Entanglement and Tensor Networks for Supervised Image Classification

Tensor networks, originally designed to address computational problems in quantum many-body physics, have recently been applied to machine learning tasks. However, while the success of tensor network approaches in quantum physics is well understood, very little is known about why these techniques work for machine learning. Here, we investigate entanglement properties of tensor network models in current machine learning applications in order to uncover general principles that may guide future developments. We revisit the use of tensor networks for supervised image classification, as pioneered by Stoudenmire and Schwab. Firstly, we hypothesize a plausible candidate state that the tensor network might learn during training and discover that this hypothesis state is too entangled to be approximated by the tensor networks used in previous works, indicating that tensor networks must learn a very different state. Secondly, we use tensor networks with a block product structure and find that these states are extremely expressive, suggesting that long-range entanglement may not be essential for image classification. However, in our current implementation, optimization leads to overfitting, resulting in test accuracies that are not competitive with other current approaches.