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Brauer’s Group Equivariant Neural Networks
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:27461-27482, 2023.
Abstract
We provide a full characterisation of all of the possible group equivariant neural networks whose layers are some tensor power of Rn for three symmetry groups that are missing from the machine learning literature: O(n), the orthogonal group; SO(n), the special orthogonal group; and Sp(n), the symplectic group. In particular, we find a spanning set of matrices for the learnable, linear, equivariant layer functions between such tensor power spaces in the standard basis of Rn when the group is O(n) or SO(n), and in the symplectic basis of Rn when the group is Sp(n).