ProPRL: Property-Aware Prerequisite Relation Learning in Educational Knowledge Graphs

Synthesis: ProPRL advances prerequisite relation learning by going beyond conventional link prediction to adaptively integrate complementary educational evidence from concept-resource hypergraphs and directed learning-behavior graphs. The Irreversibility Constraint — an anti-symmetry regularizer that penalizes contradictory bidirectional predictions — addresses a fundamental issue in educational knowledge graphs: the asymmetry of prerequisite relationships. Experiments on multiple real-world educational datasets demonstrate state-of-the-art performance, with ablations confirming that multi-hop behavioral propagation, pair-conditioned fusion, and directional regularization each contribute to the gains.

Key Findings

1. ProPRL achieves state-of-the-art prerequisite relation learning, ranking first on all nine dataset–metric combinations (ACC, F1, AUC) across MOOC, LectureBank, and University Course (UCD), with relative improvements from 1.96% to 6.11% over the strongest baseline (DGCPL in most cases).
2. The Irreversibility Constraint — an anti-symmetry regularizer penalizing high confidence in both directions of a concept pair — sharply reduces contradictory bidirectional predictions, raising the proportion of correctly ordered relations from 88.0% to 90.0% and widening the forward–reverse confidence margin from 0.605 to 0.695.
3. Direction-preserving personalized multi-hop propagation over the learning-behavior graph is the single most impactful component: removing it degrades F1 on UCD from 0.8788 to 0.7831, the largest ablation drop across all three datasets.
4. The Pair-conditioned Gate, which learns pair-specific weighting of resource-aware versus behavior-aware evidence, outperforms fixed uniform fusion, with dataset-dependent benefits (largest on MOOC).

Background: Why Conventional Link Prediction Fails

Prerequisite relation learning is central to adaptive instruction and Personalized Learning, which depend on accurate domain knowledge structures. Yet real-world modeling is hampered by scarce expert annotations and noisy automated extraction. Existing methods typically reduce the task to conventional link prediction over node embeddings, which fails on three properties the authors identify as intrinsic to prerequisite relations:

• Directional asymmetry: prerequisite relations are irreversible (if ci is a prerequisite of cj, assigning high confidence to cj → ci is a directional contradiction), yet conventional models score directed pairs independently.
• Multi-hop behavioral evidence: prerequisites often surface as latent dependencies (ci → ck → cj) rather than explicit one-step learner transitions, which local transition heuristics miss.
• Pair-specific relevance: a relation is defined over a specific ordered concept pair, so the representation of ci should adapt to whether it is paired with cj or ck — fixed node-level representations cannot.

The ProPRL Framework

ProPRL combines three components over an educational knowledge graph:

Multi-view Concept Representation. Two complementary views are learned. A directed learning-behavior graph is built from learner interaction sequences, and direction-preserving personalized propagation (inspired by APPNP) aggregates multi-hop forward and backward transitional evidence via direction-specific graph convolutional networks. A concept-resource hypergraph, where each learning resource is a hyperedge connecting the concepts it teaches, is encoded with a Hypergraph Convolutional Network to capture resource-mediated high-order associations.

Pair-conditioned Gate. Because the same concept can be a prerequisite in one pair and a target in another, ProPRL composes role-specific pair representations (concatenation, signed difference, and Hadamard compatibility) for each view, then learns a gate that adaptively weights and fuses the resource-aware and behavior-aware views per candidate ordered pair — rather than relying on a fixed node-level fusion.

Irreversibility Constraint. An anti-symmetry regularizer evaluates each positive pair's reverse direction with the same scoring function and penalizes simultaneously high probabilities in both directions via a co-activation margin. A teacher-detached multi-view consistency loss aligns the two single-view branches with the stronger fused prediction.

Experiments and Results

ProPRL is evaluated on three Benchmark datasets — MOOC1, LectureBank2, and University Course (UCD) — using ACC, F1, and AUC, against general-purpose baselines (NB, SVM, RF, RefD, GAE, VGAE) and task-specific prerequisite models (HGAPNet, MHAVGAE, ConLearn, LCPRE, DGCPL). It ranks first across all nine dataset–metric combinations, outperforming even the strongest baseline in every comparison; the largest relative AUC gain (6.11%) occurs on UCD.

Ablation studies confirm each component contributes: removing multi-hop propagation causes the most pronounced degradation on UCD, removing the pair gate hurts most on MOOC, and removing anti-symmetry regularization affects LectureBank most strongly. A case study on the reversed-order evaluation shows ProPRL produces a stronger separation between the annotated direction and its reversal rather than merely correcting a few reversed rankings. Hyperparameter analysis shows stability across propagation coefficient and depth (gains saturate around k = 5), while a small learning rate (~10⁻⁴) is needed for reliable optimization. Efficiency-wise, ProPRL stays lightweight — under 40 MB GPU memory, under 0.18 s inference — and is faster than DGCPL on MOOC and UCD.

What this means for practice

• Designers. Score the two directions of a concept pair together rather than independently: the Irreversibility Constraint raised correctly ordered relations from 88.0% to 90.0% and widened the forward-reverse confidence margin from 0.605 to 0.695, so a pipeline that ignores anti-symmetry will keep producing contradictory chains.
• Designers. Do not drop direction-preserving multi-hop propagation when learner interaction sequences exist: removing it was the largest ablation loss, cutting F1 on the University Course dataset from 0.8788 to 0.7831.
• Designers. Fuse resource-aware and behavior-aware evidence per candidate pair instead of at a fixed weight: the Pair-conditioned Gate beat uniform fusion, with the largest benefit on MOOC, matching the finding that a relation is defined over a specific ordered pair rather than a node.
• Designers. Feed the learned ordering into sequencing and hint generation only where the dependency is validated: personalized pathways, knowledge tracing, and Scaffolding all inherit the directionality of the graph they read from.
• Researchers. Evaluate reversals, not just accuracy: the reversed-order case study shows the gain comes from separating the annotated direction from its reversal rather than from correcting a handful of inverted rankings.

Limitations

• Evaluation uses three benchmark datasets inherited from prior work (MOOC, LectureBank, and University Course), split 8:1:1, so the 1.96% to 6.11% relative gains rest on those datasets' existing labels and include no newly collected human annotation.
• All results are link-prediction metrics (ACC, F1, AUC) on those benchmarks; no experiment tests whether the sharper ordering improves learner outcomes in a tutoring, sequencing, or knowledge-tracing system.
• Key hyperparameters are chosen per dataset — propagation coefficient α is 0.05 for MOOC and LectureBank but 0.2 for UCD, and λ is 1×10⁻³ or 5×10⁻³ — so the first-place result across all nine dataset-metric combinations reflects dataset-specific configuration.
• Runs are reported for a single fixed seed (42) with no variance or confidence intervals, and gains saturate around propagation depth k = 5; ProPRL is also slower than DGCPL on LectureBank.

Citation

Cheng, X., Wang, J., He, C., Dong, R., & Guan, Q. (2026). ProPRL: Property-Aware Prerequisite Relation Learning in Educational Knowledge Graphs. v1.