Theory of Computing Seminar

Friday January 8, 2016 12:00 PM

Super-Linear Gate and Super-Quadratic Wire Lower Bounds for Depth-Two and Depth-Three Threshold Circuits

Speaker: Ryan Williams, Stanford
Location: Annenberg 107

Abstract:

Low-depth threshold circuits provide a clean way to model low-depth neural networks. We prove the first super-linear gate lower bounds and the first super-quadratic wire lower bounds for depth-two linear threshold circuits with arbitrary weights, and depth-three majority circuits computing an explicit function. The key is a new random restriction lemma for linear threshold functions. Our main analytical tool is the Littlewood-Offord Lemma from additive combinatorics. 
 
Joint work with Daniel Kane (UCSD). Paper available at http://arxiv.org/abs/1511.07860
 

 

Series Theory of Computing Seminar Series

Contact: Thomas Vidick vidick@cms.caltech.edu