1. E.D. Sontag. Critical points for least-squares problems involving certain analytic functions, with applications to sigmoidal nets. Adv. Comput. Math., 5(2-3):245-268, 1996. [PDF] Keyword(s): subanalytic sets, semianalytic sets, analytic geometry, critical points, approximation theory, neural networks. Abstract:

   This paper deals with nonlinear least-squares problems involving the fitting to data of parameterized analytic functions. For generic regression data, a general result establishes the countability, and under stronger assumptions finiteness, of the set of functions giving rise to critical points of the quadratic loss function. In the special case of what are usually called "single-hidden layer neural networks", which are built upon the standard sigmoidal activation tanh(x) or equivalently 1/(1+exp(-x)), a rough upper bound for this cardinality is provided as well.

1. E.D. Sontag. Critical points for neural net least-squares problems. In Proc. 1995 IEEE Internat. Conf. Neural Networks, IEEE Publications, 1995, pages 2949-2954, 1995. Keyword(s): neural networks.

This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders.

This document was translated from BibT_EX by bibtex2html