Title: On the Impact of Hard Adversarial Instances on Overfitting in Adversarial Training. Abstract: Adversarial training is a popular method to robustify models against adversarial attacks.
However, it exhibits much more severe overfitting than training on clean inputs.
In this work, we investigate this phenomenon from the perspective of training instances, i.e., training input-target pairs.
To this end, we provide a quantitative and model-agnostic metric measuring the difficulty of an instance in the training set and analyze the model's behavior on instances of different difficulty levels.
This lets us show that the decay in generalization performance of adversarial training is a result of the model's attempt to fit hard adversarial instances.
We theoretically verify our observations for both linear and general nonlinear models, proving that models trained on hard instances have worse generalization performance than ones trained on easy instances.
In addition, this gap in generalization performance is larger in adversarial training.
Finally, we investigate solutions to mitigating adversarial overfitting in several scenarios, including when relying on fast adversarial training and in the context of fine-tuning a pretrained model with additional data.
Our results demonstrate adaptively using training data can improve model's robustness.