Proof Artifact Co-Training for Theorem Proving with Language Models

Labeled data for imitation learning of theorem proving in large libraries of formalized mathematics is scarce, as such libraries require years of concentrated effort by human specialists to be built. This is particularly challenging when applying large Transformer language models to tactic prediction, because the scaling of performance with respect to model size is quickly disrupted in the data-scarce, easily-overfitted regime. We propose PACT (Proof Artifact Co-Training), a general methodology for extracting abundant self-supervised data from kernel-level proof terms for joint training alongside the usual tactic prediction objective. We apply this methodology to Lean, a proof assistant host to some of the most sophisticated formalized mathematics to date. We instrument Lean with a neural theorem prover driven by a Transformer language model and show that PACT improves theorem proving success rate on a held-out suite of test theorems from 32% to 48%. * Work performed while Jason Rute was at CIBO Technologies. † Work performed while Yuhuai Wu was at University of Toronto. ‡ Work performed while Edward W. Ayers was at University of Cambridge.