# River of No Return: Graph Percolation Embeddings for Efficient Knowledge Graph Reasoning

arXiv: https://arxiv.org/abs/2305.09974 · HTML: https://mlsanity.com/paper/2305.09974/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 43 references that are in the map.
- First posted on arXiv 17 May 2023.

## Builds on (most cited first, 29 of 29)

- [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)
- [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)
- [A Survey on Knowledge Graphs: Representation, Acquisition and Applications](https://mlsanity.com/paper/2002.00388/) (2020)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [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)
- [DeepPath: A Reinforcement Learning Method for Knowledge Graph Reasoning](https://mlsanity.com/paper/1707.06690/) (2017)
- [Inductive Relation Prediction by Subgraph Reasoning](https://mlsanity.com/paper/1911.06962/) (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)
- [DRUM: End-To-End Differentiable Rule Mining On Knowledge Graphs](https://mlsanity.com/paper/1911.00055/) (2019)
- [RNNLogic: Learning Logic Rules for Reasoning on Knowledge Graphs](https://mlsanity.com/paper/2010.04029/) (2020)
- [Knowledge Graph Reasoning with Relational Digraph](https://mlsanity.com/paper/2108.06040/) (2021)
- [ConE: Cone Embeddings for Multi-Hop Reasoning over Knowledge Graphs](https://mlsanity.com/paper/2110.13715/) (2021)
- [A Semantic Matching Energy Function for Learning with Multi-relational Data](https://mlsanity.com/paper/1301.3485/) (2013)
- [Relational Message Passing for Knowledge Graph Completion](https://mlsanity.com/paper/2002.06757/) (2020)
- [Modeling Relation Paths for Representation Learning of Knowledge Bases](https://mlsanity.com/paper/1506.00379/) (2015)
- [A*Net: A Scalable Path-based Reasoning Approach for Knowledge Graphs](https://mlsanity.com/paper/2206.04798/) (2022)
- [Chains of Reasoning over Entities, Relations, and Text using Recurrent Neural Networks](https://mlsanity.com/paper/1607.01426/) (2016)
- [Contrastive Language-Image Pre-Training with Knowledge Graphs](https://mlsanity.com/paper/2210.08901/) (2022)
- [Compositional Vector Space Models for Knowledge Base Completion](https://mlsanity.com/paper/1504.06662/) (2015)
- [Model Degradation Hinders Deep Graph Neural Networks](https://mlsanity.com/paper/2206.04361/) (2022)
- [Learning to Sample and Aggregate: Few-shot Reasoning over Temporal Knowledge Graphs](https://mlsanity.com/paper/2210.08654/) (2022)
- [Rethinking Knowledge Graph Evaluation Under the Open-World Assumption](https://mlsanity.com/paper/2209.08858/) (2022)
- [Hyperbolic Geometry is Not Necessary: Lightweight Euclidean-Based Models for Low-Dimensional Knowledge Graph Embeddings](https://mlsanity.com/paper/2103.14930/) (2021)
- [Swift and Sure: Hardness-aware Contrastive Learning for Low-dimensional Knowledge Graph Embeddings](https://mlsanity.com/paper/2201.00565/) (2022)
- [SalKG: Learning From Knowledge Graph Explanations for Commonsense Reasoning](https://mlsanity.com/paper/2104.08793/) (2021)

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

- [LLM as Prompter: Low-resource Inductive Reasoning on Arbitrary Knowledge Graphs](https://mlsanity.com/paper/2402.11804/) (2024)
- [Diagnosing and Mitigating Semantic Inconsistencies in Wikidata's Classification Hierarchy](https://mlsanity.com/paper/2511.04926/) (2025)

## Abstract (arXiv)

We study Graph Neural Networks (GNNs)-based embedding techniques for knowledge graph (KG) reasoning. For the first time, we link the path redundancy issue in the state-of-the-art KG reasoning models based on path encoding and message passing to the transformation error in model training, which brings us new theoretical insights into KG reasoning, as well as high efficacy in practice. On the theoretical side, we analyze the entropy of transformation error in KG paths and point out query-specific redundant paths causing entropy increases. These findings guide us to maintain the shortest paths and remove redundant paths for minimized-entropy message passing. To achieve this goal, on the practical side, we propose an efficient Graph Percolation Process motivated by the percolation model in Fluid Mechanics, and design a lightweight GNN-based KG reasoning framework called Graph Percolation Embeddings (GraPE). GraPE outperforms previous state-of-the-art methods in both transductive and inductive reasoning tasks while requiring fewer training parameters and less inference time.