Geometrical interpretation of the back-propagation algorithm for the perceptron

Marco Budinich and Edoardo Milotti

Physica A: Statistical Mechanics and its Applications, 1992, vol. 185, issue 1, 369-377

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.

Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:185:y:1992:i:1:p:369-377

DOI: 10.1016/0378-4371(92)90477-8

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