A Pseudorandom Generator for Polynomial Threshold Functions of Gaussian with Subpolynomial Seed Length

We develop and analyze a new family of pseudorandom generators for polynomial threshold functions with respect to the Gaussian distribution. In particular, for any fixed degree we develop a generator whose seed length is subpolynomial in the error parameter, epsilon. We get particularly nice results for degree 1 and degree 2 threshold functions, in which cases our seed length is O(log(n) + log^{3/2}(1/epsilon)) and exp(O~(log^{2/3}(1/epsilon))), respectively.