A Small PRG for Polynomial Threshold Functions of Gaussians

We develop a pseudo-random generator to fool degree-$d$ polynomial threshold functions with respect to the Gaussian distribution. For $c>0$ any constant, we construct a pseudo-random generator that fools such functions to within $ϵ$ and has seed length $\log (n)2^{O(d)}{ϵ}^{-4-c}$.