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Enhancing Knowledge Tracing via Adversarial Training
Xiaopeng Guo, Zhijie Huang, Jie Gao, Mingyu Shang, Maojing Shu, Jun Sun
TL;DR
Knowledge tracing predicts students’ future performance from their learning histories, while DNN-based KT may overfit, especially on small datasets. ATKT jointly trains on clean and adversarially perturbed interaction embeddings with an attentive-LSTM backbone, and achieves new state-of-the-art results on four public benchmarks.
Problem
Knowledge tracing predicts future performance from students’ histories, but DNN-based KT may overfit, particularly on small datasets, limiting generalization.
Source: §1 · p. 2, §3.1 · p. 3Method
ATKT perturbs interaction embeddings to create adversarial examples and jointly trains them with clean inputs using an attentive-LSTM KT backbone.
Source: §1 · p. 2, §3.3 · p. 5Results
ATKT achieves new state-of-the-art performance on four public benchmark datasets.
Source: §1 · pp. 2–3Takeaways & Limitations
The authors report that adversarial training is effective for KT modeling and improves generalization over original inputs as well as robustness to adversarial examples.
Source: §1 · p. 2, §3.3 · p. 5At the first time step, the previous knowledge hidden state is initialized to a zero vector.
Source: §3.2.2 · p. 4
Abstract
from arXiv · showhide
We study the problem of knowledge tracing (KT) where the goal is to trace the students' knowledge mastery over time so as to make predictions on their future performance. Owing to the good representation capacity of deep neural networks (DNNs), recent advances on KT have increasingly concentrated on exploring DNNs to improve the performance of KT. However, we empirically reveal that the DNNs based KT models may run the risk of overfitting, especially on small datasets, leading to limited generalization. In this paper, by leveraging the current advances in adversarial training (AT), we propose an efficient AT based KT method (ATKT) to enhance KT model's generalization and thus push the limit of KT. Specifically, we first construct adversarial perturbations and add them on the original interaction embeddings as adversarial examples. The original and adversarial examples are further used to jointly train the KT model, forcing it is not only to be robust to the adversarial examples, but also to enhance the generalization over the original ones. To better implement AT, we then present an efficient attentive-LSTM model as KT backbone, where the key is a proposed knowledge hidden state attention module that adaptively aggregates information from previous knowledge hidden states while simultaneously highlighting the importance of current knowledge hidden state to make a more accurate prediction. Extensive experiments on four public benchmark datasets demonstrate that our ATKT achieves new state-of-the-art performance. Code is available at: \color{blue} {\url{https://github.com/xiaopengguo/ATKT}}.
1 INTRODUCTION
Knowledge tracing predicts future student performance from historical interactions, but DNN-based KT can overfit, particularly on small datasets. ATKT combines adversarial training with an attentive-LSTM backbone, and the authors report state-of-the-art performance on four public benchmarks.
1 INTRODUCTION
- KT uses students’ historical learning data to model knowledge mastery and predict future performance; prior approaches include probabilistic models and DNNs using recurrent networks or attention.The introduction notes that probabilistic methods may rely on simplifying assumptions, while DNNs have become a recent direction.Source: §1 · pp. 1–2
- On small Statics2011, validation loss begins increasing after 20 epochs even as training loss falls, illustrating potential overfitting in DNN-based KT.The authors use the loss curves for a DNN-based KT method as evidence that generalization may be limited.Source: §1 · p. 2, Figure 2 · p. 2
- ATKT achieves new state-of-the-art performance on four public benchmark datasets.The authors present this as evidence of adversarial training’s effectiveness for KT modeling.Source: §1 · p. 2
- ATKT jointly trains on clean interaction embeddings and perturbed adversarial examples, using an attentive-LSTM whose attention aggregates prior knowledge hidden states while emphasizing the current state.KS and response embeddings are concatenated to represent each interaction; the KHS attention output is combined with the current KHS for prediction.Source: §1 · pp. 2–3
2 RELATED WORK
Prior KT research includes probabilistic models and DNN approaches that use recurrent networks, attention, or both. Adversarial training has been explored in other tasks, but its impact on KT had not been thoroughly investigated.
2.1 Knowledge Tracing (KT)
- KT methods progressed from probabilistic approaches such as BKT to DNN models, including recurrent and attention-based methods; this paper instead focuses on improving KT model generalization with adversarial training.Earlier probabilistic methods may rely on simplified assumptions, and later DNN work has also incorporated multiple learning factors.Source: §2.1 · p. 3
2.2 Adversarial Training (AT)
- Adversarial training has been applied to image, text, relation extraction, reading comprehension, part-of-speech tagging, and neural machine translation, but its impact on KT remained underexplored.For text, one approach perturbs continuous word embeddings because one-hot representations do not admit perturbations.Source: §2.2 · p. 3
3 APPROACH
The approach formulates knowledge tracing as predicting correctness on the next exercise from a student’s interaction history and its knowledge-skill index. ATKT combines interaction embeddings, an attentive-LSTM backbone, and adversarial training on perturbed embeddings.
3.1 Problem Formulation
- KT predicts the probability of a correct response to the next exercise from the student’s history and the next exercise’s knowledge-skill index.Source: §3.1 · p. 3
3.2 KT framework
- Interaction Projection embeds knowledge-skill and response indexes, using a response-aware scheme to form each interaction representation.Source: §3.2.1 · p. 3
- The LSTM recurrently updates knowledge hidden states from interaction embeddings, and the framework initializes the first state as a zero vector.Source: §3.2.2 · p. 4
- KHS attention weights previous hidden states for aggregation and concatenates that aggregate with the current state to form the prediction representation.The framework then feeds this composite representation through an MLP and sigmoid to predict the next response.Source: §3.2.2 · p. 4, Figure 3 · p. 4, §3.2.3 · p. 4
3.3 ATKT
- ATKT perturbs interaction embeddings in a loss-increasing direction and jointly trains on original and adversarial examples.The perturbation uses a fast gradient approximation with an L2 norm constraint; β controls the relative importance of normal training and adversarial training.Source: §3.3 · p. 5
4.1 Experimental Setting
The evaluation uses four public benchmark datasets, compares ATKT with six established methods using AUC, and follows a shared cross-validation and training setup.
4.1.1 Benchmark Datasets.
- Four benchmarks cover different response, student, and knowledge-skill counts, with ASSISTments2017 having the most responses.The study uses the preprocessed versions of all four datasets for comparison.Source: §4.1.1 · p. 5
4.1.2 Baseline Methods and Evaluation Metric.
- Six baselines include BKT+ and five DNN-based methods; AUC measures prediction performance, with higher values indicating better performance.AUC of 0.5 corresponds to random guessing.Source: §4.1.2 · pp. 5–6
4.1.3 Implementation Details.
- The comparison uses standard 5-fold cross-validation with each fold divided into training, validation, and test sets at 3:1:1.For fairness, the study uses the first AKT variant, which models KT with KS information only.Source: §4.1.3 · p. 6
- The attentive-LSTM uses one unidirectional layer with 80 hidden units, while interaction sequences longer than 500 are truncated.Training uses batch size 24, Adam, early stopping, and validation-set tuning of ε and β.Source: §4.1.3 · p. 6
- Figure 4 plots validation-loss curves with and without AT across the four benchmark datasets.Panels (a)–(d) correspond to Statics2011, ASSISTments2009, ASSISTments2015, and ASSISTments2017.Source: Figure 4 · p. 6
4.2 Comparison with State-of-the-Arts
ATKT outperforms the compared methods on all four datasets, achieving the best prediction performance for students’ future responses.
4.2 Comparison with State-of-the-Arts
- ATKT consistently outperforms the other methods across all four datasets, with the best result on each.The comparison reports averages and standard deviations across five test folds.Source: §4.2 · p. 6
4.3 Ablation Studies
The ablations examine AT’s effect and the KHS attention module’s contribution; results show AUC gains from AT and higher average AUC with KHS attention.
4.3.1 Effectiveness of the AT Implementation.
- AT raises test-set AUC scores across the datasets using the searched hyperparameter combination.Table 4 compares average AUC with and without AT on four test sets.Source: §4.3.1 · p. 7, Table 4 · p. 7
- For each ε, AUC first increases and then decreases as β rises, and an excessively large β can lower AUC below the no-AT case.β = 0 represents no AT implementation.Source: §4.3.1 · p. 7, Table 3 · p. 7
- The best AUC uses a smaller β on the small datasets and may use a larger β on the larger datasets.The authors relate this pattern to the backbone’s differing overfitting risk across dataset sizes.Source: §4.3.1 · p. 7
4.3.2 Effectiveness of the proposed Attensive-LSTM.
- Adding KHS attention to the attentive-LSTM improves average AUC across all four datasets compared with a sole LSTM.Table 5 reports average AUC on the test sets with and without the attention module.Source: §4.3.2 · p. 7, Table 5 · p. 7
4.4 Visualization
The visualizations show predicted mastery for five knowledge skills over 35 exercises, including how mastery changes over time and differs across skills.
4.4 Visualization
- The five-skill visualization tracks predicted mastery across 35 exercise steps, with deeper heatmap colors representing better mastery.The top row records exercise performance, and each color denotes a distinct KS contained in an exercise.Source: §4.4 · pp. 7–8, Figure 5 · p. 8
- Correct responses improve the relevant KS mastery, while the predicted mastery of a KS can also change before the student practices it.The authors attribute such cross-skill changes to potential connections between KSs.Source: §4.4 · p. 8
- Students show relatively low mastery of the KS “Addition and Subtraction Fractions”; Figure 6 compares mastery of each KS at the initial time point (t=1) and final time point (t=35).Source: §4.4 · p. 8, Figure 6 · p. 8
5 CONCLUSION
ATKT combines an attentive-LSTM backbone with adversarial training, and the authors report state-of-the-art AUC performance among current methods.
5 CONCLUSION
- ATKT uses an efficient attentive-LSTM backbone for knowledge tracing.The authors also visualize predicted mastery for each knowledge skill during exercising.Source: §5 · p. 8
- ATKT jointly trains the backbone on clean interaction inputs and adversarial examples to improve robustness and generalization.Source: §5 · p. 8
- ATKT outperforms current state-of-the-art methods on the AUC metric in extensive experiments.Source: §5 · p. 8