Adversarial robustness for latent models: Revisiting the robust-standard accuracies tradeoff
This addresses the robustness-generalization tradeoff in adversarial machine learning, offering a theoretical insight that could benefit practitioners in security-sensitive domains, though it appears incremental by building on existing tradeoff studies.
The paper revisits the tradeoff between standard and robust accuracy in adversarial training for latent models, showing that when data has a low-dimensional manifold structure, models can achieve near-optimal performance in both measures, supported by theoretical analysis and numerical experiments on datasets like MNIST.
Over the past few years, several adversarial training methods have been proposed to improve the robustness of machine learning models against adversarial perturbations in the input. Despite remarkable progress in this regard, adversarial training is often observed to drop the standard test accuracy. This phenomenon has intrigued the research community to investigate the potential tradeoff between standard accuracy (a.k.a generalization) and robust accuracy (a.k.a robust generalization) as two performance measures. In this paper, we revisit this tradeoff for latent models and argue that this tradeoff is mitigated when the data enjoys a low-dimensional structure. In particular, we consider binary classification under two data generative models, namely Gaussian mixture model and generalized linear model, where the features data lie on a low-dimensional manifold. We develop a theory to show that the low-dimensional manifold structure allows one to obtain models that are nearly optimal with respect to both, the standard accuracy and the robust accuracy measures. We further corroborate our theory with several numerical experiments, including Mixture of Factor Analyzers (MFA) model trained on the MNIST dataset.