Understanding Neural Network Systems for Image Analysis using Vector Spaces and Inverse Maps
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912976197386240 |
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| author | Pattichis, Rebecca Pattichis, Marios S. |
| author_facet | Pattichis, Rebecca Pattichis, Marios S. |
| contents | There is strong interest in developing mathematical methods that can be used to understand complex neural networks used in image analysis. In this paper, we introduce techniques from Linear Algebra to model neural network layers as maps between signal spaces. First, we demonstrate how signal spaces can be used to visualize weight spaces and convolutional layer kernels. We also demonstrate how residual vector spaces can be used to further visualize information lost at each layer. Second, we study invertible networks using vector spaces for computing input images that yield specific outputs. We demonstrate our approach on two invertible networks and ResNet18. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_00261 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Understanding Neural Network Systems for Image Analysis using Vector Spaces and Inverse Maps Pattichis, Rebecca Pattichis, Marios S. Computer Vision and Pattern Recognition Machine Learning There is strong interest in developing mathematical methods that can be used to understand complex neural networks used in image analysis. In this paper, we introduce techniques from Linear Algebra to model neural network layers as maps between signal spaces. First, we demonstrate how signal spaces can be used to visualize weight spaces and convolutional layer kernels. We also demonstrate how residual vector spaces can be used to further visualize information lost at each layer. Second, we study invertible networks using vector spaces for computing input images that yield specific outputs. We demonstrate our approach on two invertible networks and ResNet18. |
| title | Understanding Neural Network Systems for Image Analysis using Vector Spaces and Inverse Maps |
| topic | Computer Vision and Pattern Recognition Machine Learning |
| url | https://arxiv.org/abs/2402.00261 |