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

Fuente: arXiv
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Autori principali: Singh, Joykirat, Chakraborty, Tanmoy, Nambi, Akshay
Natura: Preprint
Pubblicazione: 2025
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author Singh, Joykirat
Chakraborty, Tanmoy
Nambi, Akshay
author_facet Singh, Joykirat
Chakraborty, Tanmoy
Nambi, Akshay
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2503_04813
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Self-Evolved Preference Optimization for Enhancing Mathematical Reasoning in Small Language Models
Singh, Joykirat
Chakraborty, Tanmoy
Nambi, Akshay
Machine Learning
Artificial Intelligence
Computation and Language
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.
title Self-Evolved Preference Optimization for Enhancing Mathematical Reasoning in Small Language Models
topic Machine Learning
Artificial Intelligence
Computation and Language
url https://arxiv.org/abs/2503.04813