Analytical approaches to the neural net architecture design

Artiicial Neural Networks (ANN) have often been used successfully in problems of classiication. Their main drawback is the long training times required particularly for problems of large dimensionality. This is in contrast to the human vision system which is capable of learning from a small number of examples. Another problem with ANNs is the lack of any theoretical guidance concerning the choice of number of nodes, activation functions etc. In this paper we rst formulate the problem of object labelling and classii-cation on rm mathematical foundations, within the framework of probabilistic relaxation and then we map it onto the conventional architecture of a multilayer perceptron. This way we can give deenite interpretation to the weights, response functions and nodes of the system with speciic guidance concerning the choice of the various functions and parameters. Further, we end up with a system which requires very few samples for training, thus emulating the human vision system in that respect.