提出无需梯度的持续遗忘方法，实现高效精确删知识且保护隐私

In Continual Learning (CL), using a Pre-Trained Model (PTM) as the feature extractor has become a popular practice. Accompanied by analytic classifiers, the PTM-based methods have achieved state-of-the-art performance in CL, in pursuit of the non-forgetting goal. Meanwhile, actively forgetting specific knowledge acquired during the CL phase is also essential in most service construction paradigms, for example, Mobile Crowd Sensing (MCS), where mobile edge nodes continuously collect sensory data and demand not only non-forgetting adaptation but also specific knowledge forgetting for privacy preservation. Thus, a unique problem, called Continual Unlearning (CU), arises when the forgetting requests show sequentially in CL. However, existing unlearning methods focus on single-shot joint forgetting and prove highly inadequate when applied to CU, including (1) violating the historical data privacy in CL and (2) vulnerably being overwhelmed or degraded with adversarially frequent requests. To handle the challenges of CU, we propose a gradient-free approach, called Analytic Continual Unlearning (ACU), for efficient and exact forgetting with historical data privacy preservation in PTM-based CL. In response to each unlearning request, our ACU recursively derives the analytical (i.e., closed-form) solutions via least squares in an interpretable manner. By meticulous design, our ACU is compatible with both sample-level and class-level unlearning requests. The theoretical and experimental evaluations validate our ACU's superiority in unlearning effectiveness, model fidelity, and system efficiency.