DeepAI AI Chat
Log In Sign Up

Group Equivariant Subsampling

by   Jin Xu, et al.

Subsampling is used in convolutional neural networks (CNNs) in the form of pooling or strided convolutions, to reduce the spatial dimensions of feature maps and to allow the receptive fields to grow exponentially with depth. However, it is known that such subsampling operations are not translation equivariant, unlike convolutions that are translation equivariant. Here, we first introduce translation equivariant subsampling/upsampling layers that can be used to construct exact translation equivariant CNNs. We then generalise these layers beyond translations to general groups, thus proposing group equivariant subsampling/upsampling. We use these layers to construct group equivariant autoencoders (GAEs) that allow us to learn low-dimensional equivariant representations. We empirically verify on images that the representations are indeed equivariant to input translations and rotations, and thus generalise well to unseen positions and orientations. We further use GAEs in models that learn object-centric representations on multi-object datasets, and show improved data efficiency and decomposition compared to non-equivariant baselines.


page 8

page 20


Group Equivariant Convolutional Networks

We introduce Group equivariant Convolutional Neural Networks (G-CNNs), a...

Roto-Translation Covariant Convolutional Networks for Medical Image Analysis

We propose a framework for rotation and translation covariant deep learn...

Multi-scale Octave Convolutions for Robust Speech Recognition

We propose a multi-scale octave convolution layer to learn robust speech...

SO(2) and O(2) Equivariance in Image Recognition with Bessel-Convolutional Neural Networks

For many years, it has been shown how much exploiting equivariances can ...

Harmonic Networks: Deep Translation and Rotation Equivariance

Translating or rotating an input image should not affect the results of ...

Equivariant and Steerable Neural Networks: A review with special emphasis on the symmetric group

Convolutional neural networks revolutionized computer vision and natrual...

B-Spline CNNs on Lie Groups

Group convolutional neural networks (G-CNNs) can be used to improve clas...