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One of the remarkable properties of robust computer vision models is thattheir input-gradients are often aligned with human perception, referred to inthe literature as perceptually-aligned gradients (PAGs). Despite only beingtrained for classification, PAGs cause robust models to have rudimentarygenerative capabilities, including image generation, denoising, andin-painting. However, the underlying mechanisms behind these phenomena remainunknown. In this work, we provide a first explanation of PAGs via\emph{off-manifold robustness}, which states that models must be more robustoff- the data manifold than they are on-manifold. We first demonstratetheoretically that off-manifold robustness leads input gradients to lieapproximately on the data manifold, explaining their perceptual alignment. Wethen show that Bayes optimal models satisfy off-manifold robustness, andconfirm the same empirically for robust models trained via gradient normregularization, noise augmentation, and randomized smoothing. Quantifying theperceptual alignment of model gradients via their similarity with the gradientsof generative models, we show that off-manifold robustness correlates well withperceptual alignment. Finally, based on the levels of on- and off-manifoldrobustness, we identify three different regimes of robustness that affect bothperceptual alignment and model accuracy: weak robustness, bayes-alignedrobustness, and excessive robustness.

Which Models have Perceptually-Aligned Gradients? An Explanation via Off-Manifold Robustness