<#251#> SCCS report: 774<#251#>

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<#256#> Some Issues of Reducibility and Equivalence in Feedforward Neural Networks <#256#>

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Saleh Elmohamed
Northeast Parallel Architectures Center
Syracuse University,
Syracuse, NY 13244-4100 , USA .
saleh@npac.syr.edu
<#262#>ABSTRACT<#262#> We show how sigmoidal (#tex2html_wrap_inline2543#) feedforward net reducibility and equivalence conditions proposed by Sussmann and later by Sontag can be adapted to feedforward neural structures using piecewise rational activation functions. In addition, the uniqueness results demonstrated for the #tex2html_wrap_inline2545# nets are shown to be applicable in part to networks of piecewise rationals, but not to piecewise linear (<#263#> clipping<#263#>) networks. <#264#> Key words : neural net, piecewise linear function, piecewise linear network, epoch, tanh function, squashing function, sigmoid function, clip function, linear affine function, piecewise rational function, reducibility, uniqueness, independence property.<#264#> %