Huang S C, Huang Y F
Dept. of Electr. Eng., Notre Dame Univ., IN.
IEEE Trans Neural Netw. 1991;2(1):47-55. doi: 10.1109/72.80290.
Fundamental issues concerning the capability of multilayer perceptrons with one hidden layer are investigated. The studies are focused on realizations of functions which map from a finite subset of E(n) into E(d). Real-valued and binary-valued functions are considered. In particular, a least upper bound is derived for the number of hidden neurons needed to realize an arbitrary function which maps from a finite subset of E(n ) into E(d). A nontrivial lower bound is also obtained for realizations of injective functions. This result can be applied in studies of pattern recognition and database retrieval. An upper bound is given for realizing binary-valued functions that are related to pattern-classification problems.
研究了关于具有一个隐藏层的多层感知器能力的基本问题。这些研究集中于从E(n)的有限子集映射到E(d)的函数的实现。考虑了实值函数和二值函数。特别地，推导出了实现从E(n)的有限子集映射到E(d)的任意函数所需的隐藏神经元数量的最小上界。对于单射函数的实现也获得了一个非平凡的下界。该结果可应用于模式识别和数据库检索研究。给出了与模式分类问题相关的二值函数实现的一个上界。
