Year: 2021
Type: preprint
Abstract: We give a pseudorandom generator that fools degree-$d$ polynomial threshold functions over $n$-dimensional Gaussian space with seed length $\mathrm{poly}(d)\cdot \log n$. All previous generators had a seed length with at least a $2^d$ dependence on $d$. The key new ingredient is a Local Hyperconcentration Theorem, which shows that every degree-$d$ Gaussian polynomial is hyperconcentrated almost everywhere at scale $d^{-O(1)}$.
Source: arXiv (Cornell University)
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
Awards: AF: Medium: Collaborative Research: Circuit Lower Bounds via Projections, AF: Small: The Complexity of Random CSPs, BIGDATA: F: Big Data Analysis via Non-Standard Property Testing, AF: Small: Collaborative Research: Boolean Function Analysis Meets Stochastic Design, AF: Medium: Collaborative Research: Circuit Lower Bounds via Projections
OpenAlex ID: W3136974637