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.

翻译：数据分布适合深度学习的基本条件是一个重要的未解问题。本文聚焦于局部连接神经网络（包括卷积神经网络、循环神经网络以及局部自注意力模型等主流架构），通过引入量子物理学中的理论工具来探讨这一问题。我们的主要理论结果表明，当且仅当数据分布在特定规范特征分割下具有低量子纠缠度时，某种局部连接神经网络能够对该数据分布进行准确预测。基于这一结果，我们推导出一种预处理方法，用于增强数据分布对局部连接神经网络的适用性。在多种数据集上使用广泛模型的实验验证了我们的发现。希望我们对量子纠缠的运用能促进更多物理学工具被正式用于论证深度学习与现实世界数据之间的关系。