As public consciousness regarding the collection and use of personal information by corporations grows, it is of increasing importance that consumers be active participants in the curation of corporate datasets. In light of this, data governance frameworks such as the General Data Protection Regulation (GDPR) have outlined the right to be forgotten as a key principle allowing individuals to request that their personal data be deleted from the databases and models used by organizations. To achieve forgetting in practice, several machine unlearning methods have been proposed to address the computational inefficiencies of retraining a model from scratch with each unlearning request. While efficient online alternatives to retraining, it is unclear how these methods impact other properties critical to real-world applications, such as fairness. In this work, we propose the first fair machine unlearning method that can provably and efficiently unlearn data instances while preserving group fairness. We derive theoretical results which demonstrate that our method can provably unlearn data instances while maintaining fairness objectives. Extensive experimentation with real-world datasets highlight the efficacy of our method at unlearning data instances while preserving fairness.

One of the remarkable properties of robust computer vision models is that their input-gradients are often aligned with human perception, referred to in the literature as perceptually-aligned gradients (PAGs). Despite only being trained for classification, PAGs cause robust models to have rudimentary generative capabilities, including image generation, denoising, and in-painting. However, the underlying mechanisms behind these phenomena remain unknown. In this work, we provide a first explanation of PAGs via \emph{off-manifold robustness}, which states that models must be more robust off- the data manifold than they are on-manifold. We first demonstrate theoretically that off-manifold robustness leads input gradients to lie approximately on the data manifold, explaining their perceptual alignment. We then show that Bayes optimal models satisfy off-manifold robustness, and confirm the same empirically for robust models trained via gradient norm regularization, noise augmentation, and randomized smoothing. Quantifying the perceptual alignment of model gradients via their similarity with the gradients of generative models, we show that off-manifold robustness correlates well with perceptual alignment. Finally, based on the levels of on- and off-manifold robustness, we identify three different regimes of robustness that affect both perceptual alignment and model accuracy: weak robustness, bayes-aligned robustness, and excessive robustness.