# Rule Learning for Knowledge Graph Reasoning under Agnostic Distribution Shift

arXiv: https://arxiv.org/abs/2507.05110 · HTML: https://mlsanity.com/paper/2507.05110/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 39 of its 75 references that are in the map.
- First posted on arXiv 7 Jul 2025.

## Builds on (most cited first, 30 of 39)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems](https://mlsanity.com/paper/2005.01643/) (2020)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (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)
- [Learning to Generalize: Meta-Learning for Domain Generalization](https://mlsanity.com/paper/1710.03463/) (2017)
- [Generalizing to Unseen Domains via Adversarial Data Augmentation](https://mlsanity.com/paper/1805.12018/) (2018)
- [Domain Generalization by Solving Jigsaw Puzzles](https://mlsanity.com/paper/1903.06864/) (2019)
- [Domain Generalization via Model-Agnostic Learning of Semantic Features](https://mlsanity.com/paper/1910.13580/) (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)
- [Pretrained Transformers Improve Out-of-Distribution Robustness](https://mlsanity.com/paper/2004.06100/) (2020)
- [Neural Bellman-Ford Networks: A General Graph Neural Network Framework for Link Prediction](https://mlsanity.com/paper/2106.06935/) (2021)
- [Generalizing Across Domains via Cross-Gradient Training](https://mlsanity.com/paper/1804.10745/) (2018)
- [Episodic Training for Domain Generalization](https://mlsanity.com/paper/1902.00113/) (2019)
- [Inductive Relation Prediction by Subgraph Reasoning](https://mlsanity.com/paper/1911.06962/) (2019)
- [DRUM: End-To-End Differentiable Rule Mining On Knowledge Graphs](https://mlsanity.com/paper/1911.00055/) (2019)
- [End-to-End Differentiable Proving](https://mlsanity.com/paper/1705.11040/) (2017)
- [Learning to Optimize Domain Specific Normalization for Domain Generalization](https://mlsanity.com/paper/1907.04275/) (2019)
- [Deep Stable Learning for Out-Of-Distribution Generalization](https://mlsanity.com/paper/2104.07876/) (2021)
- [Efficient Domain Generalization via Common-Specific Low-Rank Decomposition](https://mlsanity.com/paper/2003.12815/) (2020)
- [An Empirical Study on Robustness to Spurious Correlations using Pre-trained Language Models](https://mlsanity.com/paper/2007.06778/) (2020)
- [From Local Structures to Size Generalization in Graph Neural Networks](https://mlsanity.com/paper/2010.08853/) (2020)
- [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)
- [Size-Invariant Graph Representations for Graph Classification Extrapolations](https://mlsanity.com/paper/2103.05045/) (2021)
- [OOD-GNN: Out-of-Distribution Generalized Graph Neural Network](https://mlsanity.com/paper/2112.03806/) (2021)

## Abstract (arXiv)

Logical rule learning, a prominent category of knowledge graph (KG) reasoning methods, constitutes a critical research area aimed at learning explicit rules from observed facts to infer missing knowledge. However, like all KG reasoning methods, rule learning suffers from a critical weakness-its dependence on the I.I.D. assumption. This assumption can easily be violated due to selection bias during training or agnostic distribution shifts during testing (e.g., as in query shift scenarios), ultimately undermining model performance and reliability. To enable robust KG reasoning in wild environments, this study investigates logical rule learning in the presence of agnostic test-time distribution shifts. We formally define this challenge as out-of-distribution (OOD) KG reasoning-a previously underexplored problem, and propose the Stable Rule Learning (StableRule) framework as a solution. StableRule is an end-to-end framework that combines feature decorrelation with rule learning network, to enhance OOD generalization in KG reasoning. By leveraging feature decorrelation, StableRule mitigates the adverse effects of covariate shifts arising in OOD scenarios, improving the robustness of the rule learning network. Extensive experiments on seven benchmark KGs demonstrate the framework's superior effectiveness and stability across diverse heterogeneous environments, highlighting its practical significance for real-world applications.