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：什么使得数据分布适用于深度学习是一个基本开放问题。聚焦于局域连接神经网络（一类包含卷积神经网络、循环神经网络及局部自注意力模型的常见架构），我们通过采用量子物理的理论工具来解决该问题。我们的主要理论结果表明：当且仅当数据分布在特定特征规范划分下具有低量子纠缠时，某类局域连接神经网络才能对该数据分布实现精确预测。作为该理论的实际应用，我们推导出一种预处理方法，用于增强数据分布对局域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。我们期望通过引入量子纠缠，能鼓励更多利用物理学工具对深度学习与真实世界数据之间的关系进行形式化推理的研究。