  Originating from condensed matter physics, tensor networks are compact
representations of high-dimensional tensors. In this paper, the prowess of
tensor networks is demonstrated on the particular task of one-class anomaly
detection. We exploit the memory and computational efficiency of tensor
networks to learn a linear transformation over a space with dimension
exponential in the number of original features. The linearity of our model
enables us to ensure a tight fit around training instances by penalizing the
model's global tendency to a predict normality via its Frobenius norm---a task
that is infeasible for most deep learning models. Our method outperforms deep
and classical algorithms on tabular datasets and produces competitive results
on image datasets, despite not exploiting the locality of images.
