  Tensor networks are factorisations of high rank tensors into networks of
lower rank tensors and have primarily been used to analyse quantum many-body
problems. Tensor networks have seen a recent surge of interest in relation to
supervised learning tasks with a focus on image classification. In this work,
we improve upon the matrix product state (MPS) tensor networks that can operate
on one-dimensional vectors to be useful for working with 2D and 3D medical
images. We treat small image regions as orderless, squeeze their spatial
information into feature dimensions and then perform MPS operations on these
locally orderless regions. These local representations are then aggregated in a
hierarchical manner to retain global structure. The proposed locally orderless
tensor network (LoTeNet) is compared with relevant methods on three datasets.
The architecture of LoTeNet is fixed in all experiments and we show it requires
lesser computational resources to attain performance on par or superior to the
compared methods.
