Machine unlearning is a key requirement of many data protection regulations such as GDPR. Prior work on unlearning has mostly considered superficial unlearning tasks where a single or a few related pieces of information are required to be removed. However, the task of unlearning a fact is much more challenging in recent large language models (LLMs), because the facts in LLMs can be deduced from each other. In this work, we investigate whether current unlearning methods for LLMs succeed beyond superficial unlearning of facts. Specifically, we formally propose a framework and a definition for deep unlearning facts that are interrelated. We design the metric, recall, to quantify the extent of deep unlearning. To systematically evaluate deep unlearning, we construct a synthetic dataset EDU-RELAT, which consists of a synthetic knowledge base of family relationships and biographies, together with a realistic logical rule set that connects them. We use this dataset to test four unlearning methods in four LLMs at different sizes. Our findings reveal that in the task of deep unlearning only a single fact, they either fail to properly unlearn with high recall, or end up unlearning many other irrelevant facts. Our dataset and code are publicly available at: https://github.com/wrh14/deep_unlearning.

The automatic generation of Multiple Choice Questions (MCQ) has the potential to reduce the time educators spend on student assessment significantly. However, existing evaluation metrics for MCQ generation, such as BLEU, ROUGE, and METEOR, focus on the n-gram based similarity of the generated MCQ to the gold sample in the dataset and disregard their educational value. They fail to evaluate the MCQ's ability to assess the student's knowledge of the corresponding target fact. To tackle this issue, we propose a novel automatic evaluation metric, coined Knowledge Dependent Answerability (KDA), which measures the MCQ's answerability given knowledge of the target fact. Specifically, we first show how to measure KDA based on student responses from a human survey. Then, we propose two automatic evaluation metrics, KDA_disc and KDA_cont, that approximate KDA by leveraging pre-trained language models to imitate students' problem-solving behavior. Through our human studies, we show that KDA_disc and KDA_soft have strong correlations with both (1) KDA and (2) usability in an actual classroom setting, labeled by experts. Furthermore, when combined with n-gram based similarity metrics, KDA_disc and KDA_cont are shown to have a strong predictive power for various expert-labeled MCQ quality measures.