By Topic

A Regularity Lemma, and Low-Weight Approximators, for Low-Degree Polynomial Threshold Functions

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

4 Author(s)
Diakonikolas, I. ; Dept. of Comput. Sci., Columbia Univ., New York, NY, USA ; Servedio, R.A. ; Li-Yang Tan ; Wan, A.

We give a "regularity lemma" for degree-d polynomial threshold functions (PTFs) over the Boolean cube {-1,1}n. Roughly speaking, this result shows that every degree-d PTF can be decomposed into a constant number of subfunctions such that almost all of the subfunctions are close to being regular PTFs. Here a "regular" PTF is a PTF sign(p(x)) where the influence of each variable on the polynomial p(x) is a small fraction of the total influence of p. As an application of this regularity lemma, we prove that for any constants d ≥ 1, ϵ > 0, every degree-d PTF over n variables can be approximated to accuracy eps by a constant degree PTF that has integer weights of total magnitude O(nd). This weight bound is shown to be optimal up to logarithmic factors.

Published in:

Computational Complexity (CCC), 2010 IEEE 25th Annual Conference on

Date of Conference:

9-12 June 2010