Educational Cone Model in Embedding Vector Spaces
This work addresses a domain-specific problem for educational technology developers by providing an incremental improvement in evaluating embedding methods for text difficulty analysis.
The paper tackles the challenge of selecting embedding methods for analyzing text difficulty in educational systems by proposing the Educational Cone Model, a geometric framework that assumes easier texts are less diverse and harder texts more diverse, creating cone-shaped distributions in embedding spaces. Empirical tests on real-world datasets validated the model's effectiveness and speed in identifying embedding spaces aligned with difficulty-annotated texts.
Human-annotated datasets with explicit difficulty ratings are essential in intelligent educational systems. Although embedding vector spaces are widely used to represent semantic closeness and are promising for analyzing text difficulty, the abundance of embedding methods creates a challenge in selecting the most suitable method. This study proposes the Educational Cone Model, which is a geometric framework based on the assumption that easier texts are less diverse (focusing on fundamental concepts), whereas harder texts are more diverse. This assumption leads to a cone-shaped distribution in the embedding space regardless of the embedding method used. The model frames the evaluation of embeddings as an optimization problem with the aim of detecting structured difficulty-based patterns. By designing specific loss functions, efficient closed-form solutions are derived that avoid costly computation. Empirical tests on real-world datasets validated the model's effectiveness and speed in identifying the embedding spaces that are best aligned with difficulty-annotated educational texts.