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We study the phenomenon that some modules of deep neural networks (DNNs) aremore critical than others. Meaning that rewinding their parameter values backto initialization, while keeping other modules fixed at the trained parameters,results in a large drop in the network's performance. Our analysis revealsinteresting properties of the loss landscape which leads us to propose acomplexity measure, called module criticality, based on the shape of thevalleys that connects the initial and final values of the module parameters. Weformulate how generalization relates to the module criticality, and show thatthis measure is able to explain the superior generalization performance of somearchitectures over others, whereas earlier measures fail to do so.

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