What Makes Data Suitable for a Locally Connected Neural Network? A Necessary and Sufficient Condition Based on Quantum Entanglement.

Yotam Alexander, Nimrod De La Vega, Noam Razin, Nadav Cohen

Keywords: Deep Learning, Locally Connected Neural Networks, Data Distributions, Quantum Entanglement, Tensor Networks

TL;DR: Importing tools from quantum physics and tensor analysis, we study what makes a data distribution suitable for locally connected neural networks, and develop, based on our theory, an algorithm for enhancing the suitability of data to such models.

Abstract: The question of what makes a data distribution suitable for deep learning is a fundamental open problem. Focusing on locally connected neural networks (a prevalent family of architectures that includes convolutional and recurrent neural networks as well as local self-attention models), we address this problem by adopting theoretical tools from quantum physics. Our main theoretical result states that a certain locally connected neural network is capable of accurate prediction over a data distribution if and only if the data distribution admits low quantum entanglement under certain canonical partitions of features. As a practical application of this result, we derive a preprocessing method for enhancing the suitability of a data distribution to locally connected neural networks. Experiments with widespread models over various datasets demonstrate our findings. We hope that our use of quantum entanglement will encourage further adoption of tools from physics for formally reasoning about the relation between deep learning and real-world data.

Submission Number: 1857