dli@uceng.UC.EDU (dapeng li) (07/15/90)
Hi, netters, Does anyone here can give me the reference information of Kolmogorov's paper "On the representation of continous functions of many variables by superposition of continous functions of one variable and addtions" in ENGLISH VERSION ? Also, if you have any kind of information about the development of Kolmogorov's work on back propagation network, I would like to know ( papers on this topic). I will post the collected information on the net. Thanks for your help in advance. Dapeng Li University of Cincinnati
baindur@jhunix.HCF.JHU.EDU (Satyen G Baindur) (07/16/90)
In article <5458@uceng.UC.EDU> dli@uceng.UC.EDU (dapeng li) writes: > Does anyone here can give me the reference information of Kolmogorov's >paper "On the representation of continous functions of many variables by >superposition of continous functions of one variable and addtions" in ENGLISH >VERSION ? > > Also, if you have any kind of information about the development of >Kolmogorov's work on back propagation network, I would like to know ( papers >on this topic). > > Dapeng Li The reference is Kolmogorov, A.N., "On the representation of continuous functions of many variables by superposition of continuous functions of one variable and addition.", American Mathematical Society Translations, Series 2, Volume 28, pp.55-59. It should be read in conjunction with the Girosi and Poggio paper in Vol 1 no.4 pp.465-469 of Neural Computation. They point out that the theorem is irrelevant for network learning because it can require even differentiable functions to have a representation in terms of "wildly" behaving inner functions. Then again, you may have read this already, and be asking the question because they give only the reference to the Russian original, [which is Dokl. Akad. Nauk. SSSR. vol 114 pp 953-956, (1957).] Satyen Baindur