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.