On the computational power of winner-take-all

This article initiates a rigorous theoretical analysis of the computational power of circuits that employ modules for computing winner-take-all. Computational models that involve competitive stages have so far been neglected in computational complexity theory, although they are widely used in comput...

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Bibliographic Details
Published in:Neural computation Vol. 12; no. 11; p. 2519
Main Author: Maass, W
Format: Journal Article
Language:English
Published: United States 01.11.2000
Subjects:
Animals
Brain - physiology
Models, Neurological
Models, Theoretical
Neural Networks (Computer)
Neuronal Plasticity
ISSN:0899-7667
Online Access:Get more information
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Summary:This article initiates a rigorous theoretical analysis of the computational power of circuits that employ modules for computing winner-take-all. Computational models that involve competitive stages have so far been neglected in computational complexity theory, although they are widely used in computational brain models, artificial neural networks, and analog VLSI. Our theoretical analysis shows that winner-take-all is a surprisingly powerful computational module in comparison with threshold gates (also referred to as McCulloch-Pitts neurons) and sigmoidal gates. We prove an optimal quadratic lower bound for computing winner-take-all in any feedforward circuit consisting of threshold gates. In addition we show that arbitrary continuous functions can be approximated by circuits employing a single soft winner-take-all gate as their only nonlinear operation. Our theoretical analysis also provides answers to two basic questions raised by neurophysiologists in view of the well-known asymmetry between excitatory and inhibitory connections in cortical circuits: how much computational power of neural networks is lost if only positive weights are employed in weighted sums and how much adaptive capability is lost if only the positive weights are subject to plasticity.
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ISSN:0899-7667
DOI:10.1162/089976600300014827