A Guide to Learning Arithmetic Circuits.

An arithmetic circuit is a directed acyclic graph in which the operations aref+;g . In this paper, we exhibit several connections between learning algorithms for arithmetic circuits and other problems. In particular, we show that: Ecient learning algorithms for arithmetic circuit classes imply explicit exponential lower bounds. General circuits and formulas can be learned eciently with membership and equivalence queries i they can be learned eciently 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.