Spectrum Extraction and Clipping for Implicitly Linear Layers
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912061479452672 |
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| author | Boroojeny, Ali Ebrahimpour Telgarsky, Matus Sundaram, Hari |
| author_facet | Boroojeny, Ali Ebrahimpour Telgarsky, Matus Sundaram, Hari |
| contents | We show the effectiveness of automatic differentiation in efficiently and correctly computing and controlling the spectrum of implicitly linear operators, a rich family of layer types including all standard convolutional and dense layers. We provide the first clipping method which is correct for general convolution layers, and illuminate the representational limitation that caused correctness issues in prior work. We study the effect of the batch normalization layers when concatenated with convolutional layers and show how our clipping method can be applied to their composition. By comparing the accuracy and performance of our algorithms to the state-of-the-art methods, using various experiments, we show they are more precise and efficient and lead to better generalization and adversarial robustness. We provide the code for using our methods at https://github.com/Ali-E/FastClip. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_16017 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectrum Extraction and Clipping for Implicitly Linear Layers Boroojeny, Ali Ebrahimpour Telgarsky, Matus Sundaram, Hari Machine Learning Computer Vision and Pattern Recognition We show the effectiveness of automatic differentiation in efficiently and correctly computing and controlling the spectrum of implicitly linear operators, a rich family of layer types including all standard convolutional and dense layers. We provide the first clipping method which is correct for general convolution layers, and illuminate the representational limitation that caused correctness issues in prior work. We study the effect of the batch normalization layers when concatenated with convolutional layers and show how our clipping method can be applied to their composition. By comparing the accuracy and performance of our algorithms to the state-of-the-art methods, using various experiments, we show they are more precise and efficient and lead to better generalization and adversarial robustness. We provide the code for using our methods at https://github.com/Ali-E/FastClip. |
| title | Spectrum Extraction and Clipping for Implicitly Linear Layers |
| topic | Machine Learning Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2402.16017 |