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Learning the reversed-wedge problem using a multi-interacting perceptron with correlated weights

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  • Botelho, E

Abstract

We consider the task of learning the so-called reversed-wedge problem, using a multi-interacting perceptron with first- and third-order synap-ses, where the third-order synaptic couplings are expressed as products of the first-order synapses associated to the neurons involved in the corresponding multi-interaction. This correlation condition allows the training of the multi-interacting perceptron to be achieved by adjusting the set of first-order weights, in such a way that the learning rates scales with the dimensionality of a simple perceptron. Remarkably, if the width of the “reversed” inner region (wedge) is smaller than 23, the high-temperature approach predicts a transition from 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 simulation results are in excellent agreement with the analytical predictions.

Suggested Citation

  • Botelho, E, 1998. "Learning the reversed-wedge problem using a multi-interacting perceptron with correlated weights," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 253(1), pages 323-332.
    • Handle: RePEc:eee:phsmap:v:253:y:1998:i:1:p:323-332
    DOI: 10.1016/S0378-4371(97)00657-2
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    1. de Almeida, R.M.C. & Botelho, E., 1997. "A multi-interacting perceptron model with continuous outputs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 242(1), pages 27-37.
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