- Poincaré embeddings (Nickel and Kiela, 2017) is a method that better fit for data with latent hierarchies than other embedding models using the Euclidean vector space.
- Dhingra et al. (2018) introduced a method to obtain Poincaré word embeddings from natural language text.
- This paper combines the two methods above to obtain prerequisite relations between concepts from two datasets in the domain of Natural Language Processing. 

Improved Concept Embeddings for Learning Prerequisite Chains: Methods

Löffel, E. P. (2019). Improved Concept Embeddings for Learning Prerequisite Chains

Paper: https://pdfs.semanticscholar.org/6073/0900a80fcee29e9059fd293a1fa38742abf3.pdf

Github: https://github.com/eloffel/improved_embeddings

Improved Concept Embeddings for Learning Prerequisite Chains: Reference

 Löffel, E. P. (2019) generated prerequisite relations between concepts in the domain of Natural Language Processing from two datasets, TutorialBank and LectureBank, by representing natural language text corpora as Poincaré embedding.

University of Michigan - Ann Arbor

- Löffel, E. P. (2019). Improved Concept Embeddings for Learning Prerequisite Chains.
- Li, I., Fabbri, A. R., Tung, R. R., & Radev, D. R. (2019, July). What should i learn first: Introducing lecturebank for nlp education and prerequisite chain learning. In Proceedings of the AAAI Conference on Artificial Intelligence (Vol. 33, pp. 6674-6681).

Examples of identifying and predicting prerequisite relationship

Improved Concept Embeddings for Learning Prerequisite Chains

Li, I., etc.(2019) introduced a new dataset, LectureBank, in 5 different domains with 208 manually-labeled prerequisite relation topics, and evaluated four binary classifiers and two Graph Convolutional Networks (GCNs) models in predicting prerequisite relationship.

What Should I Learn First: Introducing LectureBank for NLP Education and Prerequisite Chain Learning

Chen Liang and collaborators contributed two foundational works to the concept-prerequisite-learning line cited in the paper. The earlier work, **Measuring Prerequisite Relations Among Concepts** (Liang, Wu, Huang, Giles, EMNLP 2015), introduces a single link-based metric called **Reference Distance (RefD)** that measures how asymmetrically two concepts cite each other in a reference network, and shows that this unsupervised metric outperforms then-current supervised classifiers across seven domains on two evaluation datasets. The follow-up work, **Recovering Concept Prerequisite Relations from University Course Dependencies** (Liang, Ye, Wu, Pursel, Giles, AAAI 2017), formalizes the problem of recovering **concept-level** prerequisite relations from observed **course-level** prerequisite dependencies, proposes an optimization-based framework that jointly models concept relations and course-concept memberships, and releases the first real dataset built from university computer-science course listings. Together these papers establish a core supply of prerequisite-relation methods and benchmarks that subsequent prerequisite-learning work (e.g., LectureBank, MOOC-CS, hetGNN-style approaches) builds on or compares against, and they are part of the substrate the paper reuses rather than re-derives.

Liang et al. (2015) Recovering Concept Prerequisite Relations

**PREREQ** is a supervised method for inferring prerequisite relations between educational concepts, introduced by Roy, Madhyastha, Lawrence, and Rajan at IAAI-19 (AAAI 2019). Concepts are represented by latent topic vectors learned with **Pairwise Latent Dirichlet Allocation (Pairwise-LDA)** over concept-aligned online educational text (e.g., course materials and Wikipedia), and a **Siamese neural network** then scores an ordered pair of concept representations to predict whether the first concept is a prerequisite of the second. The method targets the asymmetric, directed nature of prerequisite links and is evaluated on online-course and university-course concept datasets, where it outperforms prior unsupervised and supervised baselines. The work is one of the standard references in the subsequent prerequisite-learning literature alongside Liang et al. (2015) and the LectureBank line.

Roy et al. (2019) PREREQ Concept Prerequisite Inference

**CPRL** (Concept Prerequisite Relation Learning) is a method introduced by Jia, Shen, Tang, Sun, and Lu at NAACL 2021 for predicting prerequisite relations between educational concepts. It builds a **heterogeneous graph** over concepts together with auxiliary node types such as learning objects, applies a heterogeneous graph neural network to obtain concept representations, and feeds those representations together with **concept-pairwise features** to a classifier that predicts whether one concept is a prerequisite of another. The authors further extend CPRL to **weakly supervised** settings, leveraging learning-object dependencies and **data programming** to generate training labels when explicit concept-pair annotations are scarce. CPRL reports state-of-the-art results across four prerequisite-relation benchmarks and is a standard recent reference in the prerequisite-learning literature alongside Liang et al. (2015) and Roy et al. (2019).

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