北京大学学报（自然科学版）2026，Vol.62Issue(4)：710-718,9.DOI:10.13209/j.0479-8023.2025.088
基于结构化双向编码的数学知识图谱表示学习模型
Structural Bidirectional Encoding-Based Representation Learning on Mathematical Knowledge Graphs
摘要
Abstract
Most existing studies on knowledge graph representation learning simply characterize knowledge as entities and relations,and ignore complex relation learning and multi-associative knowledge chains.It is difficult to accurately build a subject knowledge system,which affects the generation of learning paths.Thus,we propose a structural Bidirectional Encoding-Based Representation Learning model(SBE)for disciplinary knowledge graphs.Graph data augmentation is used to characterize entities and relations as initialized vector sequences.Additionally,the model combines structured bidirectional encoding and decoding to accurately represent positional information in context and complex relationship chains.Moreover,an inference strategy is proposed based on counterfactual link generation.Experimental results demonstrate that the proposed model can enhance the accuracy of both link prediction and knowledge recommendation.Furthermore,a case study on middle school mathematics reveals that the SBE model can generate learning paths tailored to student needs and effectively improve the precision,compre-hensiveness,and interpretability.关键词
数学知识图谱表示学习/结构化双向编码/反事实链路/学习路径Key words
mathematical knowledge graph representation learning/structural bidirectional encoding/counter-factual link generation/learning paths引用本文复制引用
金郎俊卿,尚亚蓉,池铠淇,于超..基于结构化双向编码的数学知识图谱表示学习模型[J].北京大学学报（自然科学版）,2026,62(4):710-718,9.基金项目
广东省深圳市宝安区青年教师专项课题(BAQN2024013)资助 （BAQN2024013）
