Learning to Discover Efficient Mathematical Identities
This work addresses the challenge of automating mathematical identity discovery for symbolic computation, representing an incremental advance in applying machine learning to mathematical reasoning.
The paper tackles the problem of discovering efficient mathematical identities by introducing an attribute grammar framework and two novel learning approaches (n-gram model and recursive neural-network) to guide tree search, enabling the derivation of complex identities beyond brute-force or human capabilities.
In this paper we explore how machine learning techniques can be applied to the discovery of efficient mathematical identities. We introduce an attribute grammar framework for representing symbolic expressions. Given a set of grammar rules we build trees that combine different rules, looking for branches which yield compositions that are analytically equivalent to a target expression, but of lower computational complexity. However, as the size of the trees grows exponentially with the complexity of the target expression, brute force search is impractical for all but the simplest of expressions. Consequently, we introduce two novel learning approaches that are able to learn from simpler expressions to guide the tree search. The first of these is a simple n-gram model, the other being a recursive neural-network. We show how these approaches enable us to derive complex identities, beyond reach of brute-force search, or human derivation.