“HTPS: HyperTree Proof Search for Neural Theorem Proving”, Guillaume Lample, Marie-Anne Lachaux, Thibaut Lavril, Xavier Martinet, Amaury Hayat, Gabriel Ebner, Aurélien Rodriguez, Timothée Lacroix2022-05-23 (Transformer, math, AlphaGo)⁠:

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 3 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, substantially 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 31% → 42% proving accuracy.