, offering a principled route toward more concise, efficient, and interpretable LRMs.