Recently, I asked a question on the concept of a manifold and received an answer that points to a relatively new subfield of deep learning named geometric deep learning.

In the preface of the paper titled Geometric Deep Learning Grids, Groups, Graphs, Geodesics, and Gauges, there is a mention of three types of geometry that do exist in the literature.

For instance, Euclidean geometry is concerned with lengths and angles, because these properties are preserved by the group of Euclidean transformations (rotations and translations), while affine geometry studies parallelism, which is preserved by the group of affine transformations. The relation between these geometries is immediately apparent when considering the respective groups, because the Euclidean group is a subgroup of the affine group, which in turn is a subgroup of the group of projective transformations.

The three types of geometry they mentioned are Euclidean, affine and projective. I want to know the complete list of types of geometry that do exist in the literature, if relevant to geometric deep learning.

What are the types of geometry in the literature that may be used for deep learning?


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