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Deep, Skinny Neural Networks are not Universal Approximators
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In order to choose a neural network architecture that will be effective for a particular modeling problem, one must understand the limitations imposed by each of the potential options. These limitations are typically described in terms of information theoretic bounds, or by comparing the relative complexity needed to approximate example functions between different architectures. In this paper, we examine the topological constraints that the architecture of a neural network imposes on the level sets of all the functions that it is able to approximate. This approach is novel for both the nature of the limitations and the fact that they are independent of network depth for a broad family of activation functions.
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Cited by 1 Pith paper
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Minimum Block Width for Universal Approximation by Residual Neural Networks with Inner Width One
With inner width one, residual networks need block width exactly max(dx, dy) for L^p universal approximation and at most min(dx+dy, max(2dx+1, dy)) for uniform approximation.
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