Analog neural networks with local competition. I. Dynamics and stability

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Abstract
We introduce a neural network architecture in which analog-valued neurons compete through a constraint on a sum of neuron outputs within localized clusters. Local competition is useful in feature-extraction and pattern-classification applications. We show that with continuous-time updating, these networks converge only to fixed points, while with discrete-time, parallel updating, they converge to either fixed points or period-two limit cycles. We derive a stability criterion guaranteeing that discrete-time networks converge only to fixed points when their cluster gains, which are related to the slopes of the neuron input-output transfer functions, are sufficiently small. Numerical tests are presented showing that image-processing networks incorporating local competition operate reliably and in agreement with the stability criterion. We also describe a simple competitive analog electronic circuit that demonstrates that these networks are easily implementable.