This paper explores the bottleneck of feature representations of deep neural networks (DNNs), from the perspective of the complexity of interactions between input variables encoded in DNNs. To this end, we focus on the multi-order interaction between input variables, where the order represents the complexity of interactions. We discover that a DNN is more likely to encode both too simple interactions and too complex interactions, but usually fails to learn interactions of intermediate complexity. Such a phenomenon is widely shared by different DNNs for different tasks. This phenomenon indicates a cognition gap between DNNs and human beings, and we call it a representation bottleneck. We theoretically prove the underlying reason for the representation bottleneck. Furthermore, we propose a loss to encourage/penalize the learning of interactions of specific complexities, and analyze the representation capacities of interactions of different complexities.

本文研究了深度神经网络的特征表示瓶颈，从输入变量在 DNN 中编码的交互复杂性的角度进行探讨，发现 DNN 更可能编码过于简单和过于复杂的交互，并且通常无法学习中等复杂度的交互。该现象被称为特征表示瓶颈，本文从理论上证明了其根本原因，并提出了一种损失函数来促进或惩罚特定复杂度的交互的学习，并分析了不同复杂度交互的表示能力。

发现和解释深度神经网络中的表示瓶颈