A Guide to Learning Arithmetic Circuits

An arithmetic circuit is a directed acyclic graph in which the operations are {+,×}. In this paper, we exhibit several connections between learning algorithms for arithmetic circuits and other problems. In particular, we show that: • Efficient learning algorithms for arithmetic circuit classes imply explicit exponential lower bounds. • General circuits and formulas can be learned efficiently with membership and equivalence queries iff they can be learned efficiently with membership queries only. • Low-query learning algorithms for certain classes of circuits imply explicit rigid matrices. • Learning algorithms for multilinear depth-3 and depth-4 circuits must compute square roots.