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.

本文采用量子物理的理论工具，研究了数据分布在神经网络中应用的适宜性问题，提出了一种新的局部连接神经网络适用性的预处理方法，并在多个数据集上进行了实验验证。

局部连接神经网络的适用数据：基于量子纠缠的必要充分条件