1 research outputs found
Fooling Gaussian PTFs via Local Hyperconcentration
We give a pseudorandom generator that fools degree- polynomial threshold
functions over -dimensional Gaussian space with seed length
. All previous generators had a seed length with
at least a dependence on .
The key new ingredient is a Local Hyperconcentration Theorem, which shows
that every degree- Gaussian polynomial is hyperconcentrated almost
everywhere at scale