R. O'Donnell and R. Servedio and L.-Y. Tan.

In

We give a pseudorandom generator that fools degree-*d* polynomial threshold functions over *n*-dimensional Gaussian space with seed length
*d ^{O(log d)} log n*. All previous generators had a seed length with at least a

The key new ingredient is our *Local Hyperconcentration Theorem,* which shows that every degree-*d* Gaussian polynomial is hyperconcentrated almost everywhere at scale *d ^{-O(log d)}*.