ResNet with one-neuron hidden layers is a Universal Approximator
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We demonstrate that a very deep ResNet with stacked modules that have one neuron per hidden layer and ReLU activation functions can uniformly approximate any Lebesgue integrable function in d dimensions, i.e. ℓ1(Rd). Due to 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 [21, 11]. Hence, our result implies an increase in representational power for narrow deep networks by the ResNet architecture.
Date issued
2018-12Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer ScienceJournal
Advances in Neural Information Processing Systems
Publisher
Morgan Kaufmann Publishers
Citation
Lin, Hongzhou and Stefanie Jegelka. “ResNet with one-neuron hidden layers is a Universal Approximator.” Advances in Neural Information Processing Systems, December-2018 (December 2018) © 2018 The Author(s)
Version: Final published version
ISSN
1049-5258