Reproduce “Effect of Ambient-Intrinsic Dimension Gap on Adversarial Vulnerability” on OpenResearch

About this paper

Rajdeep Haldar, Yue Xing, Qifan Song

Research from Purdue and Michigan State demonstrates that imperceptible adversarial attacks are a direct consequence of the "dimension gap" between the intrinsic dimensionality of data and its higher-dimensional ambient space. This gap leads to off-manifold perturbations with vanishingly small l-infinity strength as the gap increases, while on-manifold attacks remain perceptible.

Key insights

• The "dimension gap" between the intrinsic and ambient dimensions of data is a fundamental cause of imperceptible, "unnatural" adversarial attacks.
• The strength of imperceptible, off-manifold adversarial perturbations scales inversely with the dimension gap, indicating they become easier to generate as the gap widens.
• Adversarial vulnerability stems from the implicit bias of training dynamics interacting with the geometric properties of low-dimensional data at network convergence.

Summary by alphaXiv.