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Preprints, Working Papers, ... Year : 2023

From CNNs to Shift-Invariant Twin Models Based on Complex Wavelets


We propose a novel antialiasing method to increase shift invariance and prediction accuracy in convolutional neural networks. Specifically, we replace the first-layer combination "real-valued convolutions + max pooling" ($\mathbb{R}$Max) by "complex-valued convolutions + modulus'' ($\mathbb{C}$Mod), which is stable to translations. To justify our approach, we claim that $\mathbb{C}$Mod and $\mathbb{R}$Max produce comparable outputs when the convolution kernel is band-pass and oriented (Gabor-like filter). In this context, $\mathbb{C}$Mod can be considered as a stable alternative to $\mathbb{R}$Max. Thus, prior to antialiasing, we force 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 antialiasing 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.
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Dates and versions

hal-03880520 , version 1 (01-12-2022)
hal-03880520 , version 2 (21-04-2023)


  • HAL Id : hal-03880520 , version 2


Hubert Leterme, Kévin Polisano, Valérie Perrier, Karteek Alahari. From CNNs to Shift-Invariant Twin Models Based on Complex Wavelets. 2023. ⟨hal-03880520v2⟩
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