A multi-interacting perceptron model with continuous outputs

We consider learning and generalization of real functions by a multi-interacting feed-forward network model with continuous outputs with invertible transfer functions. The expansion in different multi-interacting orders provides a classification for the functions to be learnt and suggests the learning rules, that reduce to the Hebb-learning rule only for the second order, linear perceptron. The over-sophistication problem is straightforwardly overcome by a natural cutoff in the multi-interacting synapses: the student is able to learn the architecture of the target rule, that is, the simpler a rule is the faster the multi-interacting perception may learn. Simulation results are in excellent agreement with analytical calculations.