From CNNs to Shift-Invariant Twin Wavelet Models

Hubert Leterme (1, 2) , Kévin Polisano (3) , Valérie Perrier (1) , Karteek Alahari (2)

1 EDP - Equations aux Dérivées Partielles
2 Thoth - Apprentissage de modèles à partir de données massives
3 SVH - Statistique pour le Vivant et l’Homme

We propose a novel antialiasing method to increase shift invariance in convolutional neural networks (CNNs). More precisely, we replace the conventional combination "real-valued convolutions + max pooling" ($\mathbb R$Max) by "complex-valued convolutions + modulus" ($\mathbb C$Mod), which produce stable feature representations for band-pass filters with well-defined orientations. In a recent work, we proved that, for such filters, the two operators yield similar outputs. Therefore, $\mathbb C$Mod can be viewed as a stable alternative to $\mathbb R$Max. To separate band-pass filters from other freely-trained kernels, in this paper, we designed a "twin" architecture based on the dual-tree complex wavelet packet transform, which generates similar outputs as standard CNNs with fewer trainable parameters. In addition to improving stability to small shifts, our experiments on AlexNet and ResNet showed increased prediction accuracy on natural image datasets such as ImageNet and CIFAR10. Furthermore, our approach outperformed recent antialiasing methods based on low-pass filtering by preserving high-frequency information, while reducing memory usage.

Domaines: Vision par ordinateur et reconnaissance de formes [cs.CV]; Intelligence artificielle [cs.AI]; Traitement du signal et de l'image [eess.SP]; Machine Learning [stat.ML]

Hubert Leterme, Kévin Polisano, Valérie Perrier, Karteek Alahari. From CNNs to Shift-Invariant Twin Wavelet Models. 2022. ⟨hal-03880520v1⟩