A difference-in-means direction at the <think> position, shared across MATH difficulty levels, causally sets the number of reasoning tokens

measured in 1 paper

Sheng et al. compute difference-in-means vectors between MATH difficulty levels 2-5 and level 1 from residual activations at the start-of-reasoning <think> position, before any reasoning token is generated [sheng-etal-2025-reasoning-strength-planning] The four vectors have pairwise cosine similarity around 0.99 in R1-Distill-Qwen, with layer-averaged cosine above 0.9 rising toward 1.0 in the final layers, while their L2 norms grow with difficulty [sheng-etal-2025-reasoning-strength-planning] Adding the averaged vector to activations with strength from -0.2 to 0.2 consistently changes the reasoning token count on R1-Distill-Qwen-1.5B/7B/14B/32B and QwQ-32B while the answer length stays largely unchanged; moderate positive strength gave small accuracy gains (average +0.46 to +2.35 points) [sheng-etal-2025-reasoning-strength-planning] The pattern also holds in R1-Distill-Llama-8B (mean cosine 0.89-0.97 in middle layers); a Lasso linear probe on the same activations predicts reasoning length with correlation above 0.8 (probe result is supporting only) [sheng-etal-2025-reasoning-strength-planning]

Structure

Linear Direction

Context

reasoning length planning, question difficulty, large reasoning models, end-of-thinking token logit

Confirmed in models

DeepSeek-R1-Distill-Qwen-1.5B · DeepSeek, DeepSeek-R1-Distill-Qwen-7B · DeepSeek, DeepSeek-R1-Distill-Qwen-14B · DeepSeek, DeepSeek-R1-Distill-Qwen-32B · DeepSeek, QwQ-32B · Qwen, DeepSeek-R1-Distill-Llama-8B · DeepSeek

Method

Difference-in-means direction, Activation Steering (Addition), Linear probing

Papers

On Reasoning Strength Planning in Large Reasoning Models — Sheng, Leheng, Zhang, An, Wu, Zijian, Zhao, Weixiang, Shen, Changshuo, Zhang, Yi, Wang, Xiang, Chua, Tat-Seng2025 · arXiv:2506.08390