  Invariance has recently proven to be a powerful inductive bias in machine
learning models. One such class of predictive or generative models are tensor
networks. We introduce a new numerical algorithm to construct a basis of
tensors that are invariant under the action of normal matrix representations of
an arbitrary discrete group. This method can be up to several orders of
magnitude faster than previous approaches. The group-invariant tensors are then
combined into a group-invariant tensor train network, which can be used as a
supervised machine learning model. We applied this model to a protein binding
classification problem, taking into account problem-specific invariances, and
obtained prediction accuracy in line with state-of-the-art deep learning
approaches.
