On the Classification Capability of Sign-Constrained Perceptrons

The perceptron (also referred to as McCulloch-Pitts neuron, or linear threshold gate) is commonly used as a simplified model for the discrimination and learning capability of a biological neuron. Criteria that tell us when a perceptron can implement (or learn to implement) all possible dichotomies over a given set of input patterns are wellknown, but only for the idealized case where one assumes that the sign of a synaptic weight can be switched during learning. We present in this article an analysis of the classification capability of the biologically more realistic model of a sign-constrained perceptron, where the signs of synaptic weights remain fixed during learning (which is the case for most types of biological synapses). In particular, the VC-dimension of sign-constrained perceptrons is determined, and a necessary and sufficient criterion is provided that tells us when all 2m dichotomies over a given set of m patterns can be learned by a signconstrained perceptron. We also show...

• Type: Journal
• Year: 2008
• Where: NECO
• Authors: Robert A. Legenstein, Wolfgang Maass
• Keywords: Input Patterns, NECO 2008, Perceptron, Synaptic Weights