Achieving continuous improvements in expert iteration for neural theorem proving

Develop training procedures for neural theorem provers that achieve continuous performance improvements under expert iteration by effectively leveraging the unlimited feedback provided by formal verifiers, rather than experiencing diminishing returns after a few iterations.

Background

Expert iteration alternates between solving new theorems and fine-tuning on the resulting proofs, but current gains tend to plateau after several iterations.

The authors identify the unmet goal of sustained improvement using formal environments’ potentially unlimited feedback, framing a key algorithmic open problem for future provers.