Measuring Generalization with Optimal Transport
This work addresses the challenge of bridging theoretical error bounds with empirical observations in deep learning, offering a method to better predict generalization for researchers and practitioners.
The paper tackles the problem of understanding generalization in deep neural networks by developing margin-based generalization bounds normalized with optimal transport costs, which robustly predict generalization error on large-scale datasets.
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}.