Self-Evolved Preference Optimization for Enhancing Mathematical Reasoning in Small Language Models
This addresses the challenge of reliable mathematical problem-solving for AI applications, offering a scalable and efficient solution, though it appears incremental as it builds on existing preference optimization methods.
The paper tackles the problem of complex multi-step mathematical reasoning in small language models (SLMs) by introducing SPHERE, a self-evolving data generation pipeline, resulting in significant gains over base models and matching or surpassing GPT-4o on certain benchmarks like MATH 500 and GSM8K.
Large language models (LLMs) have significantly improved their reasoning capabilities; however, they still struggle with complex multi-step mathematical problem-solving due to error propagation, lack of self-correction, and limited adaptability to diverse reasoning styles. Existing methods rely on static fine-tuning or prompt engineering, which fail to generalize across problem complexities, while the scarcity of high-quality preference data further hinders reliable reasoning. We introduce SPHERE, a self-evolving data generation pipeline that enhances reasoning in small language models (SLMs) by iteratively generating, correcting, and diversifying reasoning chains. SPHERE operates in three stages: (i) Self-Generation, where the model autonomously constructs problem-solving steps; (ii) Self-Correction, enabling it to identify and rectify errors; and (iii) Diversity Induction, improving robustness through multiple valid reasoning trajectories. This self-evolution mechanism strengthens mathematical reasoning and enhances model reliability. Evaluations on MATH 500, GSM8K, AIME, AMC, and Olympiad show that SPHERE-trained models achieve significant gains over their base versions and match/surpass GPT-4o on certain benchmarks. Our findings demonstrate that self-evolving models can close the reasoning gap between SLMs and state-of-the-art LLMs, making mathematical AI more reliable, scalable, and efficient.