  Understanding the generalization of deep neural networks is one of the most
important tasks in deep learning. Although much progress has been made,
theoretical error bounds still often behave disparately from empirical
observations. In this work, we develop margin-based generalization bounds,
where the margins are normalized with optimal transport costs between
independent random subsets sampled from the training distribution. In
particular, the optimal transport cost can be interpreted as a generalization
of variance which captures the structural properties of the learned feature
space. Our bounds robustly predict the generalization error, given training
data and network parameters, on large scale datasets. Theoretically, we
demonstrate that the concentration and separation of features play crucial
roles in generalization, supporting empirical results in the literature. The
code is available at \url{https://github.com/chingyaoc/kV-Margin}.
