Abstract Gradient Training: A Unified Certification Framework for Data Poisoning, Unlearning, and Differential Privacy

The impact of inference-time data perturbation (e.g., adversarial attacks) has been extensively studied in machine learning, leading to well-established certification techniques for adversarial robustness. In contrast, certifying models against training data perturbations remains a relatively under-explored area. These perturbations can arise in three critical contexts: adversarial data poisoning, where an adversary manipulates training samples to corrupt model performance; machine unlearning, which requires certifying model behavior under the removal of specific training data; and differential privacy, where guarantees must be given with respect to substituting individual data points. This work introduces Abstract Gradient Training (AGT), a unified framework for certifying robustness of a given model and training procedure to training data perturbations, including bounded perturbations, the removal of data points, and the addition of new samples. By bounding the reachable set of parameters, i.e., establishing provable parameter-space bounds, AGT provides a formal approach to analyzing the behavior of models trained via first-order optimization methods.

Certificates of Differential Privacy and Unlearning for Gradient-Based Training

Proper data stewardship requires that model owners protect the privacy of individuals' data used during training. Whether through anonymization with differential privacy or the use of unlearning in non-anonymized settings, the gold-standard techniques for providing privacy guarantees can come with significant performance penalties or be too weak to provide practical assurances. In part, this is due to the fact that the guarantee provided by differential privacy represents the worst-case privacy leakage for any individual, while the true privacy leakage of releasing the prediction for a given individual might be substantially smaller or even, as we show, non-existent. This work provides a novel framework based on convex relaxations and bounds propagation that can compute formal guarantees (certificates) that releasing specific predictions satisfies $\epsilon=0$ privacy guarantees or do not depend on data that is subject to an unlearning request. Our framework offers a new verification-centric approach to privacy and unlearning guarantees, that can be used to further engender user trust with tighter privacy guarantees, provide formal proofs of robustness to certain membership inference attacks, identify potentially vulnerable records, and enhance current unlearning approaches. We validate the effectiveness of our approach on tasks from financial services, medical imaging, and natural language processing.

Certified Robustness to Data Poisoning in Gradient-Based Training

Modern machine learning pipelines leverage large amounts of public data, making it infeasible to guarantee data quality and leaving models open to poisoning and backdoor attacks. However, provably bounding model behavior under such attacks remains an open problem. In this work, we address this challenge and develop the first framework providing provable guarantees on the behavior of models trained with potentially manipulated data. In particular, our framework certifies robustness against untargeted and targeted poisoning as well as backdoor attacks for both input and label manipulations. Our method leverages convex relaxations to over-approximate the set of all possible parameter updates for a given poisoning threat model, allowing us to bound the set of all reachable parameters for any gradient-based learning algorithm. Given this set of parameters, we provide bounds on worst-case behavior, including model performance and backdoor success rate. We demonstrate our approach on multiple real-world datasets from applications including energy consumption, medical imaging, and autonomous driving.