We present a randomized polynomial time algorithm to determine if a multivariate polynomial is zero using <italic>O(\log mnÎ´)</italic> random bits where <italic>n</italic> is the number of variables,â€¦ (More)

2006 47th Annual IEEE Symposium on Foundations ofâ€¦

2006

We give the first representation-independent hardness results for PAC learning intersections of halfspaces, a central concept class in computational learning theory. Our hardness results are derivedâ€¦ (More)

We give a query algorithm for agnostically learning decision trees with respect to the uniform distribution on inputs. Given black-box access to an *arbitrary* binary function f on the n-dimensionalâ€¦ (More)

This paper connects two fundamental ideas from theoretical computer science: hard-core set construction, a type of hardness amplification from computational complexity, and boosting, a technique fromâ€¦ (More)

We consider the complexity of properly learning concept classes, i.e. when the learner must output a hypothesis of the same form as the unknown concept. We present the following upper and lowerâ€¦ (More)

We give the first dimension-efficient algorithms for learning Rectified Linear Units (ReLUs), which are functions of the form x 7â†’ max(0, w Â· x) with w âˆˆ Snâˆ’1. Our algorithm works in the challengingâ€¦ (More)