arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2006.11259cs.LOcs.LG
收藏

从综合定理学习证明

Learning to Prove from Synthetic Theorems

DeepMind(深度思维)

Eser Aygün, Zafarali Ahmed, Ankit Anand, Vlad Firoiu, Xavier Glorot, Laurent Orseau, Doina Precup, Shibl Mourad

摘要:

将机器学习应用于自动化定理证明的一个主要挑战是训练数据的稀缺性,这是训练成功的深度学习模型的关键因素。为了解决这个问题,我们提出了一种方法,该方法依赖于从一组公理生成的合成定理的训练。我们表明,这样的定理可以用来训练一个自动化的证明和证明成功转移到人类产生的定理。我们证明了一个专门训练合成定理的证明器可以解决TPTP中的大部分问题,TPTP是一个用于比较最先进的启发式证明器的基准数据集。我们的方法在大多数公理集上都优于在人类生成的问题上训练的模型,从而显示出使用合成数据完成这项任务的希望。

英文摘要:

A major challenge in applying machine learning to automated theorem proving is the scarcity of training data, which is a key ingredient in training successful deep learning models. To tackle this problem, we propose an approach that relies on training with synthetic theorems, generated from a set of axioms. We show that such theorems can be used to train an automated prover and that the learned prover transfers successfully to human-generated theorems. We demonstrate that a prover trained exclusively on synthetic theorems can solve a substantial fraction of problems in TPTP, a benchmark dataset that is used to compare state-of-the-art heuristic provers. Our approach outperforms a model trained on human-generated problems in most axiom sets, thereby showing the promise of using synthetic data for this task.

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。

↑