We have looked at the issues of reducibility and uniqueness,
pertaining to feedforward neural nets, introduced by Hector Sussmann
to analyze nets composed of #tex2html_wrap_inline3253# units. In the course of this
analysis, two types of piecewise rational functions and one type of
piecewise linear activation have been examined to determine whether
they satisfy the above two issues.
Our results show that neither reducibility nor uniqueness holds when
the functions involved are piecewise linear (the <#758#> clip<#758#> type
functions), but they do hold when piecewise rational activations are
used.
We are very grateful to Professor Ernie Sibert, for his useful
comments and suggestions while writing this report. Also, would like
to thank Paul Coddington for his comments and Geoffrey Fox for his
support and encouragement.
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