Entangled q-Convolutional Neural Nets

Abstract

We introduce a machine learning model, the q-CNN model, sharing key features with convolutional neural networks and admitting a tensor network description. As examples, we apply q-CNN to the MNIST and Fashion MNIST classification tasks. We explain how the network associates a quantum state to each classification label, and study the entanglement structure of these network states. In both our experiments on the MNIST and Fashion-MNIST datasets, we observe a distinct increase in both the left/right as well as the up/down bipartition entanglement entropy during training as the network learns the fine features of the data. More generally, we observe a universal negative correlation between the value of the entanglement entropy and the value of the cost function, suggesting that the network needs to learn the entanglement structure in order the perform the task accurately. This supports the possibility of exploiting the entanglement structure as a guide to design the machine learning algorithm suitable for given tasks.

Tensor network to learn the wavefunction of data

“…Before we proceed with the results, we would like to explain why tensor network samplerdiscriminator/classifier is an appropriate architecture to define the full set via (1). In the recent years tensor networks, such as Matrix Product States (MPS) and Tensor Trains, have been actively used to build various classification [5,6,7,8] and generative [9,10] algorithms. They demonstrate robust performance on par with the advanced CNN architectures [7,11].…”