# Geometric Relational Embeddings

arXiv: https://arxiv.org/abs/2409.15369 · HTML: https://mlsanity.com/paper/2409.15369/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 18 Sep 2024.

## Abstract (arXiv)

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.