Perceptrons: expanded edition
Surveys in combinatorics, 1993
Circuit complexity and neural networks
Circuit complexity and neural networks
On the Size of Weights for Threshold Gates
SIAM Journal on Discrete Mathematics
Perceptrons, PP, and the polynomial hierarchy
Computational Complexity - Special issue on circuit complexity
Computing Boolean functions by polynomials and threshold circuits
Computational Complexity
On Small Depth Threshold Circuits
SWAT '92 Proceedings of the Third Scandinavian Workshop on Algorithm Theory
On Small Depth Threshold Circuits
SWAT '92 Proceedings of the Third Scandinavian Workshop on Algorithm Theory
Journal of Computer and System Sciences - STOC 2001
On Computation and Communication with Small Bias
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Problems of Information Transmission
Weights of exact threshold functions
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
| Hi-index | 0.00 |
An integer polynomial p of n variables is called a threshold gate for the Boolean function f of n variables if for all x∈{0, 1}nf(x)=1 if and only if p(x)≥0. The weight of a threshold gate is the sum of its absolute values. In this paper we study how large weight might be needed if we fix some function and some threshold degree. We prove $2^{\Omega(2^{2n/5})}$ lower bound on this value. The best previous bound was $2^{\Omega(2^{n/8})}$ [12]. In addition we present substantially simpler proof of the weaker $2^{\Omega(2^{n/4})}$ lower bound. This proof is conceptually similar to other proofs of the bounds on weights of nonlinear threshold gates, but avoids a lot of technical details arising in other proofs. We hope that this proof will help to show the ideas behind the construction used to prove these lower bounds.