Entangled q-Convolutional Neural Nets
This work addresses the challenge of leveraging quantum entanglement to guide machine learning algorithm design, but it is incremental as it builds on existing quantum-inspired models without achieving broad SOTA impact.
The paper tackles the problem of understanding the entanglement structure in quantum-inspired convolutional neural networks (q-CNNs) during training on classification tasks like MNIST and Fashion MNIST, finding a universal negative correlation between entanglement entropy and cost function value, with observed increases in bipartition entanglement entropy as the network learns fine features.
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.