Fisher-rao metric, geometry, and complexity of neural networks
© 2019 by the author(s). We study the relationship between geometry and capacity measures for deep neural networks from an invariance viewpoint. We introduce a new notion of capacity - the Fisher-Rao norm - that possesses desirable invariance properties and is motivated by Information Geometry. We d...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
2021-12-02T20:14:53Z.
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| Subjects: | |
| Online Access: | Get fulltext |
| Summary: | © 2019 by the author(s). We study the relationship between geometry and capacity measures for deep neural networks from an invariance viewpoint. We introduce a new notion of capacity - the Fisher-Rao norm - that possesses desirable invariance properties and is motivated by Information Geometry. We discover an analytical characterization of the new capacity measure, through which we establish norm-comparison inequalities and further show that the new measure serves as an umbrella for several existing norm-based complexity measures. We discuss upper bounds on the generalization error induced by the proposed measure. Extensive numerical experiments on CIFAR-10 support our theoretical findings. Our theoretical analysis rests on a key structural lemma about partial derivatives of multi-layer rectifier networks. |
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