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About Exponential Expressivity in Deep Neural Networks Through Transient Chaos
This paper introduces a theoretical framework combining Riemannian geometry and dynamical mean field theory to analyze signal propagation and expressivity in deep neural networks. The framework shows that for broad classes of nonlinearities, even random deep networks can construct hidden representations whose global curvature grows exponentially with depth but not width. This indicates deep networks can efficiently compute highly complex functions that shallow networks cannot. The theory also quantitatively demonstrates how deep networks can disentangle highly curved input manifolds into flattened hidden manifolds, supporting a key intuition about deep learning.
Detailed Information
| Author: | ['stephane Vernede'] |
|---|---|
| Publication Year: | 2020 |
| Pages: | 16 |
| Language: | English |
| Format: | |
| Price: | FREE |
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