Title: Equivariant CNNs via Hypernetworks
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
Keywords: geometric deep learning, equivariant neural networks, hypernetwork

Abstract: In geometric deep learning, numerous works have been dedicated to enhancing neural networks with the ability to preserve symmetries, a concept known as equivariance. Group Equivariant Convolutional Networks ($G$-CNNs) achieve rotation and reflection equivariance on Convolutional Neural Networks (CNNs). While showing a significant improvement when processing rotation-augmented datasets such as randomly rotated MNIST, training $G$-CNNs on a dataset with little rotational variation, such as regular MNIST, typically leads to a performance drop compared to a regular CNN. In this study, we first empirically observe the performance imbalance across different variation of MNIST in $G$-CNNs, and discuss how the $G$-CNN filters is a contributing factor to this imbalance. To avoid such imbalance, we propose a Hypernetwork-based Equivariant CNN (HE-CNN) to generate CNN filters that inherently exhibit rotational equivariance without altering the main network's CNN structure through the use of a hypernetwork. We prove that these generated filters grant the equivariance property to a regular CNN main network. Empirically, HE-CNN outperforms $G$-CNNs and achieves comparable performance to advanced state-of-the-art $G$-CNN-based methods on both types of datasets, with and without rotation augmentation.