A MODEL FOR A MULTICLASS CLASSIFICATION MACHINE

We consider the properties of multi-class neural networks, where each neuron can be in several different states. The motivations for considering such systems are manifold. In image processing for example, the different states correspond to the different grey tone levels. Another multi-class classification task implemented on a feed-forward network is the analysis of DNA sequences or the prediction of the secondary structure of proteins from the sequence of amino acids. To investigate the behaviour of such systems, one specific dynamical rule - the "winner-take-all" rule - is studied. Gauge invariances of the model are analysed. For a multi-class perceptron with N Q-state input neurons and one Q'-state output neuron, the maximal number of patterns that can be stored in the large N limit is found to be proportional to N(Q - 1) f(Q'), where f(Q') is a slowly increasing and bounded function of order 1.