评估LLM在提出数学问题新颖解法方面的创造力
Assessing the Creativity of LLMs in Proposing Novel Solutions to Mathematical Problems
AI总结：
本文提出CreativeMath框架与基准，评估LLM在已知解法之外生成数学新颖解法的创造力，发现其标准任务表现良好但创造性差异明显，Gemini-1.5-Pro表现最佳。
摘要：
AI系统的数学能力是复杂且多方面的。现有研究大多主要关注AI生成的数学问题解法的正确性。在本研究中，我们认为，除了给出正确答案之外，AI系统还应当能够针对数学挑战开发新颖解法，或协助人类完成这一工作。本研究探讨了Large Language Models（LLMs，大语言模型）在数学推理中的创造潜力，而这一方面在以往研究中受到的关注有限。我们提出了一个新颖框架与基准CreativeMath，其涵盖从初中课程到奥林匹克级别竞赛的问题，旨在评估LLM在已提供若干已知解法后提出创新解法的能力。实验表明，尽管LLM在标准数学任务上表现良好，但其创造性问题解决能力存在显著差异。值得注意的是，Gemini-1.5-Pro模型在生成新颖解法方面优于其他LLM。本研究开辟了评估AI创造力的新前沿，揭示了LLM在促进数学创新方面的优势与局限，并为AI辅助数学发现的未来发展奠定基础。
英文摘要：
The mathematical capabilities of AI systems are complex and multifaceted. Most existing research has predominantly focused on the correctness of AI-generated solutions to mathematical problems. In this work, we argue that beyond producing correct answers, AI systems should also be capable of, or assist humans in, developing novel solutions to mathematical challenges. This study explores the creative potential of Large Language Models (LLMs) in mathematical reasoning, an aspect that has received limited attention in prior research. We introduce a novel framework and benchmark, CreativeMath, which encompasses problems ranging from middle school curricula to Olympic-level competitions, designed to assess LLMs' ability to propose innovative solutions after some known solutions have been provided. Our experiments demonstrate that, while LLMs perform well on standard mathematical tasks, their capacity for creative problem-solving varies considerably. Notably, the Gemini-1.5-Pro model outperformed other LLMs in generating novel solutions. This research opens a new frontier in evaluating AI creativity, shedding light on both the strengths and limitations of LLMs in fostering mathematical innovation, and setting the stage for future developments in AI-assisted mathematical discovery.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
