# Cycle Representation Learning for Inductive Relation Prediction

arXiv: https://arxiv.org/abs/2110.02510 · HTML: https://mlsanity.com/paper/2110.02510/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 68 references that are in the map.
- First posted on arXiv 6 Oct 2021.

## Builds on (most cited first, 30 of 33)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [Convolutional 2D Knowledge Graph Embeddings](https://mlsanity.com/paper/1707.01476/) (2017)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (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)
- [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)
- [Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks](https://mlsanity.com/paper/2103.03212/) (2021)
- [Position-aware Graph Neural Networks](https://mlsanity.com/paper/1906.04817/) (2019)
- [Topology-Preserving Deep Image Segmentation](https://mlsanity.com/paper/1906.05404/) (2019)
- [DRUM: End-To-End Differentiable Rule Mining On Knowledge Graphs](https://mlsanity.com/paper/1911.00055/) (2019)
- [Variational Reasoning for Question Answering with Knowledge Graph](https://mlsanity.com/paper/1709.04071/) (2017)
- [RippleNet: Propagating User Preferences on the Knowledge Graph for Recommender Systems](https://mlsanity.com/paper/1803.03467/) (2018)
- [Encoding Sentences with Graph Convolutional Networks for Semantic Role Labeling](https://mlsanity.com/paper/1703.04826/) (2017)
- [PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures](https://mlsanity.com/paper/1904.09378/) (2019)
- [Deep Learning with Topological Signatures](https://mlsanity.com/paper/1707.04041/) (2017)
- [Line Graph Neural Networks for Link Prediction](https://mlsanity.com/paper/2010.10046/) (2020)
- [Rethinking Knowledge Graph Propagation for Zero-Shot Learning](https://mlsanity.com/paper/1805.11724/) (2018)
- [A Topological Filter for Learning with Label Noise](https://mlsanity.com/paper/2012.04835/) (2020)
- [Topology-Aware Segmentation Using Discrete Morse Theory](https://mlsanity.com/paper/2103.09992/) (2021)
- [A Re-evaluation of Knowledge Graph Completion Methods](https://mlsanity.com/paper/1911.03903/) (2019)
- [Graph Filtration Learning](https://mlsanity.com/paper/1905.10996/) (2019)
- [A Topological Regularizer for Classifiers via Persistent Homology](https://mlsanity.com/paper/1806.10714/) (2018)
- [Learning metrics for persistence-based summaries and applications for graph classification](https://mlsanity.com/paper/1904.12189/) (2019)
- [Communicative Message Passing for Inductive Relation Reasoning](https://mlsanity.com/paper/2012.08911/) (2020)
- [Link Prediction with Persistent Homology: An Interactive View](https://mlsanity.com/paper/2102.10255/) (2021)
- [Topological Detection of Trojaned Neural Networks](https://mlsanity.com/paper/2106.06469/) (2021)
- [Clique topology reveals intrinsic geometric structure in neural correlations](https://mlsanity.com/paper/1502.06172/) (2015)

## Built on by (most cited first, 23 of 23)

- [InGram: Inductive Knowledge Graph Embedding via Relation Graphs](https://mlsanity.com/paper/2305.19987/) (2023)
- [Neural Approximation of Graph Topological Features](https://mlsanity.com/paper/2201.12032/) (2022)
- [Generalizing to Unseen Elements: A Survey on Knowledge Extrapolation for Knowledge Graphs](https://mlsanity.com/paper/2302.01859/) (2023)
- [An Efficient Subgraph GNN with Provable Substructure Counting Power](https://mlsanity.com/paper/2303.10576/) (2023)
- [Cycle Invariant Positional Encoding for Graph Representation Learning](https://mlsanity.com/paper/2311.14333/) (2023)
- [Logical Reasoning with Relation Network for Inductive Knowledge Graph Completion](https://mlsanity.com/paper/2406.01140/) (2024)
- [NeuroPath: A Neural Pathway Transformer for Joining the Dots of Human Connectomes](https://mlsanity.com/paper/2409.17510/) (2024)
- [Towards Graph Foundation Models: Training on Knowledge Graphs Enables Transferability to General Graphs](https://mlsanity.com/paper/2410.12609/) (2024)
- [Enhancing Graph Representation Learning with Localized Topological Features](https://mlsanity.com/paper/2501.09178/) (2025)
- [GEFL: Extended Filtration Learning for Graph Classification](https://mlsanity.com/paper/2406.02732/) (2024)
- [FamilyTool: A Multi-hop Personalized Tool Use Benchmark](https://mlsanity.com/paper/2504.06766/) (2025)
- [Inductive Knowledge Graph Completion with GNNs and Rules: An Analysis](https://mlsanity.com/paper/2308.07942/) (2023)
- [Learning Rule-Induced Subgraph Representations for Inductive Relation Prediction](https://mlsanity.com/paper/2408.07088/) (2024)
- [Zero-Shot Relational Learning for Multimodal Knowledge Graphs](https://mlsanity.com/paper/2404.06220/) (2024)
- [Beyond Transduction: A Survey on Inductive, Few Shot, and Zero Shot Link Prediction in Knowledge Graphs](https://mlsanity.com/paper/2312.04997/) (2023)
- [Faithful Differentiable Reasoning with Reshuffled Region-based Embeddings](https://mlsanity.com/paper/2406.09529/) (2024)
- [Feature Propagation on Knowledge Graphs using Cellular Sheaves](https://mlsanity.com/paper/2309.03773/) (2023)
- [Message Detouring: A Simple Yet Effective Cycle Representation for Expressive Graph Learning](https://mlsanity.com/paper/2402.08085/) (2024)
- [S2DN: Learning to Denoise Unconvincing Knowledge for Inductive Knowledge Graph Completion](https://mlsanity.com/paper/2412.15822/) (2024)
- [Chordless Structure: A Pathway to Simple and Expressive GNNs](https://mlsanity.com/paper/2505.19188/) (2025)
- [Caterpillar GNN: Replacing Message Passing with Efficient Aggregation](https://mlsanity.com/paper/2506.06784/) (2025)
- [Scalable Topology-Preserving Graph Coarsening: Concepts and Algorithms](https://mlsanity.com/paper/2601.22943/) (2026)
- [Model Graph Inductive Learning for Knowledge Graph Completion](https://mlsanity.com/paper/2606.16509/) (2026)

## Abstract (arXiv)

In recent years, algebraic topology and its modern development, the theory of persistent homology, has shown great potential in graph representation learning. In this paper, based on the mathematics of algebraic topology, we propose a novel solution for inductive relation prediction, an important learning task for knowledge graph completion. To predict the relation between two entities, one can use the existence of rules, namely a sequence of relations. Previous works view rules as paths and primarily focus on the searching of paths between entities. The space of rules is huge, and one has to sacrifice either efficiency or accuracy. In this paper, we consider rules as cycles and show that the space of cycles has a unique structure based on the mathematics of algebraic topology. By exploring the linear structure of the cycle space, we can improve the searching efficiency of rules. We propose to collect cycle bases that span the space of cycles. We build a novel GNN framework on the collected cycles to learn the representations of cycles, and to predict the existence/non-existence of a relation. Our method achieves state-of-the-art performance on benchmarks.