TCS+ Talk

Wednesday February 17, 2021 10:00 AM

Fooling Constant-Depth Threshold Circuits

Speaker: William Hoza, University of Texas, Austin
Location: Online Event

Abstract: We present the first non-trivial pseudorandom generator (PRG) for linear threshold (LTF) circuits of arbitrary constant depth and super-linear size. This PRG fools circuits with depth d and n^{1 + delta} wires, where delta = exp(-O(d)), using seed length O(n^{1 - delta}) and with error exp(-n^{delta}). This tightly matches the best known lower bounds for this circuit class. As a consequence of our result, all the known hardness for LTF circuits has now effectively been translated into pseudorandomness. This brings the extensive effort in the last decade to construct PRGs and deterministic circuit-analysis algorithms for this class to the point where any subsequent improvement would yield breakthrough lower bounds.

A key ingredient in our construction is a pseudorandom restriction procedure that has tiny failure probability, but simplifies the function to a non-natural "hybrid computational model" that combines decision trees and LTFs. As part of our proof we also construct an "extremely low-error" PRG for the class of functions computable by an arbitrary function of s linear threshold functions that can handle even the extreme setting of parameters s = n/polylog(n) and epsilon = exp(-n/polylog(n)).

Joint work with Pooya Hatami, Avishay Tal, and Roei Tell.

To watch the talk:

  • Watching the live stream. At the announced start time of the talk (or a minute before), a live video stream will be available on our "next talk" page. Simply connect to the page and enjoy the talk. No webcam or registration is needed. Questions and comments during the talk are welcome (text only, unfortunately); simply post a comment below the live video stream on YouTube.
  • Watching the recorded talk offline. The recorded talk will be made available shortly after the talk ends on our YouTube page. (Please leave a comment if you enjoyed it!)
Series TCS+ Talks

Contact: Bonnie Leung bjleung@caltech.edu