# Generalizing Knowledge Graph Embedding with Universal Orthogonal Parameterization

arXiv: https://arxiv.org/abs/2405.08540 · HTML: https://mlsanity.com/paper/2405.08540/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 65 references that are in the map.
- First posted on arXiv 14 May 2024.

## Builds on (most cited first, 25 of 25)

- [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)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [SphereFace: Deep Hypersphere Embedding for Face Recognition](https://mlsanity.com/paper/1704.08063/) (2017)
- [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)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Composition-based Multi-Relational Graph Convolutional Networks](https://mlsanity.com/paper/1911.03082/) (2019)
- [Neural Bellman-Ford Networks: A General Graph Neural Network Framework for Link Prediction](https://mlsanity.com/paper/2106.06935/) (2021)
- [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)
- [Quaternion Knowledge Graph Embeddings](https://mlsanity.com/paper/1904.10281/) (2019)
- [Deep Bidirectional Language-Knowledge Graph Pretraining](https://mlsanity.com/paper/2210.09338/) (2022)
- [Learning on Large-scale Text-attributed Graphs via Variational Inference](https://mlsanity.com/paper/2210.14709/) (2022)
- [Canonical Tensor Decomposition for Knowledge Base Completion](https://mlsanity.com/paper/1806.07297/) (2018)
- [A Novel Embedding Model for Knowledge Base Completion Based on Convolutional Neural Network](https://mlsanity.com/paper/1712.02121/) (2017)
- [Mixed-curvature Variational Autoencoders](https://mlsanity.com/paper/1911.08411/) (2019)
- [On orthogonality and learning recurrent networks with long term dependencies](https://mlsanity.com/paper/1702.00071/) (2017)
- [PairRE: Knowledge Graph Embeddings via Paired Relation Vectors](https://mlsanity.com/paper/2011.03798/) (2020)
- [The Numerical Stability of Hyperbolic Representation Learning](https://mlsanity.com/paper/2211.00181/) (2022)
- [Efficiently Leveraging Multi-level User Intent for Session-based Recommendation via Atten-Mixer Network](https://mlsanity.com/paper/2206.12781/) (2022)
- [Orthogonal Graph Neural Networks](https://mlsanity.com/paper/2109.11338/) (2021)
- [On Procrustes Analysis in Hyperbolic Space](https://mlsanity.com/paper/2102.03723/) (2021)
- [Ripple Knowledge Graph Convolutional Networks For Recommendation Systems](https://mlsanity.com/paper/2305.01147/) (2023)
- [To Copy Rather Than Memorize: A Vertical Learning Paradigm for Knowledge Graph Completion](https://mlsanity.com/paper/2305.14126/) (2023)

## Built on by (most cited first, 7 of 7)

- [Bridging External and Parametric Knowledge: Mitigating Hallucination of LLMs with Shared-Private Semantic Synergy in Dual-Stream Knowledge](https://mlsanity.com/paper/2506.06240/) (2025)
- [Emotion Collider: Dual Hyperbolic Mirror Manifolds for Sentiment Recovery via Anti Emotion Reflection](https://mlsanity.com/paper/2602.16161/) (2026)
- [MPRM: A Markov Path-based Rule Miner for Efficient and Interpretable Knowledge Graph Reasoning](https://mlsanity.com/paper/2505.12329/) (2025)
- [Why Isn't Relational Learning Taking Over the World?](https://mlsanity.com/paper/2507.13558/) (2025)
- [Relations Are Channels: Knowledge Graph Embedding via Kraus Decompositions](https://mlsanity.com/paper/2605.10317/) (2026)
- [Spectral Initialization and Scheduled Graph Smoothness for Uncertain Knowledge Graph Completion](https://mlsanity.com/paper/2609.02519/) (2026)
- [PAGR: Proof-Carrying Algebraic-Geometric Retrieval: A Quiver-, Provenance-, and Sheaf-Theoretic Framework for Grounded LLM Retrieval](https://mlsanity.com/paper/2609.06127/) (2026)

## Abstract (arXiv)

Recent advances in knowledge graph embedding (KGE) rely on Euclidean/hyperbolic orthogonal relation transformations to model intrinsic logical patterns and topological structures. However, existing approaches are confined to rigid relational orthogonalization with restricted dimension and homogeneous geometry, leading to deficient modeling capability. In this work, we move beyond these approaches in terms of both dimension and geometry by introducing a powerful framework named GoldE, which features a universal orthogonal parameterization based on a generalized form of Householder reflection. Such parameterization can naturally achieve dimensional extension and geometric unification with theoretical guarantees, enabling our framework to simultaneously capture crucial logical patterns and inherent topological heterogeneity of knowledge graphs. Empirically, GoldE achieves state-of-the-art performance on three standard benchmarks. Codes are available at https://github.com/xxrep/GoldE.