Self-Evolved Preference Optimization for Enhancing Mathematical Reasoning in Small Language Models

• URL: http://arxiv.org/abs/2503.04813v1
• Date: Tue, 04 Mar 2025 14:43:25 GMT
• Title: Self-Evolved Preference Optimization for Enhancing Mathematical Reasoning in Small Language Models
• Authors: Joykirat Singh, Tanmoy Chakraborty, Akshay Nambi,
• Abstract summary: We introduce SPHERE, a self-evolving data generation pipeline that enhances reasoning in small language models (SLMs)<n> 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.<n>We show that SPHERE-trained models achieve significant gains over their base versions and match/surpass GPT-4o on certain benchmarks.
• Score: 17.673293240849787
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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