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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2112.01525 |
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| _version_ | 1866915253518860288 |
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| author | Singhal, Utkarsh Xing, Yifei Yu, Stella X. |
| author_facet | Singhal, Utkarsh Xing, Yifei Yu, Stella X. |
| contents | We study complex-valued scaling as a type of symmetry natural and unique to complex-valued measurements and representations. Deep Complex Networks (DCN) extends real-valued algebra to the complex domain without addressing complex-valued scaling. SurReal takes a restrictive manifold view of complex numbers, adopting a distance metric to achieve complex-scaling invariance while losing rich complex-valued information. We analyze complex-valued scaling as a co-domain transformation and design novel equivariant and invariant neural network layer functions for this special transformation. We also propose novel complex-valued representations of RGB images, where complex-valued scaling indicates hue shift or correlated changes across color channels. Benchmarked on MSTAR, CIFAR10, CIFAR100, and SVHN, our co-domain symmetric (CDS) classifiers deliver higher accuracy, better generalization, robustness to co-domain transformations, and lower model bias and variance than DCN and SurReal with far fewer parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_01525 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Co-domain Symmetry for Complex-Valued Deep Learning Singhal, Utkarsh Xing, Yifei Yu, Stella X. Computer Vision and Pattern Recognition Artificial Intelligence Machine Learning We study complex-valued scaling as a type of symmetry natural and unique to complex-valued measurements and representations. Deep Complex Networks (DCN) extends real-valued algebra to the complex domain without addressing complex-valued scaling. SurReal takes a restrictive manifold view of complex numbers, adopting a distance metric to achieve complex-scaling invariance while losing rich complex-valued information. We analyze complex-valued scaling as a co-domain transformation and design novel equivariant and invariant neural network layer functions for this special transformation. We also propose novel complex-valued representations of RGB images, where complex-valued scaling indicates hue shift or correlated changes across color channels. Benchmarked on MSTAR, CIFAR10, CIFAR100, and SVHN, our co-domain symmetric (CDS) classifiers deliver higher accuracy, better generalization, robustness to co-domain transformations, and lower model bias and variance than DCN and SurReal with far fewer parameters. |
| title | Co-domain Symmetry for Complex-Valued Deep Learning |
| topic | Computer Vision and Pattern Recognition Artificial Intelligence Machine Learning |
| url | https://arxiv.org/abs/2112.01525 |