High-quality distractors are crucial to both the assessment and pedagogical value of multiple-choice questions (MCQs), where manually crafting ones that anticipate knowledge deficiencies or misconceptions among real students is difficult. Meanwhile, automated distractor generation, even with the help of large language models (LLMs), remains challenging for subjects like math. It is crucial to not only identify plausible distractors but also understand the error behind them. In this paper, we introduce DiVERT (Distractor Generation with Variational Errors Represented as Text), a novel variational approach that learns an interpretable representation of errors behind distractors in math MCQs. Through experiments on a real-world math MCQ dataset with 1,434 questions used by hundreds of thousands of students, we show that DiVERT, despite using a base open-source LLM with 7B parameters, outperforms state-of-the-art approaches using GPT-4o on downstream distractor generation. We also conduct a human evaluation with math educators and find that DiVERT leads to error labels that are of comparable quality to human-authored ones.

The development of artificial intelligence is a challenge that has occupied the industry and the scientific community for many years since John McCarthy coined the term in 1956 during a summer course at Dartmouth University, USA. During these 65 years, progress has been coming in waves, alternating moments of unbridled optimism with others of helpless disappointment. In the last decade we have witnessed a flourishing of solutions based on artificial intelligence that has led many to speak of a new golden age for this discipline. Today, the presence of artificial intelligence is already ubiquitous. We use it to receive purchase recommendations from our favorite mobile apps, to magically get our photos labelled or to get suspicious emails automatically discarded as "spam".