Mitigating Overthinking in Large Reasoning Models via Manifold Steering

TL;DR

This work tackles the inefficiency of overthinking in Large Reasoning Models by combining mechanistic interpretability with a low-dimensional activation-manifold projection. It identifies an overthinking direction in activation space via a difference-of-means analysis and shows how naive high-dimensional steering introduces interference noise. By projecting the steering direction onto a learned activation manifold, Manifold Steering mitigates overthinking more robustly, enabling substantial token reductions (up to 71%) while preserving or improving accuracy across mathematics, coding, and knowledge tasks. The method demonstrates strong cross-domain and cross-task transferability with minimal latency, highlighting its practical impact for efficient and reliable large-scale reasoning systems.

Abstract

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.

Figures (7)

• Figure 1: Visualization of residual stream activations $\mathbf{h}^{(l)}(x)$ for $D_{\text{redundant}}$ and $D_{\text{concise}}$ across different layers of DeepSeek-R1-Distill-Qwen-7B (R1-7B). Early layers show considerable overlap between redundant and concise data, while middle-to-late layers exhibit distinct separation.
• Figure 2: (a) Performance of R1-7B with varying $\alpha$ for direct and manifold steering on Math500. (b) Cumulative variance ratio of R1-7B's activation space on $D_{\text{redundant}}$ across different hidden layers.
• Figure 3: Cross-domain performance of Manifold Steering for overthinking mitigation on LiveCodeBench (code generation) and GPQA-Diamond (disciplinary knowledge).
• Figure 4: An example of steering overthinking in model outputs. Forward steering yields concise, confident responses, eliminating hesitant phrases, while reverse steering induces verbose outputs.
• Figure 5: Hyperparameter tuning for strength $\alpha$ in R1-7B

Theorems & Definitions (4)

• Theorem 4.1
• Theorem 4.2
• proof
• proof