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Platonic CNNs

Taco Cohen

Platonic CNNs


Omnidirectional signals occur in a wide variety of domains, from climate and weather science to astronomy and omnidirectional computer vision. Neural networks for omnidirectional data should respect the topological and geometric structure and symmetries of the signal domains (typically a sphere-like manifold). Many kinds of spherical CNNs have been developed, but typically these involve non-standard and costly operations that may be hard to implement. By contrast, the gauge equivariant Icosahedral CNN (1) is implemented by performing a standard conv2d over a collection of local charts concatenated into a feature map. One downside of the method is that it requires projecting the spherical signal to the icosahedron. On the other hand, the method is very efficient, and exactly equivariant to the rotational symmetries of the icosahedron.

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