# ER: Equivariance Regularizer for Knowledge Graph Completion

arXiv: https://arxiv.org/abs/2206.12142 · HTML: https://mlsanity.com/paper/2206.12142/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 44 references that are in the map.
- First posted on arXiv 24 Jun 2022.

## Builds on (most cited first, 23 of 23)

- [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)
- [ERNIE: Enhanced Language Representation with Informative Entities](https://mlsanity.com/paper/1905.07129/) (2019)
- [TuckER: Tensor Factorization for Knowledge Graph Completion](https://mlsanity.com/paper/1901.09590/) (2019)
- [Low-Dimensional Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2005.00545/) (2020)
- [Quaternion Knowledge Graph Embeddings](https://mlsanity.com/paper/1904.10281/) (2019)
- [Canonical Tensor Decomposition for Knowledge Base Completion](https://mlsanity.com/paper/1806.07297/) (2018)
- [RippleNet: Propagating User Preferences on the Knowledge Graph for Recommender Systems](https://mlsanity.com/paper/1803.03467/) (2018)
- [Learning Hierarchy-Aware Knowledge Graph Embeddings for Link Prediction](https://mlsanity.com/paper/1911.09419/) (2019)
- [Multi-relational Poincar'e Graph Embeddings](https://mlsanity.com/paper/1905.09791/) (2019)
- [Learning Attention-based Embeddings for Relation Prediction in Knowledge Graphs](https://mlsanity.com/paper/1906.01195/) (2019)
- [Analogical Inference for Multi-Relational Embeddings](https://mlsanity.com/paper/1705.02426/) (2017)
- [The More You Know: Using Knowledge Graphs for Image Classification](https://mlsanity.com/paper/1612.04844/) (2016)
- [A Survey of Community Detection Approaches: From Statistical Modeling to Deep Learning](https://mlsanity.com/paper/2101.01669/) (2021)
- [Hypernetwork Knowledge Graph Embeddings](https://mlsanity.com/paper/1808.07018/) (2018)
- [Orthogonal Relation Transforms with Graph Context Modeling for Knowledge Graph Embedding](https://mlsanity.com/paper/1911.04910/) (2019)
- [Improving Knowledge Graph Embedding Using Simple Constraints](https://mlsanity.com/paper/1805.02408/) (2018)
- [Duality-Induced Regularizer for Tensor Factorization Based Knowledge Graph Completion](https://mlsanity.com/paper/2011.05816/) (2020)
- [Adversarial Sets for Regularising Neural Link Predictors](https://mlsanity.com/paper/1707.07596/) (2017)
- [Seeing is Knowing! Fact-based Visual Question Answering using Knowledge Graph Embeddings](https://mlsanity.com/paper/2012.15484/) (2020)
- [Knowledge Graph Fact Prediction via Knowledge-Enriched Tensor Factorization](https://mlsanity.com/paper/1902.03077/) (2019)

## Built on by (most cited first, 4 of 4)

- [Rethinking Regularization Methods for Knowledge Graph Completion](https://mlsanity.com/paper/2505.23442/) (2025)
- [Treat Different Negatives Differently: Enriching Loss Functions with Domain and Range Constraints for Link Prediction](https://mlsanity.com/paper/2303.00286/) (2023)
- [Lorentz Equivariant Model for Knowledge-Enhanced Hyperbolic Collaborative Filtering](https://mlsanity.com/paper/2302.04545/) (2023)
- [From Wide to Deep: Dimension Lifting Network for Parameter-efficient Knowledge Graph Embedding](https://mlsanity.com/paper/2303.12816/) (2023)

## Abstract (arXiv)

Tensor factorization and distanced based models play important roles in knowledge graph completion (KGC). However, the relational matrices in KGC methods often induce a high model complexity, bearing a high risk of overfitting. As a remedy, researchers propose a variety of different regularizers such as the tensor nuclear norm regularizer. Our motivation is based on the observation that the previous work only focuses on the "size" of the parametric space, while leaving the implicit semantic information widely untouched. To address this issue, we propose a new regularizer, namely, Equivariance Regularizer (ER), which can suppress overfitting by leveraging the implicit semantic information. Specifically, ER can enhance the generalization ability of the model by employing the semantic equivariance between the head and tail entities. Moreover, it is a generic solution for both distance based models and tensor factorization based models. The experimental results indicate a clear and substantial improvement over the state-of-the-art relation prediction methods.