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Weight norm $\|w\|$ and margin $\gamma$ participate in learning theory viathe normalized margin $\gamma/\|w\|$. Since standard neural net optimizers donot control normalized margin, it is hard to test whether this quantitycausally relates to generalization. This paper designs a series of experimentalstudies that explicitly control normalized margin and thereby tackle twocentral questions. First: does normalized margin always have a causal effect ongeneralization? The paper finds that no -- networks can be produced wherenormalized margin has seemingly no relationship with generalization, counter tothe theory of Bartlett et al. (2017). Second: does normalized margin ever havea causal effect on generalization? The paper finds that yes -- in a standardtraining setup, test performance closely tracks normalized margin. The papersuggests a Gaussian process model as a promising explanation for this behavior.

Investigating Generalization by Controlling Normalized Margin