From CNNs to Shift-Invariant Twin Models Based on Complex Wavelets
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866916267010555904 |
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| author | Leterme, Hubert Polisano, Kévin Perrier, Valérie Alahari, Karteek |
| author_facet | Leterme, Hubert Polisano, Kévin Perrier, Valérie Alahari, Karteek |
| contents | We propose a novel method to increase shift invariance and prediction accuracy in convolutional neural networks. Specifically, we replace the first-layer combination "real-valued convolutions + max pooling" (RMax) by "complex-valued convolutions + modulus" (CMod), which is stable to translations, or shifts. To justify our approach, we claim that CMod and RMax produce comparable outputs when the convolution kernel is band-pass and oriented (Gabor-like filter). In this context, CMod can therefore be considered as a stable alternative to RMax. To enforce this property, we constrain the convolution kernels to adopt such a Gabor-like structure. The corresponding architecture is called mathematical twin, because it employs a well-defined mathematical operator to mimic the behavior of the original, freely-trained model. Our approach achieves superior accuracy on ImageNet and CIFAR-10 classification tasks, compared to prior methods based on low-pass filtering. Arguably, our approach's emphasis on retaining high-frequency details contributes to a better balance between shift invariance and information preservation, resulting in improved performance. Furthermore, it has a lower computational cost and memory footprint than concurrent work, making it a promising solution for practical implementation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2212_00394 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | From CNNs to Shift-Invariant Twin Models Based on Complex Wavelets Leterme, Hubert Polisano, Kévin Perrier, Valérie Alahari, Karteek Computer Vision and Pattern Recognition Artificial Intelligence Image and Video Processing Machine Learning We propose a novel method to increase shift invariance and prediction accuracy in convolutional neural networks. Specifically, we replace the first-layer combination "real-valued convolutions + max pooling" (RMax) by "complex-valued convolutions + modulus" (CMod), which is stable to translations, or shifts. To justify our approach, we claim that CMod and RMax produce comparable outputs when the convolution kernel is band-pass and oriented (Gabor-like filter). In this context, CMod can therefore be considered as a stable alternative to RMax. To enforce this property, we constrain the convolution kernels to adopt such a Gabor-like structure. The corresponding architecture is called mathematical twin, because it employs a well-defined mathematical operator to mimic the behavior of the original, freely-trained model. Our approach achieves superior accuracy on ImageNet and CIFAR-10 classification tasks, compared to prior methods based on low-pass filtering. Arguably, our approach's emphasis on retaining high-frequency details contributes to a better balance between shift invariance and information preservation, resulting in improved performance. Furthermore, it has a lower computational cost and memory footprint than concurrent work, making it a promising solution for practical implementation. |
| title | From CNNs to Shift-Invariant Twin Models Based on Complex Wavelets |
| topic | Computer Vision and Pattern Recognition Artificial Intelligence Image and Video Processing Machine Learning |
| url | https://arxiv.org/abs/2212.00394 |