BoxCD: Leveraging Contrastive Probabilistic Box Embedding for Effective and Efficient Learner Modeling

In digital education, Cognitive Diagnosis (CD) is essential for modeling learners' cognitive states, such as problem-solving ability and knowledge proficiency, by analyzing their response data, like answer correctness. However, traditional CD methods struggle with effectiveness and efficiency. They fail to capture the diversity and uncertainty of learners' cognitive states. Additionally, response prediction can be time-consuming. To address these issues, we propose BoxCD, a contrastive probabilistic box embedding model for cognitive diagnosis. BoxCD utilizes high-dimensional axis-aligned hyper-rectangles (boxes) to represent learners and exercises, with the volume of intersecting boxes used to predict learners' responses. This approach effectively captures semantic diversity and uncertainty while enhancing diagnostic effectiveness. To stabilize box embeddings, we integrate contrastive learning objectives with response prediction goals, optimizing the distance between positive and negative samples of learner and exercise boxes to improve uniformity. Additionally, we develop a rank-based response prediction method that leverages the geometric properties of box embeddings to assess learners' response correctness efficiently. Comprehensive experiments on two real-world datasets demonstrate that BoxCD outperforms traditional CD models in effectiveness and efficiency. This showcases its potential to enhance personalized learning in digital education platforms.