Discovering and Explaining the Representation Bottleneck of DNNs

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. The revolution from shallow to deep models is a crucial step in the development of artificial intelligence. Deep neural networks (DNNs) usually exhibit superior performance to shallow models, which is generally believed as a result of the improvement of the representation power (Pascanu et al., 2013; Montúfar et al., 2014).