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Towards LLM-Empowered Knowledge Tracing via LLM-Student Hierarchical Behavior Alignment in Hyperbolic Space

Xingcheng Fu, Shengpeng Wang, Yisen Gao, Xianxian Li, Chunpei Li, Qingyun Sun, Dongran Yu

TL;DR

By optimizing hyperbolic curvature, the Large Language Model Hyperbolic Aligned Knowledge Tracing framework explicitly model the tree-like hierarchical structure of knowledge points, precisely characterizing differences in learning curve morphology for knowledge points at different levels.

Abstract

Knowledge Tracing (KT) diagnoses students' concept mastery through continuous learning state monitoring in education.Existing methods primarily focus on studying behavioral sequences based on ID or textual information.While existing methods rely on ID-based sequences or shallow textual features, they often fail to capture (1) the hierarchical evolution of cognitive states and (2) individualized problem difficulty perception due to limited semantic modeling. Therefore, this paper proposes a Large Language Model Hyperbolic Aligned Knowledge Tracing(L-HAKT). First, the teacher agent deeply parses question semantics and explicitly constructs hierarchical dependencies of knowledge points; the student agent simulates learning behaviors to generate synthetic data. Then, contrastive learning is performed between synthetic and real data in hyperbolic space to reduce distribution differences in key features such as question difficulty and forgetting patterns. Finally, by optimizing hyperbolic curvature, we explicitly model the tree-like hierarchical structure of knowledge points, precisely characterizing differences in learning curve morphology for knowledge points at different levels. Extensive experiments on four real-world educational datasets validate the effectiveness of our Large Language Model Hyperbolic Aligned Knowledge Tracing (L-HAKT) framework.

Towards LLM-Empowered Knowledge Tracing via LLM-Student Hierarchical Behavior Alignment in Hyperbolic Space

TL;DR

By optimizing hyperbolic curvature, the Large Language Model Hyperbolic Aligned Knowledge Tracing framework explicitly model the tree-like hierarchical structure of knowledge points, precisely characterizing differences in learning curve morphology for knowledge points at different levels.

Abstract

Knowledge Tracing (KT) diagnoses students' concept mastery through continuous learning state monitoring in education.Existing methods primarily focus on studying behavioral sequences based on ID or textual information.While existing methods rely on ID-based sequences or shallow textual features, they often fail to capture (1) the hierarchical evolution of cognitive states and (2) individualized problem difficulty perception due to limited semantic modeling. Therefore, this paper proposes a Large Language Model Hyperbolic Aligned Knowledge Tracing(L-HAKT). First, the teacher agent deeply parses question semantics and explicitly constructs hierarchical dependencies of knowledge points; the student agent simulates learning behaviors to generate synthetic data. Then, contrastive learning is performed between synthetic and real data in hyperbolic space to reduce distribution differences in key features such as question difficulty and forgetting patterns. Finally, by optimizing hyperbolic curvature, we explicitly model the tree-like hierarchical structure of knowledge points, precisely characterizing differences in learning curve morphology for knowledge points at different levels. Extensive experiments on four real-world educational datasets validate the effectiveness of our Large Language Model Hyperbolic Aligned Knowledge Tracing (L-HAKT) framework.
Paper Structure (26 sections, 9 equations, 4 figures, 3 tables)

This paper contains 26 sections, 9 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Works
  3. Knowlege Tracing
  4. Hyperbolic Machine Learning
  5. Preliminary
  6. Hyperbolic Geometry
  7. Problem Statement
  8. Method
  9. LLM-Based Teacher-Student Behavior Augmentation
  10. Teacher Agent.
  11. Student Agent.
  12. Hyperbolic Encoding & Alignment
  13. Relational-aware Hyperbolic Graph Neural Network
  14. Hyperbolic Constractive Alignment
  15. Hyperbolic Knowledge Tracing
  16. ...and 11 more sections

Figures (4)

  • Figure 1: The bar chart labels H-all, H-ek, H-e, and H-k denote hyperbolicity measures for student-question-knowledge, question-knowledge, question-question, and knowledge-knowledge relationships, respectively. Lower values indicate stronger structural alignment with tree-like or hyperbolic space characteristics.
  • Figure 2: Illustration of LLM-based Teacher-student Behavior Modeling and Data Augmentation.
  • Figure 3: Illustration of the architecture of L-HAKT.
  • Figure 4: Validation of Knowledge Graph Effectiveness. (a) Compare the predictive performance of ACC and AUC in four datasets using real data, adding synthetic data, and comparing alignment.(b)Teacher Agent generates a knowledge graph by parsing rich text information.Where (.) denotes the number of related concepts.