Group Equivariant Convolutional Networks

TL;DR

Group Equivariant Convolutional Neural Networks (G-CNNs) extend traditional CNNs by incorporating symmetry groups, leading to improved sample efficiency and state-of-the-art results on datasets with transformations like rotations and reflections.

Contribution

The paper introduces G-convolutions, a new layer type that enhances weight sharing and expressiveness in CNNs by exploiting symmetries, with minimal computational overhead.

Findings

Achieved state-of-the-art results on CIFAR10 and rotated MNIST.

G-CNNs reduce sample complexity by leveraging symmetries.

G-convolutions are easy to implement and computationally efficient.

Abstract

We introduce Group equivariant Convolutional Neural Networks (G-CNNs), a natural generalization of convolutional neural networks that reduces sample complexity by exploiting symmetries. G-CNNs use G-convolutions, a new type of layer that enjoys a substantially higher degree of weight sharing than regular convolution layers. G-convolutions increase the expressive capacity of the network without increasing the number of parameters. Group convolution layers are easy to use and can be implemented with negligible computational overhead for discrete groups generated by translations, reflections and rotations. G-CNNs achieve state of the art results on CIFAR10 and rotated MNIST.