标题： 深度、瘦小的神经网络不是通用逼近器 显示英文标题

标题： Deep, Skinny Neural Networks are not Universal Approximators

摘要： 为了选择一种对特定建模问题有效的神经网络架构，必须了解每个潜在选项所施加的限制。 这些限制通常以信息论界的形式描述，或者通过比较不同架构近似示例函数所需的相对复杂性来描述。 在本文中，我们研究了神经网络架构对所有它能够近似的函数的水平集施加的拓扑约束。 这种方法对于限制的本质及其与网络深度无关这一事实而言都是新颖的，适用于一大类激活函数。 显示英文摘要

摘要： 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.