ResNet with one-neuron hidden layers is a Universal Approximator

Code

• github.com/sivakon/resnet-approximator
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Abstract

We demonstrate that a very deep ResNet with stacked modules with one neuron per hidden layer and ReLU activation functions can uniformly approximate any Lebesgue integrable function in d dimensions, i.e. _1(R^d). Because of the identity mapping inherent to ResNets, our network has alternating layers of dimension one and d. This stands in sharp contrast to fully connected networks, which are not universal approximators if their width is the input dimension d [Lu et al, 2017; Hanin and Sellke, 2017]. Hence, our result implies an increase in representational power for narrow deep networks by the ResNet architecture.

Reproductions