miniF2F: a cross-system benchmark for formal Olympiad-level mathematics
Kunhao Zheng École Polytechnique、Jesse Michael Han OpenAI University of Pittsburgh \ANDStanislas Polu OpenAI
Abstract
We present miniF2F, a dataset of formal Olympiad-level mathematics problems statements intended to provide a unified cross-system benchmark for neural theorem proving. The miniF2F benchmark currently targets Metamath, Lean, Isabelle (partially) and HOL Light (partially) and consists of 488 problem statements drawn from the AIME, AMC, and the International Mathematical Olympiad (IMO), as well as material from high-school and undergraduate mathematics courses. We report baseline results using GPT- $f$ (Polu & Sutskever, 2020), a neural theorem prover based on GPT-3 (Brown et al., 2020) and provide an analysis of its performance. We intend for miniF2F to be a community-driven effort and hope that our benchmark will help spur advances in neural theorem proving.
中文速览
奥林匹克数学竞赛题的形式化证明长期缺乏一个能跨系统比较的统一基准，miniF2F 正是为此而生——它收录了 488 道来自 AIME、AMC、IMO 及高中/大学数学课程的竞赛题，并将这些题目的陈述同时形式化为 Metamath、Lean、Isabelle 等多个定理证明系统可用的格式。研究者用基于 GPT-3 微调的神经定理证明器 GPT-f 在该基准上做了基线测试，结果显示在 Metamath 上 Pass@8 仅约 1.6%，在 Lean 上略好但总体仍偏低，反映出当前神经定理证明方法面对竞赛级数学题时仍有极大提升空间。miniF2F 的意义在于它提供了一个端到端可机器验证、难度跨度广、可跨平台横向比较的开放社区基准，有望推动神经定理证明领域朝着最终攻克 IMO 的长远目标持续演进。
原文 arXiv:2109.00110;中英对照 + 大白话阅读 https://aha.fim.ai/paper/2109.00110v2