  Machine unlearning as an emerging research topic for data regulations, aims
to adjust a trained model to approximate a retrained one that excludes a
portion of training data. Previous studies showed that class-wise unlearning is
successful in forgetting the knowledge of a target class, through gradient
ascent on the forgetting data or fine-tuning with the remaining data. However,
while these methods are useful, they are insufficient as the class label and
the target concept are often considered to coincide. In this work, we decouple
them by considering the label domain mismatch and investigate three problems
beyond the conventional all matched forgetting, e.g., target mismatch, model
mismatch, and data mismatch forgetting. We systematically analyze the new
challenges in restrictively forgetting the target concept and also reveal
crucial forgetting dynamics in the representation level to realize these tasks.
Based on that, we propose a general framework, namely, TARget-aware Forgetting
(TARF). It enables the additional tasks to actively forget the target concept
while maintaining the rest part, by simultaneously conducting annealed gradient
ascent on the forgetting data and selected gradient descent on the
hard-to-affect remaining data. Empirically, various experiments under the newly
introduced settings are conducted to demonstrate the effectiveness of our TARF.
