  The field of Deep Learning is rich with empirical evidence of human-like
performance on a variety of prediction tasks. However, despite these successes,
the recent Predicting Generalization in Deep Learning (PGDL) NeurIPS 2020
competition suggests that there is a need for more robust and efficient
measures of network generalization. In this work, we propose a new framework
for evaluating the generalization capabilities of trained networks. We use
perturbation response (PR) curves that capture the accuracy change of a given
network as a function of varying levels of training sample perturbation. From
these PR curves, we derive novel statistics that capture generalization
capability. Specifically, we introduce two new measures for accurately
predicting generalization gaps: the Gi-score and Pal-score, which are inspired
by the Gini coefficient and Palma ratio (measures of income inequality), that
accurately predict generalization gaps. Using our framework applied to intra
and inter-class sample mixup, we attain better predictive scores than the
current state-of-the-art measures on a majority of tasks in the PGDL
competition. In addition, we show that our framework and the proposed
statistics can be used to capture to what extent a trained network is invariant
to a given parametric input transformation, such as rotation or translation.
Therefore, these generalization gap prediction statistics also provide a useful
means for selecting optimal network architectures and hyperparameters that are
invariant to a certain perturbation.
