POLYNOMIAL SOFTMAX FUNCTIONS FOR PATTERN CLASSIFICATION
A. Tuerk and S.J. Young
This report discusses softmax functions with polynomial and more general exponents and investigates the problem of optimising their parameters with regard to the cross-entropy error function. It is shown that, in this situation, the error surface is always convex and that in many cases there exists exactly one optimal set of parameters. In addition to these theoretical results, the practical estimation of the optimal parameter set is implemented using the Newton algorithm with line search and backtracking. In a number of test cases this algorithm is shown to converge reliably to the correct results.
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