Geometric Relational Embeddings
<|reference_start|>Geometric Relational Embeddings: Relational representation learning transforms relational data into continuous and low-dimensional vector representations. However, vector-based representations fall short in capturing crucial properties of relational data that are complex and symbolic. We propose geometric relational embeddings, a paradigm of relational embeddings that respect the underlying symbolic structures. Specifically, this dissertation introduces various geometric relational embedding models capable of capturing: 1) complex structured patterns like hierarchies and cycles in networks and knowledge graphs; 2) logical structures in ontologies and logical constraints applicable for constraining machine learning model outputs; and 3) high-order structures between entities and relations. Our results obtained from benchmark and real-world datasets demonstrate the efficacy of geometric relational embeddings in adeptly capturing these discrete, symbolic, and structured properties inherent in relational data.<|reference_end|>
@article{xiong2024geometric,
    title={Geometric Relational Embeddings},
    author={Bo Xiong},
    journal={arXiv preprint arXiv:2409.15369},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.15369},
    primaryClass={cs.LG cs.AI cs.SI}
}