Multilayer neural networks and polyhedral dichotomies

Authors:
Claire Kenyon;Hèléne Paugam-Moisy
Affiliations:
LRI, CNRS URA 410, Université Paris‐Sud, F‐91405 Orsay Cedex, France E-mail: Claire.Kenyon@lri.fr;LIP, CNRS URA 1398, ENS Lyon, 46 allèe d'Italie, F-69364 Lyon Cedex 07, France E-mail: Helene.Paugam-Moisy@ens-lyon.fr
Venue:
Annals of Mathematics and Artificial Intelligence
Year:
1998

Citing 8
Cited 0

On the capabilities of multilayer perceptrons

Journal of Complexity - Special Issue on Neural Computation
Multilayer feedforward networks are universal approximators

Neural Networks
On the approximate realization of continuous mappings by neural networks

Neural Networks
Approximation theory and feedforward networks

Neural Networks
Original Contribution: Separability of internal representations in multilayer perceptrons with application to learning

Neural Networks
Exact classification with two-layer neural nets

Journal of Computer and System Sciences
Exact classification with two-layer neural nets in n dimensions

Discrete Applied Mathematics
Complexity Issues in Neural Network Computations

LATIN '92 Proceedings of the 1st Latin American Symposium on Theoretical Informatics

Quantified Score

Hi-index	0.00

Visualization

Abstract

We study the number of hidden layers required by a multilayer neural network with threshold units to compute a dichotomy from \mathbb{R}^d to \{ 0,1 \}, defined by a finite set of hyperplanes. We show that this question is far more intricate than computing Boolean functions, although this well‐known problem is underlying our research. We present advanced results on the characterization of dichotomies, from \mathbb{R}^2 to \{ 0,1 \}, which require two hidden layers to be exactly realized.