HiCD: Hyperbolic Insight Through Decomposed Educational Graphs for Long-Tailed Cognitive Diagnosis

Abstract

Cognitive diagnosis (CD) aims to infer students' mastery of knowledge concepts from their response behaviors and constitutes a core component of intelligent education and personalized learning. However, existing graph-based CD models struggle to handle the pronounced long-tail distributions in educational data, where most students and concepts interact with only a limited number of exercises, resulting in suboptimal representation learning and poor generalization to low-frequency instances. To address this challenge, we propose HiCD (Hyperbolic insight for Cognitive Diagnosis), a novel hyperbolic model that embeds students, exercises, and concepts into non-Euclidean space. By exploiting the exponential representational capacity of hyperbolic geometry, HiCD naturally captures hierarchical and sparse structures, effectively alleviating long-tail bias while enhancing embedding expressiveness. A key contribution of HiCD is a hyperbolic diagnostic function that operates directly on the manifold, avoiding Euclidean approximations and preserving geometric consistency. Moreover, HiCD decomposes the educational graph into three semantically distinct subgraphs and assigns each a dedicated curvature, enabling adaptive geometric modeling of heterogeneous relations. Extensive experiments on multiple benchmark datasets demonstrate that HiCD consistently improves diagnostic accuracy and robustness, particularly under severe long-tail scenarios. The source code is available at: https://github.com/CyberXie/HiCD.