Learning Interestingness in Automated Mathematical Theory Formation

George Tsoukalas, Rahul Saha, Amitayush Thakur, Sabrina Reguyal, Swarat Chaudhuri

Keywords: automated mathematics, AI for math, interestingness, reinforcement learning, scientific discovery, theory discovery

TL;DR: We design an RL environment for automated mathematical theory formation and present an evolutionary synthesis methodology for interestingness measures to guide exploration in it

Abstract: We take two key steps in automating the open-ended discovery of new mathematical theories, a grand challenge in artificial intelligence. First, we introduce Fermat, a reinforcement learning (RL) environment that models concept discovery and theorem-proving using a set of symbolic actions, opening up a range of RL problems relevant to theory discovery. Second, we explore a specific problem through Fermat: automatically scoring the interestingness of mathematical objects. We investigate evolutionary algorithms for synthesizing nontrivial interestingness measures. In particular, we introduce an LLM-based evolutionary algorithm that features function abstraction, leading to notable improvements in discovering elementary number theory and finite fields over hard-coded baselines. We open-source the \fermat environment at github.com/trishullab/Fermat.

Primary Area: Machine learning for sciences (e.g. climate, health, life sciences, physics, social sciences)

Flagged For Ethics Review: true

Submission Number: 26397