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Jesse Michael Han

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

3 papers

1 author row

ICLR Conference 2023 Conference Paper

Formal Mathematics Statement Curriculum Learning

Stanislas Polu
Jesse Michael Han
Kunhao Zheng
Mantas Baksys
Igor Babuschkin
Ilya Sutskever

We explore the use of expert iteration in the context of language modeling applied to formal mathematics. We show that at same compute budget, expert iteration, by which we mean proof search interleaved with learning, dramatically outperforms proof search only. We also observe that when applied to a collection of formal statements of sufficiently varied difficulty, expert iteration is capable of finding and solving a curriculum of increasingly difficult problems, without the need for associated ground-truth proofs. Finally, by applying this expert iteration to a manually curated set of problem statements, we surpass previous state-of-the-art on the miniF2F benchmark, automatically solving multiple challenging problems drawn from high school olympiads.

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ICLR Conference 2022 Conference Paper

miniF2F: a cross-system benchmark for formal Olympiad-level mathematics

Kunhao Zheng
Jesse Michael Han
Stanislas Polu

We present $\textsf{miniF2F}$, a dataset of formal Olympiad-level mathematics problems statements intended to provide a unified cross-system benchmark for neural theorem proving. The $\textsf{miniF2F}$ benchmark currently targets Metamath, Lean, Isabelle (partially) and HOL Light (partially) and consists of 488 problem statements drawn from the AIME, AMC, and the International Mathematical Olympiad (IMO), as well as material from high-school and undergraduate mathematics courses. We report baseline results using GPT-f, a neural theorem prover based on GPT-3 and provide an analysis of its performance. We intend for $\textsf{miniF2F}$ to be a community-driven effort and hope that our benchmark will help spur advances in neural theorem proving.

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ICLR Conference 2022 Conference Paper

Proof Artifact Co-Training for Theorem Proving with Language Models

Jesse Michael Han
Jason Rute
Yuhuai Wu
Edward W. Ayers
Stanislas Polu

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,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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