# FFHR: Fully and Flexible Hyperbolic Representation for Knowledge Graph Completion

arXiv: https://arxiv.org/abs/2302.04088 · HTML: https://mlsanity.com/paper/2302.04088/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 47 references that are in the map.
- First posted on arXiv 7 Feb 2023.

## Builds on (most cited first, 30 of 31)

- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [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)
- [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 Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [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)
- [KGAT: Knowledge Graph Attention Network for Recommendation](https://mlsanity.com/paper/1905.07854/) (2019)
- [TuckER: Tensor Factorization for Knowledge Graph Completion](https://mlsanity.com/paper/1901.09590/) (2019)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (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)
- [A Survey on Knowledge Graph-Based Recommender Systems](https://mlsanity.com/paper/2003.00911/) (2020)
- [Canonical Tensor Decomposition for Knowledge Base Completion](https://mlsanity.com/paper/1806.07297/) (2018)
- [Multi-relational Poincar'e Graph Embeddings](https://mlsanity.com/paper/1905.09791/) (2019)
- [Orthogonal Weight Normalization: Solution to Optimization over Multiple Dependent Stiefel Manifolds in Deep Neural Networks](https://mlsanity.com/paper/1709.06079/) (2017)
- [Learning Symmetric Collaborative Dialogue Agents with Dynamic Knowledge Graph Embeddings](https://mlsanity.com/paper/1704.07130/) (2017)
- [Neural Embeddings of Graphs in Hyperbolic Space](https://mlsanity.com/paper/1705.10359/) (2017)
- [A Hyperbolic-to-Hyperbolic Graph Convolutional Network](https://mlsanity.com/paper/2104.06942/) (2021)
- [Hyperbolic Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/2202.13852/) (2022)
- [Orthogonal Relation Transforms with Graph Context Modeling for Knowledge Graph Embedding](https://mlsanity.com/paper/1911.04910/) (2019)
- [Modeling Heterogeneous Hierarchies with Relation-specific Hyperbolic Cones](https://mlsanity.com/paper/2110.14923/) (2021)
- [AutoSF: Searching Scoring Functions for Knowledge Graph Embedding](https://mlsanity.com/paper/1904.11682/) (2019)
- [DyKgChat: Benchmarking Dialogue Generation Grounding on Dynamic Knowledge Graphs](https://mlsanity.com/paper/1910.00610/) (2019)
- [Duality-Induced Regularizer for Tensor Factorization Based Knowledge Graph Completion](https://mlsanity.com/paper/2011.05816/) (2020)
- [Relation Embedding with Dihedral Group in Knowledge Graph](https://mlsanity.com/paper/1906.00687/) (2019)

## Built on by (most cited first, 1 of 1)

- [Hyperbolic Hypergraph Neural Networks for Multi-Relational Knowledge Hypergraph Representation](https://mlsanity.com/paper/2412.12158/) (2024)

## Abstract (arXiv)

Learning hyperbolic embeddings for knowledge graph (KG) has gained increasing attention due to its superiority in capturing hierarchies. However, some important operations in hyperbolic space still lack good definitions, making existing methods unable to fully leverage the merits of hyperbolic space. Specifically, they suffer from two main limitations: 1) existing Graph Convolutional Network (GCN) methods in hyperbolic space rely on tangent space approximation, which would incur approximation error in representation learning, and 2) due to the lack of inner product operation definition in hyperbolic space, existing methods can only measure the plausibility of facts (links) with hyperbolic distance, which is difficult to capture complex data patterns. In this work, we contribute: 1) a Full Poincar'e Multi-relational GCN that achieves graph information propagation in hyperbolic space without requiring any approximation, and 2) a hyperbolic generalization of Euclidean inner product that is beneficial to capture both hierarchical and complex patterns. On this basis, we further develop a Fully and Flexible Hyperbolic Representation framework (FFHR) that is able to transfer recent Euclidean-based advances to hyperbolic space. We demonstrate it by instantiating FFHR with four representative KGC methods. Extensive experiments on benchmark datasets validate the superiority of our FFHRs over their Euclidean counterparts as well as state-of-the-art hyperbolic embedding methods.