---
source_url: https://arxiv.org/abs/2604.08263
ingested: 2026-05-08
sha256: 3f91fe337daeb626d87af1f2fb444c03d83a66d9e0a8b43a5837020f527673c3
---

# Neural-Symbolic Knowledge Tracing: Injecting Educational Knowledge into Deep Learning for Responsible Learner Modelling

**Authors:** Danial Hooshyar, Gustav Šír, Yeongwook Yang, Tommi Kärkkäinen, Raija Hämäläinen, Ekaterina Krivich, Mutlu Cukurova, Dragan Gašević, Roger Azevedo
**Published:** 2026-04-09
**Categories:** cs.AI
**arXiv:** https://arxiv.org/abs/2604.08263
**PDF:** https://arxiv.org/pdf/2604.08263

## Abstract

The growing use of artificial intelligence (AI) in education, particularly large language models (LLMs), has increased interest in intelligent tutoring systems. However, LLMs often show limited adaptivity and struggle to model learners' evolving knowledge over time, highlighting the need for dedicated learner modelling approaches. Although deep knowledge tracing methods achieve strong predictive performance, their opacity and susceptibility to bias can limit alignment with pedagogical principles. To address this, the authors propose **Responsible-DKT**, a neural-symbolic deep knowledge tracing approach that integrates symbolic educational knowledge (e.g., mastery and non-mastery rules) into sequential neural models for responsible learner modelling. Experiments on a real-world dataset of students' math interactions show that Responsible-DKT outperforms both a neural-symbolic baseline and a fully data-driven PyTorch DKT model across training settings. The model achieves over 0.80 AUC with only 10% of training data and up to 0.90 AUC, improving performance by up to 13%. It also demonstrates improved temporal reliability, producing lower early- and mid-sequence prediction errors and the lowest prediction inconsistency rates across sequence lengths, indicating that prediction updates remain directionally aligned with observed student responses over time. Furthermore, the neural-symbolic approach offers intrinsic interpretability via a grounded computation graph that exposes the logic behind each prediction, enabling both local and global explanations. It also allows empirical evaluation of pedagogical assumptions, revealing that repeated incorrect responses (non-mastery) strongly influence prediction updates. These results indicate that neural-symbolic approaches enhance both performance and interpretability, mitigate data limitations, and support more responsible, human-centered AI in education.

## Key Contributions

- **Problem**: LLMs and purely data-driven DKT models lack explicit learner models, suffer from opacity, instability, and susceptibility to spurious correlations, limiting responsible use in education.
- **Solution**: Neural-symbolic DKT injecting structured educational knowledge (symbolic rules) into a recurrent neural architecture using the **Lifted Relational Neural Networks (LRNN)** paradigm via the **PyNeuraLogic** framework.
- **Responsible AI framing**: Adopts definition of responsible AI as "a human-centred approach aimed at fostering user trust through ethical and reliable decision-making, explainable outcomes, and privacy-preserving implementation" (Goellner et al., 2024).

## Research Questions

- **RQ1**: How does Responsible-DKT compare with conventional DKT in predictive accuracy?
- **RQ2**: To what extent does symbolic knowledge injection improve the sequential stability of predictions over time?
- **RQ3**: How does Responsible-DKT provide interpretable explanations of student knowledge predictions?

## Methodology

### Dataset
- **Source**: Opiq learning environment, 6th-grade Maths, collected September 2021.
- **Scale**: 167 students, 21,471 interactions, 13 skills, 1,058 quizzes.
- **Binarization**: Scores binarized using first quartile (score=37) as threshold: <37 → incorrect, ≥37 → correct.
- **Sequences**: Chronologically ordered per student; min 1, max 1437, median 46, mean 128.57 interactions.
- **Truncation**: Tukey's rule upper fence = 475; sequences capped at 475.
- **Evaluation lengths**: 10 (cold-start), 50 (median), 100, and full (475) interactions.
- **Split**: Student-level train/val/test (≈7:1:2).

### Symbolic Encoding
Interactions encoded as symbolic ground facts in PyNeuraLogic: skill_input(t, st), quiz_input(t, qt), correct_input(t, {right, wrong}), next(t, t+1). Prediction task: next-step correctness given history up to t.

### Model Architecture: Responsible-DKT
- **Embeddings**: Learnable embeddings for quiz, skill, correctness (dim=16).
- **Combined representation**: Weighted sum of embeddings + sigmoid.
- **Recurrent core**: Two-layer RNN with hidden state; temporal shift ensures prediction at t uses only past interactions.
- **Symbolic rules (learnable weights)**:
  - **mastered**: Two consecutive correct responses on same skill/quiz → increases prediction confidence.
  - **not_mastered**: Three incorrect responses on same skill/quiz → decreases prediction confidence.
  - **avg_embed**: Historical aggregation of past embeddings for the same skill/quiz.
- Rules modulate rather than override neural predictions, contributing via weighted edges.

### Baselines
- **BaseNS-DKT**: Same neural-symbolic architecture but WITHOUT injected educational knowledge rules.
- **PyTorch DKT**: Fully data-driven DKT implementation in PyTorch.

## Results

### Predictive Accuracy (RQ1)
- >0.80 AUC with only 10% training data.
- Up to 0.90 AUC with full data.
- Up to 13% improvement over baselines.
- Strong data efficiency: outperforms baselines in low-data regimes.

### Temporal Reliability (RQ2)
- Lower early- and mid-sequence prediction errors compared to baselines.
- Lowest prediction inconsistency rates across all sequence lengths (10, 50, 100, 475).
- Prediction updates remain directionally aligned with observed student responses over time — model doesn't "flip-flop" between correct/incorrect.
- Inconsistency rate: Responsible-DKT 0.013–0.039 vs. PyTorch DKT 0.075–0.138.

### Interpretability (RQ3)
- Intrinsic interpretability via grounded computation graph exposing logic behind each prediction.
- Supports both local (per-prediction) and global explanations.
- Empirical evaluation of pedagogical assumptions revealed that patterns of repeated incorrect responses (non-mastery rules) play a stronger role in prediction updates than mastery patterns.

## Broader Impact
- Enhances both performance and interpretability simultaneously.
- Mitigates data limitations — practical for real-world educational settings with sparse data.
- Supports responsible, human-centered AI in education by enabling explicit domain knowledge injection, transparent reasoning, and reduced data dependency.