On the complexity of recognizing regions computable by two-layered perceptrons

Authors:
Eddy Mayoraz
Affiliations:
IDIAP – Dalle Molle Institute for Perceptive Artificial Intelligence, P.O. Box 592, CH‐1920 Martigny, Valais, Switzerland E-mail: Eddy.Mayoraz@idiap.ch
Venue:
Annals of Mathematics and Artificial Intelligence
Year:
1998

Citing 4
Cited 1

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Abstract

This work is concerned with the computational complexity of the recognition of \mathcal{LP}_2, the class of regions of the Euclidean space that can be classified exactly by a two‐layered perceptron. Some subclasses of \mathcal{LP}_2 of particular interest are also studied, such as the class of iterated differences of polyhedra, or the class of regions V that can be classified by a two‐layered perceptron with as hidden units only the ones associated to (d-1)‐dimensional facets of V. In this paper, we show that the recognition problem for \mathcal{LP}_2 as well as most other subclasses considered here is NP‐hard in the most general case. We then identify special cases that admit polynomial time algorithms.