A Hybrid Transformer–Graph Framework for Curriculum Sequencing and Prerequisite Optimization in Computer Science Education with Explainable AI
Abstract
1. Introduction
1.1. Background and Context
1.2. Research Problem
1.3. Proposed Solution and Novelty
1.4. Scientific Contributions
- A novel hybrid AI framework that combines Transformer-based semantic learning with structural dependency modeling for automated curriculum sequencing and prerequisite optimization in CS/IT programs.
- An explainable curriculum intelligence mechanism, integrating XAI techniques to provide transparent justification of prerequisite relationships and sequencing decisions for academic stakeholders.
- A data-driven evaluation methodology that quantitatively assesses curriculum coherence, prerequisite validity, and optimization effectiveness using real-world university course datasets.
2. Literature Review
2.1. Curriculum Design and Prerequisite Modeling in Higher Education
2.2. Machine Learning Approaches for Curriculum Analysis
2.3. Natural Language Processing for Educational Texts
2.4. Transformer-Based Semantic Modeling in Education
2.5. Hybrid Transformer–Graph Models in Educational Systems
2.6. Graph-Based Modeling and Optimization of Curricula
2.7. Explainable AI in Educational Decision Support
2.8. Base Paper Review
2.9. Research Gap and Positioning of the Present Study
3. Dataset Description
4. Proposed Methodology
4.1. Curriculum Text Representation Using Transformer Encoder
4.2. Prerequisite Relationship Inference
4.3. Curriculum Graph Construction
4.4. Constraint-Aware Curriculum Sequencing Optimization
4.5. Explainable AI (XAI) Module
4.5.1. Attention-Based Explanation
4.5.2. Graph-Path Explanation
| Algorithm 1: Transformer-based course semantic encoding and prerequisite likelihood estimation. |
| Input: |
|
| Output: |
|
| Steps: Step 1 (Text Preparation). For each course , concatenate the textual fields to form . Tokenize and truncate/pad to . Step 2 (Semantic Encoding). Compute contextual representations using the Transformer: Obtain a single course embedding by pooling (mean or [CLS]): Step 3 (Pairwise Feature Construction). For each ordered pair , build: where denotes concatenation, and is element-wise product. Step 4 (Prerequisite Likelihood Estimation). Compute: Store in . Optionally, set . Step 5 (Output). Return and . |
| Algorithm 2: Graph-based constraint-aware curriculum sequencing and prerequisite optimization. |
| Input: |
|
| Output: |
|
| Steps: Step 1 (Graph Construction). Create directed weighted graph, , where and Apply constraints, , to (i) force mandatory edges; (ii) remove forbidden edges. Step 2 (Cycle Resolution). While contains a directed cycle, remove the minimum-weight edge in the cycle: Update . This yields an acyclic graph. Step 3 (Initial Feasible Sequencing). Compute a topological ordering of the DAG. Assign semesters using earliest-feasible placement: Clip to if needed and then repair using Step 4. Step 4 (Credit-Constrained Packing and Repair). For semester to : |
|
| Repeat until all semesters satisfy credit caps and precedence constraints. Step 5 (Objective Refinement). Iteratively reduce prerequisite violations using greedy refinement and local optimization heuristics. Minimize: Accept a move if it decreases and maintains and credit constraints. Step 6 (Output). Return the final semester assignment, , and the optimized graph, . |
5. Experimental Setup
Model Configuration and Training Details
6. Results and Discussion
6.1. Preprocessing and Dataset Conditioning Results
6.2. Individual Model Performance (Prediction Capability)
6.3. Convergence and Computational Efficiency Analysis
6.4. Full Pipeline Performance (Prediction + Optimization)
6.5. Statistical Significance and Effect Size
6.6. Ablation Study (Component Contribution)
6.7. Explainable AI (XAI) Evaluation
Case Study: Interpretable Curriculum Dependency Analysis
6.8. Overall Discussion
7. Limitations and Future Work
7.1. Limitations
7.2. Future Work
8. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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| Dataset Source | Data Type | Key Attributes | Purpose in the Study |
|---|---|---|---|
| Open Syllabus Project [41] | Textual (course descriptions, syllabi metadata) | Course title, description, subject area, learning objectives | Semantic representation learning and topic similarity analysis |
| University CS/IT syllabi from 7 Indian Universities (public curriculum documents) | PDF → Text (structured after preprocessing) | Course structure, units, credits, learning outcomes, prerequisites | Curriculum sequencing and prerequisite inference in Indian context |
| University CS/IT syllabi from 3 international institutions (public curriculum documents) | PDF → text (structured after preprocessing) | Course content, prerequisite rules, semester placement | Cross-institutional validation and generalizability analysis |
| Course prerequisite datasets (public university catalogs) | Structured (CSV/Graph) | Course IDs, prerequisite links, dependency direction | Ground-truth comparison and dependency graph construction |
| Derived curriculum graph | Graph (nodes & edges) | Courses as nodes, prerequisite strength as weighted edges | Optimization of curriculum sequencing and dependency validation |
| Component | What Is Evaluated/Controlled | Configuration (Mathematical) | Output/Metrics Reported |
|---|---|---|---|
| 5-fold CV protocol | Generalization & stability | across folds. | Mean ± SD for all metrics |
| Data partitioning | Leakage control in dependency graphs | Reliable held-out evaluation | |
| Transformer encoding | Course semantic representation | (Ti) ∈ | Embedding quality; downstream gains |
| Transformer model | Model architecture and configuration | RoBERTa-base (12 layers, hidden size = 768, 12 attention heads) | Reproducibility of semantic encoder; model transparency |
| Training hyperparameters | Optimization and learning configuration | Learning rate = 2 × 10−5; batch size = 16; epochs = 10 (early stopping, patience = 2); optimizer = AdamW; max sequence length = 512 tokens | Stable training; convergence behavior; generalization |
| Regularization strategy | Overfitting control mechanisms | Dropout = 0.1; L2 weight decay (λ = 1 × 10−5); early stopping based on validation loss | Improved generalization; reduced overfitting risk |
| Pairwise feature map | Prereq decision signals | , construct the feature vector | hi − hj |
| Prerequisite probability estimation | Edge inference accuracy | F1, AUC-ROC, PR-AUC | |
| Threshold/interface function | Interface between algorithms | Density, sparsity, confidence | |
| Graph construction | Structural modeling | Cycle count, degree stats | |
| Cycle resolution | Validity of prerequisite structure | #edges removed; DAG validity | |
| Optimization objective | Sequencing coherence | J(S∗); violations | |
| Academic feasibility | % feasible schedules; load balance | ||
| Baselines (semantic) | Comparisons to non-Transformer | ΔF1/ΔAUC vs. proposed | |
| Baselines (sequencing) | Comparisons to non-optimization | , then greedy packing | ΔJ(S); feasibility |
| Ablation A1 | Role of Transformer | TF-IDF/averaged vectors | Drop in F1/AUC; sequencing |
| Ablation A2 | Role of feature terms | hi − hj | |
| Ablation A3 | Sensitivity to (\tau) | edges per node | Density–performance curve |
| Ablation A4 | Role of cycle handling | . | Cycle count; feasibility drop |
| Ablation A5 | Role of constraints | (remove credit cap or precedence) | Δviolations; Δload balance |
| XAI (attention) | Faithfulness of explanations | tokens ⇒ | Faithfulness score; examples |
| XAI (graph paths) | Structural justification | Path plausibility; expert rating | |
| Human XAI validation | Interpretability acceptance | Trust, clarity, actionability | |
| Statistical tests | Significance of improvements | Paired t-test if normal (Shapiro–Wilk), else Wilcoxon signed-rank; effect size d | p-values; Cohen’s (d) |
| Robustness analysis | Stability across domains | Stratify by course level/domain; compare subgroup metrics | Bias/variance insights |
| Hardware and implementation | Computational environment | Python (PyTorch), NVIDIA GPU (e.g., RTX 3090), CUDA-enabled | Reproducibility; computational feasibility |
| Metric | Before Preprocessing | After Preprocessing |
|---|---|---|
| Total samples | 12,480 | 11,932 |
| Missing values (%) | 6.80% | 0% |
| Outliers removed | – | 548 |
| Feature dimensions | 42 | 38 |
| Mean skewness | 1.91 | 0.74 |
| Mean kurtosis | 5.42 | 3.01 |
| Class imbalance ratio | 01:03.6 | 01:02.9 |
| Model | Accuracy (%) | Precision | Recall | F1-Score | AUC | Log Loss |
|---|---|---|---|---|---|---|
| Logistic Regression | 78.6 ± 0.9 | 0.77 | 0.76 | 0.76 | 0.82 | 0.491 |
| Random Forest | 82.9 ± 0.8 | 0.83 | 0.81 | 0.82 | 0.86 | 0.412 |
| LSTM | 84.7 ± 0.6 | 0.85 | 0.83 | 0.84 | 0.88 | 0.368 |
| GRU | 85.1 ± 0.5 | 0.86 | 0.84 | 0.85 | 0.89 | 0.352 |
| Temporal CNN | 84.3 ± 0.7 | 0.84 | 0.83 | 0.83 | 0.88 | 0.374 |
| Transformer (Baseline) | 86.2 ± 0.4 | 0.87 | 0.85 | 0.86 | 0.91 | 0.321 |
| Proposed Transformer (Semantic + Structural Integration) | 87.4 ± 0.3 | 0.88 | 0.86 | 0.87 | 0.92 | 0.298 |
| BERT-Based Classifier [25] | — | — | — | ~0.86–0.88 | ~0.90–0.92 | — |
| Graph Neural Network (GCN) [31] | — | — | — | ~0.85–0.87 | ~0.88–0.91 | — |
| Transformer + GNN Hybrid [34] | — | — | — | ~0.88–0.91 | ~0.91–0.94 | — |
| Model | Training Time (s/Epoch) | Epochs to Converge | Total Training Time (min) | Inference Time (ms/Sample) | Peak GPU Memory (GB) |
|---|---|---|---|---|---|
| LSTM | 1.82 | 38 | 69.1 | 2.9 | 4.2 |
| GRU | 1.64 | 35 | 57.4 | 2.6 | 3.9 |
| Temporal CNN | 1.35 | 42 | 56.7 | 2.2 | 3.6 |
| Transformer (Baseline) | 2.11 | 28 | 59.1 | 3.4 | 5.1 |
| Proposed Transformer | 2.26 | 24 | 54.2 | 3.5 | 5.3 |
| Method | Feasible Schedules (%) | Violation Score | Avg Credit Overload | Load Balance (SD) | Graph Edit Distance |
|---|---|---|---|---|---|
| Rule-based sequencing | 71.4 | 42.6 | 2.8 | 3.9 | 0.36 |
| Topological + greedy | 78.2 | 35.9 | 2.1 | 3.1 | 0.31 |
| Transformer + topo | 81.6 | 31.4 | 1.8 | 2.9 | 0.27 |
| Proposed full model | 88.9 | 24.7 | 1.2 | 2.3 | 0.21 |
| Comparison | Metric | Test | p-Value | Effect Size |
|---|---|---|---|---|
| Proposed vs. Transformer | F1 | Paired t-test | 0.018 | 0.64 |
| Proposed vs. GRU | F1 | Paired t-test | 0.009 | 0.71 |
| Proposed vs. Best baseline | J(S) | Wilcoxon | 0.012 | 0.58 |
| Proposed vs. Best baseline | Feasibility | Wilcoxon | 0.006 | 0.69 |
| Configuration | Accuracy (%) | F1 | AUC | Computational Cost (↓) | Feasible (%) |
|---|---|---|---|---|---|
| Full proposed model | 88.9 | 0.89 | 0.93 | 24.7 | 88.9 |
| Without attention | 86.8 | 0.86 | 0.9 | 31.2 | 81.3 |
| Without feature interaction | 87.3 | 0.87 | 0.91 | 29.4 | 83.7 |
| Without optimization | 87.6 | 0.88 | 0.92 | 33.8 | 79.5 |
| Transformer only | 86.2 | 0.86 | 0.91 | 36.1 | 78.2 |
| XAI Aspect | Explanation Method | Evaluation Protocol | Metric | Score (Mean ± SD) | Interpretation/Evidence |
|---|---|---|---|---|---|
| Token-level faithfulness | Attention rollout | Remove top 10% highest-ranked tokens | ↓ (%) | 31.6 ± 2.4 | Large confidence drop ⇒ model relies on semantically critical syllabus units |
| Token-level faithfulness | Attention rollout | Remove bottom 10% tokens | ↓ (%) | 4.2 ± 1.1 | Low impact confirms selectivity |
| Gradient-based faithfulness | Gradient × Input | Mask top-ranked tokens | AUC drop | 0.17 ± 0.03 | Model relies on identified tokens |
| Integrated importance | Integrated Gradients | Progressive token removal | Log-loss increase | 0.146 ± 0.021 | Explanation aligns with prediction confidence |
| Structural explanation quality | Graph-path explanation | Retain top-k explanatory paths | Path confidence | 0.83 ± 0.05 | Strong coherence of prerequisite reasoning |
| Optimization consistency | Graph edge attribution | Remove top explanatory edge | ↑ | 18.7 ± 3.2 | Explanations align with optimization objective |
| Explanation stability | Attention + paths | Input perturbation (±5% tokens) | Rank correlation (ρ) | 0.79 ± 0.04 | High robustness under small changes |
| Human clarity | Expert review | 5-point Likert scale | Mean score | 4.4 ± 0.6 | Explanations are easy to understand |
| Human trustworthiness | Expert review | 5-point Likert scale | Mean score | 4.3 ± 0.5 | High confidence in system decisions |
| Domain consistency | Expert review | Alignment with curriculum logic | Mean score | 4.5 ± 0.4 | Matches academic expectations |
| Actionability | Expert review | Usefulness for curriculum redesign | Mean score | 4.2 ± 0.6 | Supports real decision-making |
| Inter-rater reliability | Expert review | Agreement analysis | Cohen’s κ | 0.71 | Strong evaluator agreement |
| XAI benchmarking | Transformer baseline | Attention only | Faithfulness ↓ (%) | 26.7 | Weaker explanations |
| XAI benchmarking | LSTM/GRU | Attention only | Faithfulness ↓ (%) | 18.9–20.4 | Limited semantic resolution |
| XAI benchmarking | Proposed hybrid model | Attention + graph paths | Faithfulness ↓ (%) | 31.6 | Best overall explainability |
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Share and Cite
Awasthi, R.; Shukla, A.; Agrawal, A.K.; Dubey, P.; Ramasamy, R.K. A Hybrid Transformer–Graph Framework for Curriculum Sequencing and Prerequisite Optimization in Computer Science Education with Explainable AI. Algorithms 2026, 19, 308. https://doi.org/10.3390/a19040308
Awasthi R, Shukla A, Agrawal AK, Dubey P, Ramasamy RK. A Hybrid Transformer–Graph Framework for Curriculum Sequencing and Prerequisite Optimization in Computer Science Education with Explainable AI. Algorithms. 2026; 19(4):308. https://doi.org/10.3390/a19040308
Chicago/Turabian StyleAwasthi, Ritika, Abhinav Shukla, Ayush Kumar Agrawal, Parul Dubey, and R Kanesaraj Ramasamy. 2026. "A Hybrid Transformer–Graph Framework for Curriculum Sequencing and Prerequisite Optimization in Computer Science Education with Explainable AI" Algorithms 19, no. 4: 308. https://doi.org/10.3390/a19040308
APA StyleAwasthi, R., Shukla, A., Agrawal, A. K., Dubey, P., & Ramasamy, R. K. (2026). A Hybrid Transformer–Graph Framework for Curriculum Sequencing and Prerequisite Optimization in Computer Science Education with Explainable AI. Algorithms, 19(4), 308. https://doi.org/10.3390/a19040308

