Proof Artifact Co-training for Theorem Proving with Language Models

• URL: http://arxiv.org/abs/2102.06203v1
• Date: Thu, 11 Feb 2021 18:59:24 GMT
• Title: Proof Artifact Co-training for Theorem Proving with Language Models
• Authors: Jesse Michael Han, Jason Rute, Yuhuai Wu, Edward W. Ayers, Stanislas Polu
• Abstract summary: PACT (bf Proof bf Artifact bf Co-bf Training) is a general methodology for extracting self-supervised data from kernel-level proof terms for co-training. 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%.
• Score: 4.934817254755007
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: 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 ({\bf P}roof {\bf A}rtifact {\bf C}o-{\bf T}raining), a general methodology for extracting abundant self-supervised data from kernel-level proof terms for co-training alongside the usual tactic prediction objective. We apply this methodology to Lean, an interactive proof assistant which hosts 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\%.

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