Humans tame the complexity of mathematical reasoning by developing hierarchies of abstractions. With proper abstractions, solutions to hard problems can be expressed concisely, thus making them more likely to be found. In this paper, we propose Learning Mathematical Abstractions (LEMMA): an algorithm that implements this idea for reinforcement learning agents in mathematical domains. LEMMA augments Expert Iteration with an abstraction step, where solutions found so far are revisited and rewritten in terms of new higher-level actions, which then become available to solve new problems. We evaluate LEMMA on two mathematical reasoning tasks--equation solving and fraction simplification--in a step-by-step fashion. In these two domains, LEMMA improves the ability of an existing agent, both solving more problems and generalizing more effectively to harder problems than those seen during training.
@article{arxiv.2211.08671,
title = {LEMMA: Bootstrapping High-Level Mathematical Reasoning with Learned Symbolic Abstractions},
author = {Zhening Li and Gabriel Poesia and Omar Costilla-Reyes and Noah Goodman and Armando Solar-Lezama},
journal= {arXiv preprint arXiv:2211.08671},
year = {2022}
}
Comments
10 pages, 2 figures; to appear in 2nd MATH-AI Workshop at NeurIPS'22