Jacobian Neural Network Learning Algorithms

Starting from an analytic description of a multilayer network, as a function of its weights, we first define a learning algorithm which both determines the network architecture and learns all the examples with any given precision. Second, we define a regularization technique for improving the generalization ability of the network. In case of several output units, a modular approach is proposed for reducing the number of weights. We analyse the properties of the algorithm and prove that the network can be learned in polynomial time. The complexity of the task of learning neural networks is discussed in conclusion.