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[PDF] A Comparison of Neural Network Architectures

https://personal-homepages.mis.mpg.de/montufar/50.pdf

A deep Boltzmann machine with an input layer of k binary units, L hidden layers of n2k binary units, and an output layer of n binary units is a universal approx-imator of stochastic maps, provided L is as in Theorem 7 This is based on the ability of deep Boltzmann machines to represent certain types of transformations that can be rep-resented by feedforward networks (Mont´ ufar, 2015) and on the proof of Theorem 7. A conditional restricted Boltzmann machine with k input binary units, m hidden binary units, and n out-put binary units can approximate a given stochastic map arbitrarily well, whenever it can be represented by a feed-forward network with k input binary units, m hidden linear threshold units, and n output stochastic sigmoid units.

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