Contextual Embeddings and Graph Convolutional Networks for Concept Prerequisite Learning
Bibliographic record
Abstract
Concept prerequisite learning (CPL) plays a crucial role in education. The objective of CPL is to predict prerequisite relations between different concepts. In this paper, we present a new approach for CPL using Sentence Transformers and Relational Graph Convolutional Networks (R-GCNs). This approach creates concept embeddings from single-sentence definitions extracted from Wikipedia using a Sentence Transformer. These embeddings are then used as an input feature matrix for the R-GCN, in addition to a graph structure that distinguishes prerequisites and non-prerequisites as distinct link types. Furthermore, the R-GCN is optimized simultaneously on CPL and concept domain classification to enhance prerequisite prediction generalization for unseen domains. Extensive experiments on the AL-CPL dataset show the effectiveness of our approach for the in-domain and cross-domain settings, as it outperforms the State-Of-The-Art (SOTA) methods on this dataset. Finally, we introduce a novel data split algorithm for this task to address a methodological issue found in previous studies. The new data split algorithm makes CPL more challenging to solve, but also more realistic as it excludes simple inferences by transitivity.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".