Entangled q-Convolutional Neural Nets

TL;DR

This paper introduces the q-CNN, a quantum-inspired convolutional neural network that leverages entanglement properties to improve classification, demonstrated on MNIST datasets, and suggests entanglement as a guide for designing learning algorithms.

Contribution

The paper presents the q-CNN model, linking quantum entanglement with neural network training, and explores its potential for guiding machine learning design.

Findings

Entanglement entropy increases during training as the network learns features.

Negative correlation between entanglement entropy and cost function.

Quantum entanglement structure correlates with classification performance.

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.