Generalizing convolutional neural networks for equivariance to lie groups on arbitrary continuous data

Marc Finzi, Samuel Stanton, Pavel Izmailov, Andrew Gordon Wilson

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The translation equivariance of convolutional layers enables convolutional neural networks to generalize well on image problems. While translation equivariance provides a powerful inductive bias for images, we often additionally desire equivariance to other transformations, such as rotations, especially for non-image data. We propose a general method to construct a convolutional layer that is equivariant to transformations from any specified Lie group with a surjective exponential map. Incorporating equivariance to a new group requires implementing only the group exponential and logarithm maps, enabling rapid prototyping. Showcasing the simplicity and generality of our method, we apply the same model architecture to images, ball-and-stick molecular data, and Hamiltonian dynamical systems. For Hamiltonian systems, the equivariance of our models is especially impactful, leading to exact conservation of linear and angular momentum.

Original languageEnglish (US)
Title of host publication37th International Conference on Machine Learning, ICML 2020
EditorsHal Daume, Aarti Singh
PublisherInternational Machine Learning Society (IMLS)
Pages3146-3157
Number of pages12
ISBN (Electronic)9781713821120
StatePublished - 2020
Event37th International Conference on Machine Learning, ICML 2020 - Virtual, Online
Duration: Jul 13 2020Jul 18 2020

Publication series

Name37th International Conference on Machine Learning, ICML 2020
VolumePartF168147-5

Conference

Conference37th International Conference on Machine Learning, ICML 2020
CityVirtual, Online
Period7/13/207/18/20

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Human-Computer Interaction
  • Software

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