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Geometrical interpretation of the back-propagation algorithm for the perceptron

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  • Budinich, Marco
  • Milotti, Edoardo

Abstract

It is well known that the gradient descent algorithm works well for the perceptron when the solution to the perceptron problem exists because the cost function has a simple shape — with just one minimum — in the conjugate weight-space. Working in the conjugate space we show that if a perceptron solution does not exist the cost function of a perceptron with d inputs and n patterns has an average O(nd) relative minima (for large n). In this case finding the best solution (the solution with the minimum number of errors) becomes a challenging problem. for any local search algorithm.

Suggested Citation

  • Budinich, Marco & Milotti, Edoardo, 1992. "Geometrical interpretation of the back-propagation algorithm for the perceptron," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 185(1), pages 369-377.
    • Handle: RePEc:eee:phsmap:v:185:y:1992:i:1:p:369-377
    DOI: 10.1016/0378-4371(92)90477-8
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