HyperTree Proof Search for Neural Theorem Proving
Guillaume Lample, Timothee Lacroix, Marie-anne Lachaux, Aurelien Rodriguez, Amaury Hayat, Thibaut Lavril, Gabriel Ebner, Xavier Martinet
Abstract
We propose an online training procedure for a transformer-based automated theorem prover. Our approach leverages a new search algorithm, HyperTree Proof Search (HTPS), that learns from previous proof searches through online training, allowing it to generalize to domains far from the training distribution. We report detailed ablations of our pipeline’s main components by studying performance on three environments of increasing complexity. In particular, we show that with HTPS alone, a model trained on annotated proofs manages to prove 65.4% of a held-out set of Metamath theorems, significantly outperforming the previous state of the art of 56.5% by GPT-f. Online training on these unproved theorems increases accuracy to 82.6%. With a similar computational budget, we improve the state of the art on the Lean-based miniF2F-curriculum dataset from 31% to 42% proving accuracy.
BibTeX
@inproceedings{
lample2022hypertree,
title={HyperTree Proof Search for Neural Theorem Proving},
author={Guillaume Lample and Timothee Lacroix and Marie-anne Lachaux and Aurelien Rodriguez and Amaury Hayat and Thibaut Lavril and Gabriel Ebner and Xavier Martinet},
booktitle={Advances in Neural Information Processing Systems},
editor={Alice H. Oh and Alekh Agarwal and Danielle Belgrave and Kyunghyun Cho},
year={2022},
url={https://openreview.net/forum?id=J4pX8Q8cxHH}
}