[Paper Review] Bi-CLKT: Bi-Graph Contrastive Learning based Knowledge Tracing

Xiangyu Song, Jianxin Li+4 more|arXiv (Cornell University)|Jan 22, 2022

Online Learning and Analytics4 citations

TL;DR

This paper proposes Bi-CLKT, a novel knowledge tracing model that leverages bi-graph contrastive learning to jointly learn exercise and concept representations using both 'exercise-to-exercise' (E2E) and 'concept-to-concept' (C2C) relational subgraphs. By applying node-level and graph-level contrastive learning, and integrating representations via a joint loss, Bi-CLKT achieves state-of-the-art performance across four real-world datasets, outperforming existing methods by up to 3% in accuracy and AUC.

ABSTRACT

The goal of Knowledge Tracing (KT) is to estimate how well students have mastered a concept based on their historical learning of related exercises. The benefit of knowledge tracing is that students' learning plans can be better organised and adjusted, and interventions can be made when necessary. With the recent rise of deep learning, Deep Knowledge Tracing (DKT) has utilised Recurrent Neural Networks (RNNs) to accomplish this task with some success. Other works have attempted to introduce Graph Neural Networks (GNNs) and redefine the task accordingly to achieve significant improvements. However, these efforts suffer from at least one of the following drawbacks: 1) they pay too much attention to details of the nodes rather than to high-level semantic information; 2) they struggle to effectively establish spatial associations and complex structures of the nodes; and 3) they represent either concepts or exercises only, without integrating them. Inspired by recent advances in self-supervised learning, we propose a Bi-Graph Contrastive Learning based Knowledge Tracing (Bi-CLKT) to address these limitations. Specifically, we design a two-layer contrastive learning scheme based on an "exercise-to-exercise" (E2E) relational subgraph. It involves node-level contrastive learning of subgraphs to obtain discriminative representations of exercises, and graph-level contrastive learning to obtain discriminative representations of concepts. Moreover, we designed a joint contrastive loss to obtain better representations and hence better prediction performance. Also, we explored two different variants, using RNN and memory-augmented neural networks as the prediction layer for comparison to obtain better representations of exercises and concepts respectively. Extensive experiments on four real-world datasets show that the proposed Bi-CLKT and its variants outperform other baseline models.

Motivation & Objective

• To address limitations in existing knowledge tracing models that overlook exercise-level differences and fail to model complex node relationships.
• To improve predictive performance by integrating both exercise and concept representations using self-supervised contrastive learning.
• To overcome data sparsity and model inaccuracies in cross-concept exercises by leveraging higher-order relational structures.
• To explore the effectiveness of different augmentation, embedding, and prediction mechanisms in a unified contrastive learning framework.
• To develop a unified model that captures both local (exercise-level) and global (concept-level) semantic information for better knowledge tracing.

Proposed method

• The model constructs two subgraphs: an 'exercise-to-exercise' (E2E) subgraph and a 'concept-to-concept' (C2C) subgraph based on student interaction patterns.
• Node-level contrastive learning is applied to E2E subgraphs to learn discriminative exercise representations.
• Graph-level contrastive learning is applied to C2C subgraphs to learn discriminative concept representations.
• A joint contrastive loss is designed to jointly optimize both E2E and C2C representations, enhancing feature discrimination.
• Two variants are implemented: Bi-CLKT-R using a recurrent neural network and Bi-CLKT-M using a memory-augmented network in the prediction layer.
• Exercise representations are formed by concatenating E2E and C2C embeddings, which are then used for final prediction of student performance.

Experimental results

Research questions

• RQ1 Can bi-graph contrastive learning improve knowledge tracing by jointly modeling exercise and concept relationships?
• RQ2 How do different augmentation strategies (e.g., degree, PageRank centrality) affect model generalization across datasets?
• RQ3 Does combining E2E and C2C embeddings yield better performance than using either alone?
• RQ4 Which prediction mechanism—RNN or memory-augmented network—leads to superior performance in knowledge tracing?
• RQ5 To what extent does the joint contrastive loss enhance representation learning and downstream prediction accuracy?

Key findings

• Bi-CLKT-R achieved an AUC of 0.875 and accuracy of 0.802 on the ASSISTment 2009 dataset, outperforming all baselines by at least 3%.
• The model with PageRank centrality augmentation achieved the best performance on three out of four datasets, including 0.865 AUC on STATICS 2011.
• Concatenating E2E and C2C embeddings yielded significantly better results than using either embedding alone, with the highest AUC of 0.875 on ASSISTment 2009.
• The Bi-CLKT-R variant outperformed Bi-CLKT-M by at least 2% on three datasets, particularly excelling on ASSISTment 2009 and STATICS 2011.
• The ablation study confirmed that the joint contrastive loss and multi-level graph learning significantly improve representation quality and prediction accuracy.
• The model demonstrated strong generalization, as different augmentation methods (degree vs. PageRank) performed well across diverse datasets without overfitting.