The intriguing role of module criticality in the generalization of deep networks

We study the phenomenon that some modules of deep neural networks (DNNs) are more critical than others. Meaning that rewinding their parameter values back to initialization, while keeping other modules fixed at the trained parameters, results in a large drop in the network's performance. Our analysis reveals interesting properties of the loss landscape which leads us to propose a complexity measure, called module criticality, based on the shape of the valleys that connects the initial and final values of the module parameters. We formulate how generalization relates to the module criticality, and show that this measure is able to explain the superior generalization performance of some architectures over others, whereas earlier measures fail to do so. 1 Introduction Neural networks have had tremendous practical impact in various domains such as revolutionizing many tasks in computer vision, speech and natural language processing. However, many aspects of their design and analysis have remained mysterious to this date. One of the most important questions is "what makes an architecture work better than others given a specific task?" Extensive research in this area has led to many potential explanations on why some types of architectures have better performance; however, we lack a unified view that provides a complete and satisfactory answer. In order to attain a unified view on superiority of one architecture over another in terms of generalization performance, we need to come up with a measure that effectively captures this. Analyzing the generalization behavior of neural networks has been an active area of research since Baum and Haussler (1989). Many generalization bounds and complexity measures have been proposed so far. Bartlett (1998) emphasized on the norm of the weights in predicting the generalization error.