Adversarial training and the dimension gap theory are closely related in the context of robust machine learning models. Adversarial training involves training a model on adversarially perturbed data to improve its robustness against such attacks. The dimension gap theory, as presented in the context above, highlights how the difference between intrinsic and ambient dimensions can lead to vulnerabilities in machine learning models.
When considering adversarial training in relation to the dimension gap theory, increasing the ambient dimension through padding images can help create a more challenging dataset for adversarial training. By expanding the input space with additional dimensions, we effectively increase the complexity of potential attacks that need to be defended against during training. This process aligns well with addressing vulnerabilities stemming from off-manifold or unnatural attacks caused by significant dimension gaps.