University of Bergen's GsCNN Mixes Scalars and Vectors for Spherical AI

Weather forecasts, cosmological maps, and panoramic vision systems process signals whose natural domain is a sphere. Researchers at the University of Bergen have introduced a General spherical CNN, or GsCNN, in a new paper. The architecture preserves three-dimensional rotational symmetry while processing scalar fields such as temperature, vector fields such as wind, and higher-order tensor fields.

Rotation equivariance means that rotating an input produces a corresponding rotation in the output. Encoding that behavior directly can reduce the need for rotation-based data augmentation and prevent predictions from changing because a spherical field was expressed in a different orientation.

Flat grids lose globe rotations

A planar convolution applies the same translated filter across a rectangular grid. On a latitude-longitude map, grid cells shrink toward the poles, longitude wraps around, and neighborhoods change shape with latitude. Longitude shifts correspond to rotations around the globe’s vertical axis, but the grid does not preserve arbitrary rotations in three dimensions.

Earlier spherical CNNs addressed this geometry with Fourier-domain convolutions over SO(3), the mathematical group containing every three-dimensional rotation. Spin-weighted spherical CNNs extended the approach to vector fields, including work by Esteves and collaborators.

Spin describes how a local quantity changes when the tangent coordinate frame rotates around the surface normal. A scalar has spin zero, while tangent vectors such as wind can be represented through nonzero spin components. Previous spin-weighted architectures preserved these transformation rules by limiting their kernels and nonlinear activation functions.