Is Adversarial Training with Compressed Datasets Effective?

Dataset Condensation (DC) refers to the recent class of dataset compression methods that generate a smaller, synthetic, dataset from a larger dataset. This synthetic dataset aims to retain the essential information of the original dataset, enabling models trained on it to achieve performance levels comparable to those trained on the full dataset. Most current DC methods have mainly concerned with achieving high test performance with limited data budget, and have not directly addressed the question of adversarial robustness. In this work, we investigate the impact of adversarial robustness on models trained with compressed datasets. We show that the compressed datasets obtained from DC methods are not effective in transferring adversarial robustness to models. As a solution to improve dataset compression efficiency and adversarial robustness simultaneously, we present a robustness-aware dataset compression method based on finding the Minimal Finite Covering (MFC) of the dataset. The proposed method is (1) provably robust by minimizing the generalized adversarial loss, (2) more effective than DC methods when applying adversarial training over MFC, (3) obtained by a one-time computation and is applicable for any model.