The heightened emphasis on the regulation of deep generative models, propelled by escalating concerns pertaining to privacy and compliance with regulatory frameworks, underscores the imperative need for precise control mechanisms over these models. This urgency is particularly underscored by instances in which generative models generate outputs that encompass objectionable, offensive, or potentially injurious content. In response, machine unlearning has emerged to selectively forget specific knowledge or remove the influence of undesirable data subsets from pre-trained models. However, modern machine unlearning approaches typically assume access to model parameters and architectural details during unlearning, which is not always feasible. In multitude of downstream tasks, these models function as black-box systems, with inaccessible pre-trained parameters, architectures, and training data. In such scenarios, the possibility of filtering undesired outputs becomes a practical alternative. The primary goal of this study is twofold: first, to elucidate the relationship between filtering and unlearning processes, and second, to formulate a methodology aimed at mitigating the display of undesirable outputs generated from models characterized as black-box systems. Theoretical analysis in this study demonstrates that, in the context of black-box models, filtering can be seen as a form of weak unlearning. Our proposed \textbf{\textit{Feature Aware Similarity Thresholding(FAST)}} method effectively suppresses undesired outputs by systematically encoding the representation of unwanted features in the latent space.

The increased attention to regulating the outputs of deep generative models, driven by growing concerns about privacy and regulatory compliance, has highlighted the need for effective control over these models. This necessity arises from instances where generative models produce outputs containing undesirable, offensive, or potentially harmful content. To tackle this challenge, the concept of machine unlearning has emerged, aiming to forget specific learned information or to erase the influence of undesired data subsets from a trained model. The objective of this work is to prevent the generation of outputs containing undesired features from a pre-trained GAN where the underlying training data set is inaccessible. Our approach is inspired by a crucial observation: the parameter space of GANs exhibits meaningful directions that can be leveraged to suppress specific undesired features. However, such directions usually result in the degradation of the quality of generated samples. Our proposed method, known as 'Adapt-then-Unlearn,' excels at unlearning such undesirable features while also maintaining the quality of generated samples. This method unfolds in two stages: in the initial stage, we adapt the pre-trained GAN using negative samples provided by the user, while in the subsequent stage, we focus on unlearning the undesired feature. During the latter phase, we train the pre-trained GAN using positive samples, incorporating a repulsion regularizer. This regularizer encourages the model's parameters to be away from the parameters associated with the adapted model from the first stage while also maintaining the quality of generated samples. To the best of our knowledge, our approach stands as first method addressing unlearning in GANs. We validate the effectiveness of our method through comprehensive experiments.

ABSTRACT The standard approach to compressive sampling considers recovering an unknown deterministic signal with certain known structure, and designing the sub-sampling pattern and recovery algorithm based on the known structure. This approach requires looking for a good representation that reveals the signal structure, and solving a non-smooth convex minimization problem (e.g., basis pursuit). In this paper, another approach is considered: We learn a good sub-sampling pattern based on available training signals, without knowing the signal structure in advance, and reconstruct an accordingly sub-sampled signal by computationally much cheaper linear reconstruction. We provide a theoretical guarantee on the recovery error, and show via experiments on real-world MRI data the effectiveness of the proposed compressive MRI scheme. Index Terms-- Compressive sampling, magnetic resonance imaging (MRI), learning, least squares estimation, submodular minimization 1. INTRODUCTION The standard theory of compressive sampling (CS) considers recovering an unknown deterministic signal with certain known structure, and designing sampling and recovery schemes based on the known structure [11].