$k$-Independent Gaussians Fool Polynomial Threshold Functions

TL;DR

This paper demonstrates that a specific level of independence in Gaussian families can effectively fool polynomial threshold functions of degree d, with implications for pseudorandomness and complexity theory.

Contribution

It establishes that O_d(ε^{-4d 7^d})-independent Gaussian families can ε-fool degree-d polynomial threshold functions, advancing understanding of pseudorandomness in high-dimensional spaces.

Findings

O_d(ε^{-4d 7^d})-independent Gaussians ε-fool degree-d PTFs

Provides bounds on independence needed for fooling polynomial threshold functions

Enhances techniques for pseudorandomness in high-dimensional probability

Abstract

We show that any $O_d(\epsilon^{-4d 7^d})$-independent family of Gaussians $\epsilon$-fools any degree-$d$ polynomial threshold function.