We describe a new approach for understanding the difficulty of designing efficient learning algorithms. We prove that the existence of an efficient learning algorithm for a circui...
In 2002 Jackson et al. [JKS02] asked whether AC0 circuits augmented with a threshold gate at the output can be efficiently learned from uniform random examples. We answer this ques...
A real multivariate polynomial p(x1, . . . , xn) is said to sign-represent a Boolean function f : {0, 1}n {-1, 1} if the sign of p(x) equals f(x) for all inputs x {0, 1}n. We gi...
Much work has been done on learning various classes of "simple" monotone functions under the uniform distribution. In this paper we give the first unconditional lower bo...
Given a general graph G, a fundamental problem is to find a spanning tree H that best approximates G by some measure. Often this measure is some combination of the congestion and...