Digital implementations of deep feature extractors are intrinsically informative
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915702251716608 |
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| author | Getter, Max |
| author_facet | Getter, Max |
| contents | Rapid information (energy) propagation in deep feature extractors is crucial to balance computational complexity versus expressiveness as a representation of the input. We prove an upper bound for the speed of energy propagation in a unified framework that covers different neural network models, both over Euclidean and non-Euclidean domains. Additional structural information about the signal domain can be used to explicitly determine or improve the rate of decay. To illustrate this, we show global exponential energy decay for a range of 1) feature extractors with discrete-domain input signals, and 2) convolutional neural networks (CNNs) via scattering over locally compact abelian (LCA) groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_15004 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Digital implementations of deep feature extractors are intrinsically informative Getter, Max Machine Learning Computer Vision and Pattern Recognition Functional Analysis 68T07, 43A70 I.2.10; I.5.1; I.5.2 Rapid information (energy) propagation in deep feature extractors is crucial to balance computational complexity versus expressiveness as a representation of the input. We prove an upper bound for the speed of energy propagation in a unified framework that covers different neural network models, both over Euclidean and non-Euclidean domains. Additional structural information about the signal domain can be used to explicitly determine or improve the rate of decay. To illustrate this, we show global exponential energy decay for a range of 1) feature extractors with discrete-domain input signals, and 2) convolutional neural networks (CNNs) via scattering over locally compact abelian (LCA) groups. |
| title | Digital implementations of deep feature extractors are intrinsically informative |
| topic | Machine Learning Computer Vision and Pattern Recognition Functional Analysis 68T07, 43A70 I.2.10; I.5.1; I.5.2 |
| url | https://arxiv.org/abs/2502.15004 |