Coordinate Independent Convolutional Networks -- Isometry and Gauge Equivariant Convolutions on Riemannian Manifolds

Understand

Motivated by the vast success of deep convolutional networks, there is a great interest in generalizing convolutions to non-Euclidean manifolds.

• A major complication in comparison to flat spaces is that it is unclear in which alignment a convolution kernel should be applied on a manifold.
• The underlying reason for this ambiguity is that general manifolds do not come with a canonical choice of reference frames (gauge).
• Kernels and features therefore have to be expressed relative to arbitrary coordinates.