Erasing Without Remembering: Implicit Knowledge Forgetting in Large Language Models

In this paper, we investigate knowledge forgetting in large language models with a focus on its generalisation--ensuring that models forget not only specific training samples but also related implicit knowledge. To this end, we begin by identifying a broader unlearning scope that includes both target data and logically associated samples, including rephrased, subject-replaced, one-hop reasoned, and relation-reversed data. To rigorously evaluate generalisation, we introduce UGBench, the first comprehensive benchmark specifically designed to assess the unlearning of in-scope implicit knowledge covering 13 state-of-the-art methods across three datasets. UGBench reveals that unlearned models can still recall paraphrased answers and retain target facts in intermediate layers. This motivates us to take a preliminary step toward more generalised implicit knowledge forgetting by proposing PerMU, a novel probability perturbation-based unlearning paradigm. PerMU simulates adversarial unlearning samples to eliminate fact-related tokens from the logit distribution, collectively reducing the probabilities of all answer-associated tokens. Experiments are conducted on a diverse range of datasets, including TOFU, Harry Potter, ZsRE, WMDP, and MUSE, using models ranging from 1.3B to 13B in scale. The results demonstrate that PerMU delivers up to a 50.40% improvement in unlearning vanilla target data while maintaining a 40.73% boost in forgetting implicit knowledge. Our code can be found in this https URL.