# PAC-Bayesian Generalization Bounds for Knowledge Graph Representation Learning

arXiv: https://arxiv.org/abs/2405.06418 · HTML: https://mlsanity.com/paper/2405.06418/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 62 references that are in the map.
- First posted on arXiv 10 May 2024.

## Builds on (most cited first, 30 of 40)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [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)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [Composition-based Multi-Relational Graph Convolutional Networks](https://mlsanity.com/paper/1911.03082/) (2019)
- [A PAC-Bayesian Approach to Spectrally-Normalized Margin Bounds for Neural Networks](https://mlsanity.com/paper/1707.09564/) (2017)
- [Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks](https://mlsanity.com/paper/1703.02930/) (2017)
- [Inductive Relation Prediction by Subgraph Reasoning](https://mlsanity.com/paper/1911.06962/) (2019)
- [User-friendly introduction to PAC-Bayes bounds](https://mlsanity.com/paper/2110.11216/) (2021)
- [Generalization and Representational Limits of Graph Neural Networks](https://mlsanity.com/paper/2002.06157/) (2020)
- [SimplE Embedding for Link Prediction in Knowledge Graphs](https://mlsanity.com/paper/1802.04868/) (2018)
- [Holographic Embeddings of Knowledge Graphs](https://mlsanity.com/paper/1510.04935/) (2015)
- [Quaternion Knowledge Graph Embeddings](https://mlsanity.com/paper/1904.10281/) (2019)
- [End-to-end Structure-Aware Convolutional Networks for Knowledge Base Completion](https://mlsanity.com/paper/1811.04441/) (2018)
- [A Primer on PAC-Bayesian Learning](https://mlsanity.com/paper/1901.05353/) (2019)
- [Learning Attention-based Embeddings for Relation Prediction in Knowledge Graphs](https://mlsanity.com/paper/1906.01195/) (2019)
- [CoDEx: A Comprehensive Knowledge Graph Completion Benchmark](https://mlsanity.com/paper/2009.07810/) (2020)
- [A PAC-Bayesian Approach to Generalization Bounds for Graph Neural Networks](https://mlsanity.com/paper/2012.07690/) (2020)
- [Analogical Inference for Multi-Relational Embeddings](https://mlsanity.com/paper/1705.02426/) (2017)
- [Subgroup Generalization and Fairness of Graph Neural Networks](https://mlsanity.com/paper/2106.15535/) (2021)
- [PairRE: Knowledge Graph Embeddings via Paired Relation Vectors](https://mlsanity.com/paper/2011.03798/) (2020)
- [Generalization Analysis of Message Passing Neural Networks on Large Random Graphs](https://mlsanity.com/paper/2202.00645/) (2022)

## Built on by (most cited first, 2 of 2)

- [Towards Bridging Generalization and Expressivity of Graph Neural Networks](https://mlsanity.com/paper/2410.10051/) (2024)
- [Understanding Generalization in Node and Link Prediction](https://mlsanity.com/paper/2507.00927/) (2025)

## Abstract (arXiv)

While a number of knowledge graph representation learning (KGRL) methods have been proposed over the past decade, very few theoretical analyses have been conducted on them. In this paper, we present the first PAC-Bayesian generalization bounds for KGRL methods. To analyze a broad class of KGRL models, we propose a generic framework named ReED (Relation-aware Encoder-Decoder), which consists of a relation-aware message passing encoder and a triplet classification decoder. Our ReED framework can express at least 15 different existing KGRL models, including not only graph neural network-based models such as R-GCN and CompGCN but also shallow-architecture models such as RotatE and ANALOGY. Our generalization bounds for the ReED framework provide theoretical grounds for the commonly used tricks in KGRL, e.g., parameter-sharing and weight normalization schemes, and guide desirable design choices for practical KGRL methods. We empirically show that the critical factors in our generalization bounds can explain actual generalization errors on three real-world knowledge graphs.