Paper Title:
Does Learning Mathematical Problem-Solving
Generalize to Broader Reasoning?
Paper Link:
https://arxiv.org/pdf/2507.04391
Brief Understanding:
This article explores the generalization potential of Mathematical Problem-Solving (MPS) training methods for Large Language Models (LLMs) in broader reasoning capabilities. The core question of the research is: Can learning mathematical problem-solving improve a model's performance on other reasoning tasks, or is it limited to enhancing performance on mathematical problem-solving benchmarks?
Research Background
Cognitive neuroscience research indicates that learning mathematical problem-solving can enhance human general reasoning abilities by promoting logical thinking, abstract reasoning, and transferable problem-solving strategies across domains.
This "math promotes AI" concept suggests that incorporating mathematical reasoning data into AI training may help large language models develop more complex and diverse reasoning capabilities.
However, most current research focuses on developing models specifically for solving mathematical problems, and it remains unclear whether these training methods truly help models perform better on other types of reasoning tasks.
Research Methods
The article investigates five common training strategies used to enhance LLMs' mathematical problem-solving abilities:
1. Continual Pretraining: Extending LLMs' pretraining on large-scale mathematical texts to enhance their adaptability to the mathematical domain.
2. Supervised Fine-tuning on STEM Data: Training models using diverse question-answer pairs from a wide range of STEM disciplines to improve their general reasoning capabilities.
3. Supervised Fine-tuning on MPS Samples with Short Reasoning Chains: Directly training models on mathematical problem-solving datasets where solutions are presented in concise, step-by-step forms.
4. Supervised Fine-tuning on MPS Samples with Long, Self-Reflective Reasoning Chains: An emerging paradigm that enhances a model's ability by strengthening its generation of extensive and reflective reasoning.
5. Rule-based Reinforcement Learning: Using rule-based reward mechanisms to improve a model's reasoning capabilities.
Experimental Design
Evaluation Benchmarks: Researchers selected 5 mathematical problem-solving benchmarks and 8 general reasoning benchmarks to evaluate the models.
Model Setup: Various open-source or self-trained models were used, covering the five training strategies mentioned above.
Experimental Setup: To simulate real-world scenarios, most experiments included fine-tuning with a general dialogue dataset (UltraChat).
Key Findings
1. Effect of Continual Pretraining: Continual pretraining on mathematical texts can improve model performance on 6 general reasoning tasks, but has limited improvement on mathematical problem-solving.
2. Limitations of Short Reasoning Chains: Supervised fine-tuning based on short reasoning chains performs well on mathematical problem-solving tasks but poorly on non-mathematical reasoning tasks, and in some cases even harms generalization performance.
3. Advantages of Long Reasoning Chains: Models trained with long reasoning chains (e.g., LIMO) showed significant improvement in general reasoning tasks, especially in certain benchmarks like GPQA and LogiQA, with relative improvements of 10.2% and 11.8% respectively. This long reasoning chain training activates the model's "long reasoning mode," enabling better performance across different reasoning tasks.
4. Potential of Reinforcement Learning: Rule-based reinforcement learning (e.g., SimpleRL-Zero and SimpleRL) showed improvements in both mathematical and general reasoning tasks, indicating that reinforcement learning could be an effective method for enhancing reasoning abilities.
Other Findings
Importance of Data Coverage: Data coverage analysis found that pretraining datasets (e.g., OpenWebMath) have a higher overlap with general reasoning tasks than specialized mathematical problem-solving datasets (e.g., MetaMath), which might explain their greater effectiveness in generalization tasks.
Limitations of Non-Mathematical Reasoning Data: Researchers also explored the generalization potential of other non-mathematical reasoning datasets (e.g., Magicoder-Evol-Instruct, Magpie-Reasoning, and OpenOrca), but these datasets failed to achieve satisfactory generalization across a wide range of tasks, suggesting a need for new training objectives to significantly improve generalization capabilities.
Conclusion
The article's experiments show that traditional short reasoning chain training methods have limited effectiveness in improving a model's general reasoning abilities, while long reasoning chain training and rule-based reinforcement learning demonstrate better generalization potential. These findings provide new directions for future research on how to enhance a model's general reasoning capabilities through mathematical problem-solving training.