Predicting Prerequisite Relations for Unseen Concepts (2022)

Abstract: Concept prerequisite learning (CPL) plays a key role in developing technologies that assist people to learn a new complex topic or concept. Previous work commonly assumes that all concepts are given at training time and solely focuses on predicting the unseen prerequisite relationships between them. However, many real-world scenarios deal with concepts that are left undiscovered at training time, which is relatively unexplored. This paper studies this problem and proposes a novel alternating knowledge distillation approach to take advantage of both content- and graph-based models for this task. Extensive experiments on three public benchmarks demonstrate up to 10% improvements in terms of F1 score.

## introduction as the amount of online educational data rapidly grows, it is more important than ever to develop information access systems that assist users to learn new complex topics or concepts @xcite @xcite . a fundamental step towards developing these systems is concept prerequisite learning (cpl)-the task of building a concept graph by structuring open knowledge in prerequisite relations. a prerequisite is a directed relation between two concepts, e.g., heap tree is a prerequisite of heap sort. cpl was first introduced by @xcite with the aim of formulating probabilistic planning problems for machine learning solvers. a number of cpl models use various kinds external resources including wikipedia links @xcite , textbook structures @xcite , and course dependencies @xcite in two ways: content-based @xcite @xcite and graph-based @xcite . there also exists research on active learning @xcite , unsuper-vised learning @xcite , and domain adaptation @xcite to meet data insufficiency challenges in cpl problems. however, most existing approaches assume the system to reconstruct concept prerequisite paths with vague knowledge (i.e. incomplete relations) of each concept, or to transfer graph structure information to a new domain. in practical scenarios, knowledge is updated with both new concepts and relations introduced. to jump out of the offline setting of graph completion with given concepts, we define a new task -cpl for unseen concepts, i.e. predicting prerequisite relationships for concepts that never appear in the training set. most existing graph-based cpl approaches cannot be simply used for unseen concepts, because the randomly initialized concept representations do not get updated for unseen concepts. a simple solution would be initializing the concept embeddings based on content-based models @xcite @xcite . to better take advantage of content information, we propose a novel cpl model that consists of two components: one that solely focuses on textual content associated with each concept and another one that focuses on the concept graph structure. to train our model, we propose an iterative knowledge distillation approach by alternating between these two components as "teacher" and "student". our main contributions include: ## methodology this section introduces a cpl model that uses two complementary components. the first component models prerequisite relations conditioned on textual content retrieved for each concept (i.e., a retrieval-augmented model), and the second component casts the problem as a link prediction task and models prerequisite relations conditioned on the graph structure. the proposed method uses a knowledge distillation approach that alters between these two components as the teacher and student models, iteratively. an overview of the proposed solution is presented in figure 1 . notation and problem statement: let @xmath0, e) be a directed concept graph whose vertices are associated with concepts and edges represent prerequisite relations, v h be a set of unseen concepts to dig out. the training set for concept prerequisite learning is equal to ## conclusions and future work this paper explored the challenge of predicting prerequisites for unseen concepts in cpl. it proposed an alternating knowledge distillation approach that enables us to train more effective content-based and graph-based models, as well demonstrated that content-based cpl models can benefit from retrieval augmentation. in the future, we intent to extend the proposed solution to an online setting, where concept prerequisites can be extracted for every learning-oriented query in a search engine.