# Mitigating Overthinking in Large Reasoning Models via Manifold Steering

arXiv: https://arxiv.org/abs/2505.22411 · HTML: https://mlsanity.com/paper/2505.22411/

## Key facts

- Cited by 33 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 38 of its 51 references that are in the map.
- First posted on arXiv 28 May 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, 30 of 38)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Universal and Transferable Adversarial Attacks on Aligned Language Models](https://mlsanity.com/paper/2307.15043/) (2023)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Representation Engineering: A Top-Down Approach to AI Transparency](https://mlsanity.com/paper/2310.01405/) (2023)
- [Steering Llama 2 via Contrastive Activation Addition](https://mlsanity.com/paper/2312.06681/) (2023)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [Safe RLHF: Safe Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2310.12773/) (2023)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [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)
- [Mechanistic Interpretability for AI Safety -- A Review](https://mlsanity.com/paper/2404.14082/) (2024)
- [Generating Wikipedia by Summarizing Long Sequences](https://mlsanity.com/paper/1801.10198/) (2018)
- [WebThinker: Empowering Large Reasoning Models with Deep Research Capability](https://mlsanity.com/paper/2504.21776/) (2025)
- [DeepResearcher: Scaling Deep Research via Reinforcement Learning in Real-world Environments](https://mlsanity.com/paper/2504.03160/) (2025)
- [Large Language Models for Mathematical Reasoning: Progresses and Challenges](https://mlsanity.com/paper/2402.00157/) (2024)
- [Extracting Latent Steering Vectors from Pretrained Language Models](https://mlsanity.com/paper/2205.05124/) (2022)
- [Dynamic Early Exit in Reasoning Models](https://mlsanity.com/paper/2504.15895/) (2025)
- [OpenMathInstruct-2: Accelerating AI for Math with Massive Open-Source Instruction Data](https://mlsanity.com/paper/2410.01560/) (2024)
- [Thoughts Are All Over the Place: On the Underthinking of o1-Like LLMs](https://mlsanity.com/paper/2501.18585/) (2025)
- [The Danger of Overthinking: Examining the Reasoning-Action Dilemma in Agentic Tasks](https://mlsanity.com/paper/2502.08235/) (2025)
- [A Practical Review of Mechanistic Interpretability for Transformer-Based Language Models](https://mlsanity.com/paper/2407.02646/) (2024)
- [STAIR: Improving Safety Alignment with Introspective Reasoning](https://mlsanity.com/paper/2502.02384/) (2025)
- [SEAL: Steerable Reasoning Calibration of Large Language Models for Free](https://mlsanity.com/paper/2504.07986/) (2025)
- [NExT: Teaching Large Language Models to Reason about Code Execution](https://mlsanity.com/paper/2404.14662/) (2024)
- [RealSafe-R1: Safety-Aligned DeepSeek-R1 without Compromising Reasoning Capability](https://mlsanity.com/paper/2504.10081/) (2025)
- [Efficiently Scaling LLM Reasoning with Certaindex](https://mlsanity.com/paper/2412.20993/) (2024)
- [Spectral Filters, Dark Signals, and Attention Sinks](https://mlsanity.com/paper/2402.09221/) (2024)

## Built on by (most cited first, 30 of 33)

- [Don't Overthink It: A Survey of Efficient R1-style Large Reasoning Models](https://mlsanity.com/paper/2508.02120/) (2025)
- [A Comprehensive Survey on Trustworthiness in Reasoning with Large Language Models](https://mlsanity.com/paper/2509.03871/) (2025)
- [The Geometry of Reasoning: Flowing Logics in Representation Space](https://mlsanity.com/paper/2510.09782/) (2025)
- [Early Stopping Chain-of-thoughts in Large Language Models](https://mlsanity.com/paper/2509.14004/) (2025)
- [DeceptionBench: A Comprehensive Benchmark for AI Deception Behaviors in Real-world Scenarios](https://mlsanity.com/paper/2510.15501/) (2025)
- [Towards Concise and Adaptive Thinking in Large Reasoning Models: A Survey](https://mlsanity.com/paper/2507.09662/) (2025)
- [WS-GRPO: Weakly-Supervised Group-Relative Policy Optimization for Rollout-Efficient Reasoning](https://mlsanity.com/paper/2602.17025/) (2026)
- [Contextual Rollout Bandits for Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2602.08499/) (2026)
- [Curveball Steering: The Right Direction To Steer Isn't Always Linear](https://mlsanity.com/paper/2603.09313/) (2026)
- [Understanding and Steering the Cognitive Behaviors of Reasoning Models at Test-Time](https://mlsanity.com/paper/2512.24574/) (2025)
- [Towards a Mechanistic Understanding of Large Reasoning Models: A Survey of Training, Inference, and Failures](https://mlsanity.com/paper/2601.19928/) (2026)
- [Mitigating Overthinking in Large Reasoning Models via Difficulty-aware Reinforcement Learning](https://mlsanity.com/paper/2601.21418/) (2026)
- [Concept Heterogeneity-aware Representation Steering](https://mlsanity.com/paper/2603.02237/) (2026)
- [Fantastic Reasoning Behaviors and Where to Find Them: Unsupervised Discovery of the Reasoning Process](https://mlsanity.com/paper/2512.23988/) (2025)
- [Internalizing LLM Reasoning via Discovery and Replay of Latent Actions](https://mlsanity.com/paper/2602.04925/) (2026)
- [Steering Large Reasoning Models towards Concise Reasoning via Flow Matching](https://mlsanity.com/paper/2602.05539/) (2026)
- [Efficient Reasoning with Balanced Thinking](https://mlsanity.com/paper/2603.12372/) (2026)
- [Distractor Injection Attacks on Large Reasoning Models: Characterization and Defense](https://mlsanity.com/paper/2510.16259/) (2025)
- [Can Confidence Estimates Decide When Chain-of-Thought Is Necessary for LLMs?](https://mlsanity.com/paper/2510.21007/) (2025)
- [Time Travel Engine: A Shared Latent Chronological Manifold Enables Historical Navigation in Large Language Models](https://mlsanity.com/paper/2601.06437/) (2026)
- [Nudging Hidden States: Training-Free Model Steering for Chain-of-Thought Reasoning in Large Audio-Language Models](https://mlsanity.com/paper/2603.14636/) (2026)
- [CLEAR: Revealing How Noise and Ambiguity Degrade Reliability in LLMs for Medicine](https://mlsanity.com/paper/2605.01011/) (2026)
- [Reasoning Models Don't Just Think Longer, They Move Differently](https://mlsanity.com/paper/2605.15454/) (2026)
- [Batch Prompting Suppresses Overthinking Reasoning Under Constraint: How Batch Prompting Suppresses Overthinking in Reasoning Models](https://mlsanity.com/paper/2511.04108/) (2025)
- [Transcoder Adapters for Reasoning-Model Diffing](https://mlsanity.com/paper/2602.20904/) (2026)
- [Reliable Control-Point Selection for Steering Reasoning in Large Language Models](https://mlsanity.com/paper/2604.02113/) (2026)
- [Benchmarking and Evolving Reason-Reflect-Rectify for Reflective Visual Generation](https://mlsanity.com/paper/2605.19639/) (2026)
- [Right Direction, Wrong Step: Geometric Analysis of Finite-Step Failure in Looped Transformers](https://mlsanity.com/paper/2609.16665/) (2026)
- [Nice Fold or Hero Call: Learning Budget-Efficient Thinking for Adaptive Reasoning](https://mlsanity.com/paper/2605.11625/) (2026)
- [DyCon: Dynamic Reasoning Control via Evolving Difficulty Modeling](https://mlsanity.com/paper/2606.07108/) (2026)

## Abstract (arXiv)

Recent advances in Large Reasoning Models (LRMs) have demonstrated remarkable capabilities in solving complex tasks such as mathematics and coding. However, these models frequently exhibit a phenomenon known as overthinking during inference, characterized by excessive validation loops and redundant deliberation, leading to substantial computational overheads. In this paper, we aim to mitigate overthinking by investigating the underlying mechanisms from the perspective of mechanistic interpretability. We first showcase that the tendency of overthinking can be effectively captured by a single direction in the model's activation space and the issue can be eased by intervening the activations along this direction. However, this efficacy soon reaches a plateau and even deteriorates as the intervention strength increases. We therefore systematically explore the activation space and find that the overthinking phenomenon is actually tied to a low-dimensional manifold, which indicates that the limited effect stems from the noises introduced by the high-dimensional steering direction. Based on this insight, we propose Manifold Steering, a novel approach that elegantly projects the steering direction onto the low-dimensional activation manifold given the theoretical approximation of the interference noise. Extensive experiments on DeepSeek-R1 distilled models validate that our method reduces output tokens by up to 71% while maintaining and even improving the accuracy on several mathematical benchmarks. Our method also exhibits robust cross-domain transferability, delivering consistent token reduction performance in code generation and knowledge-based QA tasks. Code is available at: https://github.com/Aries-iai/Manifold_Steering.