APOLLO: Automated LLM and Lean Collaboration for Advanced Formal Reasoning

在这里插入图片描述

一、文章主要内容总结

本文提出了APOLLO系统,这是一种将大型语言模型(LLM)与Lean形式验证系统相结合的自动化定理证明框架,旨在解决传统方法中LLM生成证明效率低、错误率高的问题。APOLLO通过模块化流程实现了对LLM生成证明的自动化修复,具体包括语法修正(Syntax Refiner)、错误块隔离(Sorrifier)、自动求解(Auto Solver)和递归修复(Recursive repair)等步骤。通过Lean编译器的实时反馈,APOLLO能够定位证明中的语法错误和逻辑漏洞,将复杂定理分解为子引理,并利用LLM和自动求解器逐步修复,最终组合成完整有效的证明。

在miniF2F基准测试中,APOLLO显著提升了多种模型的性能:

  • 对于7B参数模型,APOLLO将Kimina-Prover-Preview-Distill-7B的准确率提升至75.0%,刷新了当前最优结果(SOTA),同时将采样预算从数千次降低至数百次。
  • 通用模型(如o3-mini、o4-mini)的准确率从3-7%提升至40%以上,证明了框架对非专用模型的有效性。
  • Goedel-Prover-SFT的准确率从64.7%提升至65.6%,采样成本降低了两个数量级。

二、文章创新点

「文智助手」全场景办公AI助理AI+OPC全流程实践方案(大赛作品) 阅读详情

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nn.output = 'softmax'; % use softmax outputopts.numepochs = 5; % Number of full sweeps through dataopts.batchsize = 1000; % Take a mean gradient step over this many samplesopts.plot = 1; % enable plottingnn = nntrain(nn, tx, ty, opts, vx, vy); % nntrain takes validation set as last two arguments (optionally)[er, bad] = nntest(nn, test_x, test_y);assert(er < 0.1, 'Too big error');```[![Bitdeli Badge](https://d2weczhvl823v0.cloudfront.net/rasmusbergpalm/deeplearntoolbox/trend.png)](https://bitdeli.com/free "Bitdeli Badge")

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