LEARNING AND GENERALIZATION IN MULTINEURON INTERACTING FEEDFORWARD NEURAL NETWORKS

We consider learning and generalization in the multi-interacting feed- forward network model recently proposed by H-O Carmesin. With an a pri ori definition of the net architecture, based on symmetries presented by the function to be learnt, we define a generalized Hebb rule, exten d the maximum stability learning algorithm to multi-interactions, and obtain training and generalization curves. For rules where different o rders of synapses are not correlated the results obtained for the simp le perceptron concerning the Hebb rule and through replica calculation s in the space of couplings may be straightforwardly adapted to multi- interactions through a simple renormalization of the total number of i ndependent couplings. Analytical and numerical simulation results are compared and show excellent agreement.