用几何锥形模型识别文本难易度的最优嵌入方法
Educational Cone Model in Embedding Vector Spaces
- 基于文本难易度差异的几何假设，构建嵌入空间锥形分布模型
- 在真实教育数据集上验证，可高效识别最适配难易标注的嵌入空间
- 适合教育智能系统、文本难度分析的研究者使用
人工标注且带有明确难度评级的数据集对智能教育系统至关重要。尽管嵌入向量空间广泛用于表征语义相似性，并在分析文本难度方面具有潜力，但嵌入方法的多样性带来了选择合适方法的挑战。本研究提出教育锥形模型（Educational Cone Model），基于一个假设：较简单的文本多样性较低（聚焦基础概念），而较难的文本多样性更高。该假设导致无论使用何种嵌入方法，嵌入空间中均呈现锥形分布。模型将嵌入评估建模为优化问题，旨在检测基于难度的结构化模式。通过设计特定损失函数，推导出高效的闭式解，避免高成本计算。在真实世界数据集上的实证测试验证了该模型在识别与难度标注教育文本最匹配的嵌入空间方面的有效性和速度。
原文摘要 · Abstract (English)
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.
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