On margin-based generalization prediction in deep neural networks

Abstract

Understanding generalization in deep neural networks is an active area of research. A promising avenue of exploration has been that of margin measurements: the shortest distance to the decision boundary for a given sample or that sample's representation internal to the network. Margin-based complexity measures have been shown to be correlated with the generalization ability of deep neural networks in some circumstances but not others. The reasons behind the success or failure of these metrics are currently unclear. In this study, we examine margin-based generalization prediction methods in different settings. We motivate why these metrics sometimes fail to accurately predict generalization and how they can be improved. First, we analyze the relationship between margins measured in the input space and sample noise. We find that different types of sample noise can have a very different effect on the overall margin of a network that has modeled noisy data. Following this, we empirically evaluate how robust margins measured at different representational spaces are at predicting generalization. We find that these metrics have several limitations and that a large margin does not exhibit a strong correlation with empirical risk in many cases. Finally, we introduce a new margin-based measure that incorporates an approximation of the underlying data manifold. It is empirically demonstrated that this measure is generally more predictive of generalization than all other margin-based measures. Furthermore, we find that this measurement also outperforms other contemporary complexity measures on a well-known generalization prediction benchmark. In addition, we analyze the utility and limitations of this approach and find that this metric is well aligned with intuitions expressed in prior work.