Machine unlearning facilitates personal data ownership, including the ``right to be forgotten''. The proliferation of applications of \emph{neural networks} (NNs) trained on users' personal data calls for the need to develop algorithms to unlearn an NN. Since retraining is costly, efficiency is often achieved through approximate unlearning which aims to unlearn a trained NN to be close to the retrained one (in distribution). Though the Newton's method has been used by previous works to approximately unlearn linear models, adapting it for unlearning an NN often encounters degenerate Hessians that make computing the Newton's update impossible. In this paper, we will first show that when coupled with naive yet often effective solutions to mitigate the degeneracy issue for unlearning, the Newton's method surprisingly suffers from catastrophic forgetting. To overcome this difficulty, we revise the Newton's method to include a theoretically justified regularizer and propose a cubic-regularized Newton's method for unlearning an NN. The cubic regularizer comes with the benefits of not requiring manual finetuning and affording a natural interpretation. Empirical evaluation on several models and real-world datasets shows that our method is more resilient to catastrophic forgetting and performs better than the baselines, especially in sequential unlearning.

机器去学习的研究，通过开发算法来近似去学习神经网络以增加个人数据拥有权，特别是``被遗忘的权利''。研究发现采用改进的三次正则化牛顿法在序列去学习中相比基准方法更具抗性和优越性。

关于牛顿法用于取消神经网络的研究