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Learning to Discover Efficient Mathematical Identities
Wojciech Zaremba · Karol Kurach · Rob Fergus

Tue Dec 09 02:40 PM -- 03:00 PM (PST) @ Level 2, room 210

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 grammar of math operators, we build trees that combine them in different ways, looking for compositions that are analytically equivalent to a target expression but of lower computational complexity. However, as the space of 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.

Author Information

Wojciech Zaremba (OpenAI)
Karol Kurach (Google Brain)
Rob Fergus (DeepMind / NYU)

Rob Fergus is an Associate Professor of Computer Science at the Courant Institute of Mathematical Sciences, New York University. He received a Masters in Electrical Engineering with Prof. Pietro Perona at Caltech, before completing a PhD with Prof. Andrew Zisserman at the University of Oxford in 2005. Before coming to NYU, he spent two years as a post-doc in the Computer Science and Artificial Intelligence Lab (CSAIL) at MIT, working with Prof. William Freeman. He has received several awards including a CVPR best paper prize, a Sloan Fellowship & NSF Career award and the IEEE Longuet-Higgins prize.

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