Ocampo, Jeremy; Price, Matthew; McEwen, Jason; (2023) Scalable and equivariant spherical CNNs by discrete-continuous (DISCO) convolutions. In: Proceedings of the 11th International Conference on Learning Representations: ICLR 2023. ICLR

Preview

Text McEwen_3325_scalable_and_equivariant_spher.pdf Download (4MB) | Preview

Abstract

No existing spherical convolutional neural network (CNN) framework is both computationally scalable and rotationally equivariant. Continuous approaches capture rotational equivariance but are often prohibitively computationally demanding. Discrete approaches offer more favorable computational performance but at the cost of equivariance. We develop a hybrid discrete-continuous (DISCO) group convolution that is simultaneously equivariant and computationally scalable to high-resolution. While our framework can be applied to any compact group, we specialize to the sphere. Our DISCO spherical convolutions exhibit SO(3) rotational equivariance, where SO(n) is the special orthogonal group representing rotations in n-dimensions. When restricting rotations of the convolution to the quotient space SO(3)/SO(2) for further computational enhancements, we recover a form of asymptotic SO(3) rotational equivariance. Through a sparse tensor implementation we achieve linear scaling in number of pixels on the sphere for both computational cost and memory usage. For 4k spherical images we realize a saving of 109 in computational cost and 104 in memory usage when compared to the most efficient alternative equivariant spherical convolution. We apply the DISCO spherical CNN framework to a number of benchmark dense-prediction problems on the sphere, such as semantic segmentation and depth estimation, on all of which we achieve the state-of-the-art performance.

Download activity - last month

Export as CSVJSONXML

Download activity - last 12 months

Export as CSVJSONXML

Downloads by country - last 12 months

Export as XMLJSONCSV

Archive Staff Only

View Item