Efficient and Generalizable Certified Unlearning: A Hessian-free Recollection Approach

Machine unlearning strives to uphold the data owners' right to be forgotten by enabling models to selectively forget specific data. Recent advances suggest precomputing and storing statistics extracted from second-order information and implementing unlearning through Newton-style updates. However, the theoretical analysis of these works often depends on restrictive assumptions of convexity and smoothness, and those mentioned operations on Hessian matrix are extremely costly. As a result, applying these works to high-dimensional models becomes challenging. In this paper, we propose an efficient Hessian-free certified unlearning. We propose to maintain a statistical vector for each data, computed through affine stochastic recursion approximation of the difference between retrained and learned models. Our analysis does not involve inverting Hessian and thus can be extended to non-convex non-smooth objectives. Under same assumptions, we demonstrate advancements of proposed method beyond the state-of-the-art theoretical studies, in terms of generalization, unlearning guarantee, deletion capacity, and computation/storage complexity, and we show that the unlearned model of our proposed approach is close to or same as the retrained model. Based on the strategy of recollecting statistics for forgetting data, we develop an algorithm that achieves near-instantaneous unlearning as it only requires a vector addition operation. Experiments demonstrate that the proposed scheme surpasses existing results by orders of magnitude in terms of time/storage costs, while also enhancing accuracy.