M2A: Synergizing Mathematical and Agentic Reasoning in Large Language Models

TL;DR

M2A introduces a parameter-space merging approach to enhance the synergy between mathematical and agentic reasoning in large language models, leading to improved reasoning depth and performance.

Contribution

The paper proposes a novel parameter-space merging method that combines mathematical and agentic reasoning without additional training, improving reasoning capabilities.

Findings

M2A improves reasoning depth in real-world coding tasks.

Applying M2A to Qwen3-8B increases the verified resolved rate from 44.0% to 51.2%.

The method requires no gradient updates and uses a simple merging coefficient.

Abstract

While reasoning has become a central capability of large language models (LLMs), the reasoning patterns required for different scenarios are often misaligned. Mathematical reasoning typically relies on intrinsic logic to solve closed-world problems in a single response, whereas agentic reasoning requires not only internal reasoning but also multi-turn interaction with external environments, interleaving thought and action. This misalignment prevents mathematical and agentic reasoning from effectively benefiting from each other, often yielding unstable reasoning behavior and only limited performance gains under multi-task learning. In this paper, we propose M2A, a novel paradigm that synergizes mathematical and agentic reasoning via model merging. To avoid overfitting to superficial reasoning patterns under joint training, M2A operates directly in parameter space: it identifies the feature subspace critical for agent behavior, and merges the mathematical reasoning task vector only along its null space, thereby injecting reasoning capability along directions that do not perturb agent behavior. Unlike SFT or RL, M2A requires no additional gradient-update and exposes the merging coefficient as a simple knob for controlling reasoning length. Experiments in a challenging real-world coding agent setting show that our method effectively extends agentic reasoning depth and delivers substantial performance improvements. Applied to a fine-tuned Qwen3-8B, M2A improves its SWE-Bench Verified resolved rate from 44.0% to 51.2% without retraining the model. Code is available at https://github.com/laplucky/M2A.git.