Deep convolutional tensor network

Tensor networks are linear algebraic representations of quantum many-body states based on their entanglement structure. People are exploring their applications to machine learning. Deep convolutional neural networks achieve state of the art results in computer vision and other areas. Supposedly this happens because of parameter sharing, locality, and deepness. We devise a novel tensor network based model called Deep convolutional tensor network (DCTN) for image classification, which has parameter sharing, locality, and deepness. It is based on the Entangled plaquette states (EPS) tensor network. We show how Entangled plaquette states can be implemented as a backpropagatable layer which can be used in neural networks. We test our model on FashionMNIST dataset and find that deepness increases overfitting and decreases test accuracy. Also, we find that the shallow version performs well considering its low parameter count. We discuss how hyperparameters of DCTN affect its training and overfitting.