# Pseudo-Riemannian Embedding Models for Multi-Relational Graph Representations

arXiv: https://arxiv.org/abs/2212.03720 · HTML: https://mlsanity.com/paper/2212.03720/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 39 references that are in the map.
- First posted on arXiv 2 Dec 2022.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [Complex Embeddings for Simple Link Prediction](https://mlsanity.com/paper/1606.06357/) (2016)
- [Convolutional 2D Knowledge Graph Embeddings](https://mlsanity.com/paper/1707.01476/) (2017)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [TuckER: Tensor Factorization for Knowledge Graph Completion](https://mlsanity.com/paper/1901.09590/) (2019)
- [A Review of Relational Machine Learning for Knowledge Graphs](https://mlsanity.com/paper/1503.00759/) (2015)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Low-Dimensional Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2005.00545/) (2020)
- [Multi-relational Poincar'e Graph Embeddings](https://mlsanity.com/paper/1905.09791/) (2019)
- [The impossibility of low rank representations for triangle-rich complex networks](https://mlsanity.com/paper/2003.12635/) (2020)
- [Symmetric Spaces for Graph Embeddings: A Finsler-Riemannian Approach](https://mlsanity.com/paper/2106.04941/) (2021)
- [Scientific Language Models for Biomedical Knowledge Base Completion: An Empirical Study](https://mlsanity.com/paper/2106.09700/) (2021)
- [Hyperbolic Disk Embeddings for Directed Acyclic Graphs](https://mlsanity.com/paper/1902.04335/) (2019)
- [Memory-Efficient Adaptive Optimization](https://mlsanity.com/paper/1901.11150/) (2019)
- [Ultrahyperbolic Representation Learning](https://mlsanity.com/paper/2007.00211/) (2020)
- [On Evaluating Embedding Models for Knowledge Base Completion](https://mlsanity.com/paper/1810.07180/) (2018)
- [Directed Graph Embeddings in Pseudo-Riemannian Manifolds](https://mlsanity.com/paper/2106.08678/) (2021)
- [Embedding Graphs in Lorentzian Spacetime](https://mlsanity.com/paper/1602.03103/) (2016)
- [Semi-Riemannian Manifold Optimization](https://mlsanity.com/paper/1812.07643/) (2018)

## Abstract (arXiv)

In this paper we generalize single-relation pseudo-Riemannian graph embedding models to multi-relational networks, and show that the typical approach of encoding relations as manifold transformations translates from the Riemannian to the pseudo-Riemannian case. In addition we construct a view of relations as separate spacetime submanifolds of multi-time manifolds, and consider an interpolation between a pseudo-Riemannian embedding model and its Wick-rotated Riemannian counterpart. We validate these extensions in the task of link prediction, focusing on flat Lorentzian manifolds, and demonstrate their use in both knowledge graph completion and knowledge discovery in a biological domain.