Year: 2023
Type: article
Abstract: In this dissertation we present several contributions to the nascent field of neural theorem proving, deep learning-driven automated theorem proving over large libraries of formalized mathematics. We work primarily with the Lean theorem prover along with its standard mathematical library, mathlib. We focus on addressing the issue of data scarcity for training autoregressive language models to perform high-level reasoning steps at the same level of abstraction as humans. Labeled data for imitation learning of human proof steps is extremely scarce as formal mathematics libraries require years of concentrated effort by human specialists to be built. We show that this paucity of data can be addressed by (1) extracting data from mathlib's low-level proof artifacts, (2) synthesizing those low-level proof artifacts from a language model, and (3) creating new training data from autonomous proof attempts in an expert iteration loop. We demonstrate an application of these kinds of techniques to achieve state-of-the-art performance on solving formalized Olympiad-level mathematics problems.
Author: Han, Jesse Michael
Institution: University of Pittsburgh
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7027666545