LEARNING THE REVERSED-WEDGE PROBLEM USING A MULTI-INTERACTING PERCEPTRON WITH CORRELATED WEIGHTS

We consider the task of learning the so-called reversed-wedge problem, using a multi-interacting perceptron with first- and third-order syna pses, where the third-order synaptic couplings are expressed as produc ts of the first-order synapses associated to the neurons involved in t he corresponding multi-interaction. This correlation condition allows the training of the multi-interacting perceptron to be achieved by adj usting the set of first-order weights, in such a way that the learning rates scales with the dimensionality of a simple perceptron. Remarkab ly, if the width of the ''reversed'' inner region (wedge) is smaller t han 2 root 3, the high-temperature approach pre diets a transition fro m a poor generalization regime to a state with good performance, where the generalization error is identical to the results for the problem of a simple perceptron learning a linearly separable rule. The simulat ion results are in excellent agreement with the analytical predictions . (C) 1998 Elsevier Science B.V. All rights reserved.