Conclusion

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. %