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

Locally orderless tensor networks for classifying two- and three-dimensional medical images