Exploring Solution Divergence and Its Effect on Large Language Model Problem Solving

Large language models (LLMs) have been widely used for problem-solving tasks. Most recent work improves their performance through supervised fine-tuning (SFT) with labeled data or reinforcement learning (RL) from task feedback. In this paper, we study a new perspective: the divergence in solutions generated by LLMs for a single problem. We show that higher solution divergence is positively related to better problem-solving abilities across various models. Based on this finding, we propose solution divergence as a novel metric that can support both SFT and RL strategies. We test this idea on three representative problem domains and find that using solution divergence consistently improves success rates. These results suggest that solution divergence is a simple but effective tool for advancing LLM training and evaluation. The rise of large language models (LLMs) and their remarkable general problem-solving capabilities have accelerated research on advanced artificial intelligence (AI) solutions across diverse domains, including science (Ren et al., 2025), finance (Li et al., 2023), and education (Wang et al., 2024).