Reasoning Vectors: Transferring Chain-of-Thought Capabilities via Task Arithmetic

🤗 Upvotes: 25 | cs.CL

Authors:
Mohammad Zbeeb, Hasan Abed Al Kader Hammoud, Bernard Ghanem

Title:
Reasoning Vectors: Transferring Chain-of-Thought Capabilities via Task Arithmetic

Arxiv:
http://arxiv.org/abs/2509.01363v1

Abstract:
Large language models often require costly optimization, such as reinforcement learning, to master complex reasoning tasks. This work demonstrates that reasoning ability, once learned, can be extracted and transferred between models as a compact task vector. We source two publicly available, identically initialized Qwen2.5 models, one fine-tuned with supervised fine-tuning (SFT) and the other with group relative policy optimization (GRPO) on the same dataset. From these, we extract a reasoning vector: $v_{\text{reason}} = \theta_{\text{GRPO}} - \theta_{\text{SFT}}$. We hypothesize that this vector captures the reasoning capability instilled by reinforcement learning while factoring out shared knowledge from the SFT process. When added to compatible instruction-tuned models through simple arithmetic, this vector consistently improves performance across diverse reasoning benchmarks: GSM8K (+4.9%), HumanEval (+4.3%), SciQ (+1.7%), and BigBenchHard (+12.3% for the 1.5B model). The performance improvements persist under adversarial conditions. Conversely, subtracting the vector causes significant performance degradation (-11.8% on GSM8K), demonstrating the vector's strong contribution to the model's reasoning abilities. This work shows how reasoning capabilities, typically developed through expensive training, can be extracted from existing open-source models and reused through simple tensor arithmetic, offering a practical way to enhance models by recycling prior computational investments.

What is Daily Paper Cast?

We update every weekday to discuss highest-voted papers from Huggingface Daily Paper (https://huggingface.co/papers). Both the podcast scripts and audio are generated by AI. Feedback and suggestions are welcome! Email us: [e-mail]

Creator:
Jingwen Liang, 3D ML, https://www.linkedin.com/in/jingwen-liang/
Gengyu Wang, LLM ML, http://wanggengyu.com

Listen on:
Spotify: https://open.spotify.com/show/21nrhmdaA8qoBiH8q03NXL
Apple Podcast: https://podcasts.apple.com/us/podcast/daily-paper-cast/id1777620236

Cover Image by Kawen Kuang https://kawen.art