用深度学习自动学出隐藏知识点，提升个性化推荐效果

Personalized recommendation is a key feature of intelligent tutoring systems, typically relying on accurate models of student knowledge. Knowledge Tracing (KT) models enable this by estimating a student's mastery based on their historical interactions. Many KT models rely on human-annotated knowledge concepts (KCs), which tag each exercise with one or more skills or concepts believed to be necessary for solving it. However, these KCs can be incomplete, error-prone, or overly general. In this paper, we propose a deep learning model that learns sparse binary representations of exercises, where each bit indicates the presence or absence of a latent concept. We refer to these representations as auxiliary KCs. These representations capture conceptual structure beyond human-defined annotations and are compatible with both classical models (e.g., BKT) and modern deep learning KT architectures. We demonstrate that incorporating auxiliary KCs improves both student modeling and adaptive exercise recommendation. For student modeling, we show that augmenting classical models like BKT with auxiliary KCs leads to improved predictive performance. For recommendation, we show that using auxiliary KCs enhances both reinforcement learning-based policies and a simple planning-based method (expectimax), resulting in measurable gains in student learning outcomes within a simulated student environment.