Proving Theorems using Incremental Learning and Hindsight Experience Replay

Eser Aygün, Laurent Orseau, Ankit Anand, Xavier Glorot, Vlad Firoiu, Lei M Zhang, Doina Precup, Shibl Mourad

Keywords: theorem proving, incremental learning, hindsight experience replay, transformers

Abstract: Traditional automated theorem provers for first-order logic depend on speed-optimized search and many handcrafted heuristics that are designed to work best over a wide range of domains. Machine learning approaches in literature either depend on these traditional provers to bootstrap themselves or fall short on reaching comparable performance. In this paper, we propose a general incremental learning algorithm for training domain-specific provers for first-order logic without equality, based only on a basic given-clause algorithm, but using a learned clause-scoring function. Clauses are represented as graphs and presented to transformer networks with spectral features. To address the sparsity and the initial lack of training data as well as the lack of a natural curriculum, we adapt hindsight experience replay to theorem proving, so as to be able to learn even when no proof can be found. We show that provers trained this way can match and sometimes surpass state-of-the-art traditional provers on the TPTP dataset in terms of both quantity and quality of the proofs.

One-sentence Summary: We match the performance of a state-of-the-art automated first-order theorem proving system by combining a rudimentary proof search algorithm with incremental learning and hindsight experience replay.