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Deep, Skinny Neural Networks are not Universal Approximators

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arxiv 1810.00393 v1 pith:L3MHAOWA submitted 2018-09-30 cs.LG stat.ML

classification cs.LGstat.ML
keywords functionslimitationsnetworkneuralapproximatearchitectureableactivation
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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

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Minimum Block Width for Universal Approximation by Residual Neural Networks with Inner Width One

    cs.LG 2026-07 accept novelty 6.5 of 10

    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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