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Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data
Marc Finzi · Samuel Stanton · Pavel Izmailov · Andrew Wilson

Tue Jul 14 10:00 AM -- 10:45 AM & Tue Jul 14 09:00 PM -- 09:45 PM (PDT) @ None #None

The translation equivariance of convolutional layers enables CNNs 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.

Author Information

Marc Finzi (New York University)
Samuel Stanton (New York University)
Pavel Izmailov (New York University)
Andrew Wilson (New York University)
Andrew Wilson

Andrew Gordon Wilson is faculty in the Courant Institute and Center for Data Science at NYU. His interests include probabilistic modelling, Gaussian processes, Bayesian statistics, physics inspired machine learning, and loss surfaces and generalization in deep learning. His webpage is https://cims.nyu.edu/~andrewgw.

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