Machine unlearning (MU) has emerged to enhance the privacy and trustworthiness of deep neural networks. Approximate MU is a practical method for large-scale models. Our investigation into approximate MU starts with identifying the steepest descent direction, minimizing the output Kullback-Leibler divergence to exact MU inside a parameters' neighborhood. This probed direction decomposes into three components: weighted forgetting gradient ascent, fine-tuning retaining gradient descent, and a weight saliency matrix. Such decomposition derived from Euclidean metric encompasses most existing gradient-based MU methods. Nevertheless, adhering to Euclidean space may result in sub-optimal iterative trajectories due to the overlooked geometric structure of the output probability space. We suggest embedding the unlearning update into a manifold rendered by the remaining geometry, incorporating second-order Hessian from the remaining data. It helps prevent effective unlearning from interfering with the retained performance. However, computing the second-order Hessian for large-scale models is intractable. To efficiently leverage the benefits of Hessian modulation, we propose a fast-slow parameter update strategy to implicitly approximate the up-to-date salient unlearning direction. Free from specific modal constraints, our approach is adaptable across computer vision unlearning tasks, including classification and generation. Extensive experiments validate our efficacy and efficiency. Notably, our method successfully performs class-forgetting on ImageNet using DiT and forgets a class on CIFAR-10 using DDPM in just 50 steps, compared to thousands of steps required by previous methods.

该研究解决了现有机器遗忘方法在大规模模型中效率低下的问题，提出了一种通过嵌入剩余几何的方式来优化遗忘更新的新方法。研究结果表明，该方法能够在不影响保留性能的情况下，显著提升遗忘效率，在ImageNet和CIFAR-10等数据集上验证了其有效性。

统一的基于梯度的机器遗忘与剩余几何增强