G2Sphere: Learning High-Frequnecy Spherical Signals From Geometric Data

Colin Kohler, Purvik Patel, Nathan Vaska, Justin Goodwin, Matthew C. Jones, Robert Platt, Rajmonda S. Caceres, Robin Walters

Keywords: Equivariance, Geometric, Fourier, Spherical Signals, SO(3), Radar

TL;DR: This paper introduces and evaluates G2Sphere, a general method for mapping object geometries to spherical signals using equivariant neural networks and the Fourier Transform.

Abstract: Many modeling tasks from disparate domains can be framed the same way, computing spherical signals from a geometric input, for example, computing the radar response or aerodynamics drag of different objects, or navigating through an environment. This paper introduces G2Sphere, a general method for mapping object geometries to spherical signals. G2Sphere operates entirely in Fourier space, encoding geometric structure into latent Fourier features using equivariant neural networks and then outputting the Fourier coefficients of the output signal. Combining these coefficients with spherical harmonics enables the simultaneous prediction of all values of the continuous spherical signal at any resolution. We perform experiments on various challenging domains including radar response modeling, aerodynamics drag prediction, and policy learning for manipulation and navigation. We find that G2Sphere significantly outperforms baselines in terms of accuracy and inference time. We also demonstrate that equivariance and Fourier features lead to improved sample efficiency and generalization.

Primary Area: learning on graphs and other geometries & topologies

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Submission Number: 8068