Generative Language Modeling for Automated Theorem Proving
This addresses the bottleneck of generating novel terms in automated theorem proving for formal mathematics communities, representing a novel method rather than an incremental improvement.
The authors tackled the problem of automated theorem proving by using transformer-based language models to generate original mathematical terms, resulting in GPT-f, which produced new short proofs accepted into the Metamath library, marking the first deep-learning system to contribute adopted proofs in formal mathematics.
We explore the application of transformer-based language models to automated theorem proving. This work is motivated by the possibility that a major limitation of automated theorem provers compared to humans -- the generation of original mathematical terms -- might be addressable via generation from language models. We present an automated prover and proof assistant, GPT-f, for the Metamath formalization language, and analyze its performance. GPT-f found new short proofs that were accepted into the main Metamath library, which is to our knowledge, the first time a deep-learning based system has contributed proofs that were adopted by a formal mathematics community.