HyperTree Proof Search for Neural Theorem Proving

TL;DR

This paper introduces HyperTree Proof Search (HTPS), a novel search algorithm for transformer-based theorem proving that, combined with online training, significantly improves proof accuracy across multiple formal mathematics datasets.

Contribution

The paper presents HTPS, a new search algorithm inspired by AlphaZero, and demonstrates its effectiveness with online training in improving theorem proving accuracy.

Findings

Proves 65.4% of Metamath theorems with HTPS alone.

Online training increases accuracy to 82.6%.

Improves miniF2F-curriculum proof accuracy from 31% to 42%.

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), inspired by the recent success of AlphaZero. Our model 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.