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.
show that the AlexNet CNN @cite_5 trained on imagenet spontaneously learns representations that are equivariant to flips, scaling and rotation. This supports the idea that equivariance is a good inductive bias for deep convolutional networks. show that useful representations can be learned in an unsupervised manner by training a convolutional network to be equivariant to ego-motion.
@cite_5
2220894487
We seek to improve deep neural networks by generalizing the pooling operations that play a central role in current architectures. We pursue a careful exploration of approaches to allow pooling to learn and to adapt to complex and variable patterns. The two primary directions lie in (1) learning a pooling function via (two strategies of) combining of max and average pooling, and (2) learning a pooling function in the form of a tree-structured fusion of pooling filters that are themselves learned. In our experiments every generalized pooling operation we explore improves performance when used in place of average or max pooling. We experimentally demonstrate that the proposed pooling operations provide a boost in invariance properties relative to conventional pooling and set the state of the art on several widely adopted benchmark datasets; they are also easy to implement, and can be applied within various deep neural network architectures. These benefits come with only a light increase in computational overhead during training and a very modest increase in the number of model parameters.