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Uncertainty-aware Knowledge Tracing
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Proposes UKT, a knowledge tracing model that represents students with Gaussian (mean and covariance) stochastic embeddings, uses Wasserstein self-attention, and adds an aleatory-uncertainty-aware contrastive loss, evaluated on six KT datasets.
Problem
Deterministic knowledge tracing representations ignore uncertainty in student interactions (epistemic and aleatory, e.g., guessing or careless errors), so they fail to model true knowledge states.
Approach
Model each student's interaction history as a Gaussian distribution with mean (knowledge level) and covariance (uncertainty), apply attention scored by the 2-Wasserstein distance between distributions, and use contrastive learning with negatives built by flipping prior correct/incorrect responses to gain robustness to aleatory noise.
Key results
- UKT reaches AUC 0.8563 on AS2009 and 0.9320 on AL2005, outperforming AKT (0.8474, 0.9294) and SimpleKT.
- UKT achieves the best AUC on POJ (0.6301) and accuracy on AS2009, AL2005, BD2006, and POJ, but slightly underperforms AKT on AS2015 (0.7267 vs 0.7282 AUC).
- Ablation on AS2009 shows removing contrastive learning drops AUC from 0.8563 to 0.8507, and removing Wasserstein distance or stochastic embedding drops it further to about 0.845.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use UKT instead of AKT | KT model · AS2009 | AUC: 0.8474±0.0017 -> 0.8563±0.0014 | Helped |
| Use UKT instead of AKT | KT model · AL2005 | AUC: 0.9294±0.0019 -> 0.9320±0.0012 | Helped |
| Use UKT instead of AKT | KT model · BD2006 | AUC: 0.8167±0.0007 -> 0.8178±0.0009 | Helped |
| Use UKT instead of SimpleKT | KT model · NIPS34 | AUC: 0.7966±0.0000 -> 0.8035±0.0004 | Helped |
| Use UKT instead of AKT | KT model · AS2015 | AUC: 0.7282±0.0004 -> 0.7267±0.0007 | Hurt |
| Use UKT instead of AKT | KT model · POJ | AUC: 0.6218±0.0013 -> 0.6301±0.0005 | Helped |
| Add aleatory uncertainty-aware contrastive learning (ablation) | UKT · AS2009 | AUC: 0.8507±0.0020 -> 0.8563±0.0018 | Helped |
| Add aleatory uncertainty-aware contrastive learning (ablation) | UKT · Algebra2005 | AUC: 0.9258±0.0018 -> 0.9320±0.0012 | Helped |
| Add Wasserstein distance in self-attention (ablation) | UKT · AS2009 | AUC: 0.8450±0.0024 -> 0.8563±0.0018 | Helped |
| Add Wasserstein distance in self-attention (ablation) | UKT · Algebra2005 | AUC: 0.9208±0.0019 -> 0.9320±0.0012 | Helped |
| Add stochastic embeddings (ablation) | UKT · AS2009 | AUC: 0.8445±0.0028 -> 0.8563±0.0018 | Helped |
| Add stochastic embeddings (ablation) | UKT · Algebra2005 | AUC: 0.9217±0.0022 -> 0.9320±0.0012 | Helped |
Surprising findings
- UKT slightly underperforms AKT on the large ASSISTments2015 dataset, which the authors attribute to dataset size and student diversity.
- Excessive contrastive loss weight degrades performance, indicating over-emphasis on aleatory uncertainty diverts training.
Limitations
- Aleatory uncertainty contrastive gains are sensitive to the weight lambda; too large a weight hurts performance.
- Underperforms AKT on the largest dataset (AS2015).
Experimental setup
Datasets: ASSISTments2009 Algebra2005 Bridge2006 NIPS34 ASSISTments2015 POJ
Benchmarks: ASSISTments2009 Algebra2005 Bridge2006 NIPS34 ASSISTments2015 POJ
Metrics: AUC accuracy
Baselines: DKT SAKT SAINT ATKT AKT SimpleKT
Builds on: AKT SimpleKT SAKT
Closest papers by meaning
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- PLD: A Choice-Theoretic List-Wise Knowledge Distillation (NeurIPS 2025 · similarity 0.85)
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