Compact Matrix Quantum Group Equivariant Neural Networks
Edward Pearce-Crump
We derive the existence of a new type of neural network, called a compact
matrix quantum group equivariant neural network, that learns from data that has
an underlying quantum symmetry. We apply the Woronowicz formulation of
Tannaka-Krein duality to characterise the weight matrices that appear in these
neural networks for any easy compact matrix quantum group. We show that compact
matrix quantum group equivariant neural networks contain, as a subclass, all
compact matrix group equivariant neural networks. Moreover, we obtain
characterisations of the weight matrices for many compact matrix group
equivariant neural networks that have not previously appeared in the machine
learning literature.