Source-linked AI summary
Bi-CLKT: Bi-Graph Contrastive Learning based Knowledge Tracing
Xiangyu Song, Jianxin Li, Qi Lei, Wei Zhao, Yunliang Chen, Ajmal Mian
TL;DR
Knowledge Tracing needs to model student mastery while addressing limitations in concept-focused and graph-based methods. Bi-CLKT uses two-layer contrastive learning over exercise and concept relations, and experiments report consistent improvements over baseline KT models across four datasets.
Problem
Existing KT and graph-based methods can overlook exercise-specific differences, complex associations, or integrated exercise–concept representations.
Method
Bi-CLKT constructs exercise influence subgraphs and applies node-level and graph-level contrastive learning to learn E2E and C2C representations.
Results
Bi-CLKT consistently outperforms baseline KT models across four datasets, with reported improvements of at least 5% over other baseline models.
Takeaways & Limitations
The framework provides a self-supervised KT approach that integrates exercise and concept structural information for prediction.
Takeaways & Limitations
The approach assumes that exercises jointly answered correctly by many students have high similarity or correlation, and its view-generation analysis adopts an extension hypothesis.
Abstract
from arXiv · showhide
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.
1. Introduction
Knowledge Tracing predicts students’ mastery from exercise interactions, but existing methods often overlook exercise-specific differences, cross-concept structure, and integrated exercise–concept information. Bi-CLKT addresses these issues with a two-layer self-supervised contrastive framework and shows stronger performance across four benchmark datasets.
- Knowledge Tracing predicts whether students will correctly answer subsequent exercises using their historical interactions and corresponding concepts.
- Existing methods often model concepts rather than distinguishing exercises, despite differences in exercise difficulty affecting correctness probabilities.
- Traditional KT models struggle with exercises associated with multiple concepts, often splitting them into single-concept exercises and reducing overall accuracy.
- Graph-based KT efforts may emphasize node details, fail to establish complex spatial associations, or represent concepts and exercises separately.
- Bi-CLKT uses global- and local-bilayer contrastive learning to extract E2E and C2C relational information, combining exercise and concept representations for prediction.
- Experiments on four real-world datasets report that Bi-CLKT and its variants outperform baseline models, with ablations used to examine individual modules.
2. Related Work
Related work spans traditional and deep Knowledge Tracing, self-supervised learning, and graph contrastive learning. These approaches motivate combining exercise information with concept representations while balancing local and global graph structure.
- 2.1. Knowledge Tracing: Traditional KT includes Bayesian Knowledge Tracing, factor-analysis models, item response theory, and performance factor analysis.
- 2.1. Knowledge Tracing: Deep KT methods such as DKT and DKVMN learn representations for large datasets, but classical models often omit exercise features.
- 2.1. Knowledge Tracing: Exercise-aware methods incorporate textual exercise information or problem difficulty, although collecting text can be difficult and may interfere with embeddings.
- 2.2. Self-supervised Learning: Self-supervised learning includes generative and contrastive branches; graph generative methods reconstruct graph structure and properties from learned node embeddings.
- 2.3. Contrastive Learning on Graphs: Graph contrastive learning brings similar representations closer and dissimilar ones farther apart while balancing local and global structural information.
3. Preliminary and Problem Statement
The paper formulates KT as predicting the next exercise response from a student’s interaction sequence and mastery of associated concepts. It constructs exercise influence subgraphs to represent E2E and C2C relations, then learns combined representations for prediction.
- 3. Preliminary and Problem Statement: The KT task records exercise–response sequences and predicts the correctness of the student’s next exercise.
- 3.1. Problem Definition: The method extracts E2E relationships from exercise–concept sequence data and constructs an influence graph for each concept.
- 3.1. Problem Definition: The influence graph assumes that exercises jointly answered correctly by many students have stronger similarity or correlation and therefore higher edge weights.
- 3.1. Problem Definition: An exercise influence subgraph represents exercises as vertices and exercise interactions as edges, with edge weights based on co-occurrence and co-correctness information.
- 3.1. Problem Definition: The graph construction supplies E2E and C2C relational information, addressing models’ difficulty with linking concepts and handling multi-concept exercises.
- 3.1. Problem Definition: Node-level and graph-level GCNs learn exercise and concept embeddings, which are combined as exercise attributes for the prediction layer.
4. The Bi-Graph Contrastive Knowledge Tracing
Bi-CLKT combines node-level and graph-level contrastive learning to capture exercise-to-exercise and concept-to-concept relations. It uses tailored graph augmentations, GCN encoders, projection heads, and a joint NT-Xent objective.
- The framework generates paired graph views through edge removal, node removal, and node-feature masking, using separate augmentation processes for the exercise and concept levels.
- Bi-CLKT integrates local exercise-to-exercise and global concept-to-concept relational information in one bi-graph contrastive learning framework.
- Node-level GCNs learn exercise embeddings, while graph-level GCNs learn concept embeddings for the two contrastive learning layers.
- Exercise-level augmentation preferentially removes less important edges or nodes while preserving important graph structure.
- Node representations concatenate linearly transformed features from encoder layers, and graph representations use a sigmoid READOUT over summed node representations.
- Bi-CLKT maps representations into a shared latent space and uses NT-Xent to differentiate overlapping positive and negative samples in both contrastive modules.
5. Experimental Settings and Results
The study evaluates Bi-CLKT on four real-world knowledge-tracing datasets and uses self-supervised representations for downstream classification experiments. It also includes ablation experiments to assess the contribution of each module.
- Experiments evaluate Bi-CLKT on four widely used knowledge-tracing datasets: ASSISTment 2009, ASSISTment 2015, ASSISTment Challenge, and STATICS 2011.
- The study conducts extensive ablation experiments to validate the role of each Bi-CLKT module and improve model interpretability.
- Bi-CLKT representations are evaluated through node-level and graph-level classification using a simple logistic-regression classifier.
- STATICS 2011 contains 189,297 interactions from 333 students across 1,223 concepts, making it the most intensive of the four datasets.
5.2. Evaluation Methods
Bi-CLKT is compared with classical, recurrent, memory-based, self-attentive, exercise-enhanced, and Transformer-based knowledge-tracing baselines.
- The evaluation compares Bi-CLKT with Bayesian Knowledge Tracing and Deep Knowledge Tracing as classical and recurrent baselines.
- Dynamic Key-Value Memory Networks provides the memory-augmented baseline by storing and updating concepts and students’ learning states.
- SAKT represents a self-attentive baseline that predicts from relevant historical exercises rather than modeling interactions with recurrent neural networks.
- EKT extends exercise-enhanced recurrent modeling by incorporating the knowledge concepts present in each exercise.
- SAINT+ is a Transformer-based baseline that separately embeds exercise and response information and includes elapsed-time and lag-time features.
5.3. Experiment discussion
Across four datasets, Bi-CLKT consistently outperforms the baseline knowledge-tracing models and remains competitive with recent deep-learning methods.
- AUC and Accuracy are used to evaluate predictive performance in the comparison.
- Bi-CLKT consistently outperforms all other baseline knowledge-tracing models by a wide margin across the evaluated datasets.
- Bi-CLKT also competes with models based on the latest deep-learning methods on all four datasets.
5.4. Overall Performance
Bi-CLKT achieves the best predictive performance across all four datasets and improves on baseline models by at least 5%.
- Bi-CLKT achieves the best AUC and ACC performance on ASSISTment 2009, ASSISTment 2015, ASSISTment Challenge3, and STATICS 2011.Table 2 compares these metrics across the four datasets, with best runs marked in boldface.
- Deep learning models consistently outperform traditional machine-learning models such as BKT among the baselines.
- SAINT+ is the strongest baseline, while Bi-CLKT continues to advance performance across all four datasets.
5.5. Ablation Studies
Ablation studies examine augmentation, embedding, and predictive-layer components, showing that both relational embeddings and flexible augmentation contribute to performance.
- Nine comparative settings evaluate augmentation methods, embedding methods, and the predictive layer.The studies are reported in Tables 3 and 4.
- Effects of Augmentation methods: All three node-centrality augmentation variants outperform the existing KT baseline on every dataset.
- Effects of Augmentation methods: PageRank augmentation performs best on ASSISTment 2009, ASSISTment Challenge3, and STATICS 2011, whereas Degree augmentation wins on ASSISTment 2015.
- Embedding methods: Concatenating E2E and C2C embeddings performs significantly better than using either embedding alone.
- Embedding methods: C2C embeddings perform better in the memory-augmented variant, while E2E embeddings perform better alone in selected DKT settings.
5.8. Effects of Different Predictive Layers
Bi-CLKT compares recurrent and memory-augmented prediction layers, with Bi-CLKT-R selected for its strongest overall results.
- Bi-CLKT-R uses a Recurrent Neural Network, whereas Bi-CLKT-M uses a Memory-augmented Neural Network in the prediction layer.
- Bi-CLKT-R improves overall performance by at least 3% over the other baseline KT models.
- The two variants perform fairly close on ASSISTment 2015, while the other three datasets show a gap of at least 2%.
- Bi-CLKT-R is chosen as the final predictive layer because it provides the best reported results.
6. Conclusion
Bi-CLKT reformulates Knowledge Tracing as a graph problem and combines local and global contrastive learning to represent exercises and concepts.
- Bi-CLKT uses contrastive learning to learn from large amounts of unlabelled data after transforming Knowledge Tracing into graph form.
- Local-local and global-global contrastive frameworks model E2E and C2C implicit relationships, respectively.
- Node-level and graph-level GCNs produce E2E and C2C embeddings that are concatenated as exercise attributes for prediction.
- Bi-CLKT achieves significantly better performance than previous state-of-the-art Knowledge Tracing methods on multiple challenging datasets.