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Compact Matrix Quantum Group Equivariant Neural Networks
Edward Pearce-Crump
Group equivariant neural networks have proven effective in modelling a wide range of tasks where the data lives in a classical geometric space and exhibits well-defined group symme…
Graph Automorphism Group Equivariant Neural Networks
Edward Pearce-Crump, William J. Knottenbelt
Permutation equivariant neural networks are typically used to learn from data that lives on a graph. However, for any graph that has vertices, using the symmetric group $S_…
An Algorithm for Computing with Brauer's Group Equivariant Neural Network Layers
Edward Pearce-Crump
The learnable, linear neural network layers between tensor power spaces of that are equivariant to the orthogonal group, , the special orthogonal group, $SO(…
Categorification of Group Equivariant Neural Networks
Edward Pearce-Crump
We present a novel application of category theory for deep learning. We show how category theory can be used to understand and work with the linear layer functions of group equivar…
How Jellyfish Characterise Alternating Group Equivariant Neural Networks
Edward Pearce-Crump
We provide a full characterisation of all of the possible alternating group () equivariant neural networks whose layers are some tensor power of . In particula…