Mellon Fellowship Talks

Speaker: Jesse Han

Title: Proof Artifact Co-training for Theorem Proving with Language Models

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 (Proof Artifact Co-Training), 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%.

Speaker: Derek Orr

Title: Oscillations with noise-driven excitable cells

Abstract: Our goal is to understand how excitable cells generate macroscopic oscillations within a network. We will focus on all-to-all coupled excitable cells. However, these will not create oscillations alone so we added noise to these cells so the cells can oscillate randomly. We performed mean-field theory (MFT) methods on this system and chose Gaussian white noise as well as different heterogeneous noise distributions. We found that macroscopic oscillations can occur as long as one has the right set of coupling strengths, the right noise distribution, and/or the right coupling function.