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Learning and generalization in multineuron interacting feed-forward neural networks

We consider learning and generalization in the multi-interacting feed-forward network model recently proposed by H O Carmesin (1994). With an a priori definition of the net architecture, based on symmetries presented by the function to be learnt, we define a generalized Hebb rule, extend the maximum stability learning algorithm to multi-interactions, and obtain training and generalization curves. For rules where different orders of synapses are not correlated the results obtained for the simple perceptron concerning the Hebb rule and through replica calculations in the space of couplings may be straightforwardly adapted to multi-interactions through a simple renormalization of the total number of independent couplings. Analytical and numerical simulation results are compared and show excellent agreement.