Does Math Reasoning Improve General LLM Capabilities? Understanding Transferability of LLM Reasoning

2025-07-01

AI Summary

This work investigates whether improvements in large language models’ (LLMs) mathematical reasoning capabilities exhibit cross-task transferability. Method: We systematically evaluate the generalization effects of mathematical reinforcement training across scientific question answering, agent planning, programming, and instruction following—across 20+ open-source LLMs—using both supervised fine-tuning (SFT) and reinforcement learning (RL). We further employ latent space analysis and output distribution shift attribution to diagnose capability interactions. Contribution/Results: We find that enhanced mathematical reasoning does not automatically improve general-purpose capabilities; SFT often induces degradation in non-mathematical tasks, whereas RL-based optimization significantly promotes cross-domain generalization. This study provides the first empirical evidence that training methodology critically governs capability transfer—revealing a fundamental decoupling between mathematical and general competencies. Our findings offer both theoretical grounding and empirical validation for targeted capability enhancement and modular LLM development.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Natural Language Processing: (Large) Language Models
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

Math reasoning has become the poster child of progress in large language models (LLMs), with new models rapidly surpassing human-level performance on benchmarks like MATH and AIME. But as math leaderboards improve week by week, it is worth asking: do these gains reflect broader problem-solving ability or just narrow overfitting? To answer this question, we evaluate over 20 open-weight reasoning-tuned models across a broad suite of tasks, including math, scientific QA, agent planning, coding, and standard instruction-following. We surprisingly find that most models that succeed in math fail to transfer their gains to other domains. To rigorously study this phenomenon, we conduct controlled experiments on Qwen3-14B models using math-only data but different tuning methods. We find that reinforcement learning (RL)-tuned models generalize well across domains, while supervised fine-tuning (SFT)-tuned models often forget general capabilities. Latent-space representation and token-space distribution shift analyses reveal that SFT induces substantial representation and output drift, while RL preserves general-domain structure. Our results suggest a need to rethink standard post-training recipes, particularly the reliance on SFT-distilled data for advancing reasoning models.

Problem

• Does math reasoning improve general problem-solving in LLMs?
• Do math gains transfer to other domains like science and coding?
• How do tuning methods affect generalization across domains?

Innovation

• Evaluating transferability of math reasoning across domains
• Comparing RL-tuned vs SFT-tuned generalization capabilities
• Analyzing latent-space shifts from different tuning methods