# Subgraph Aggregation for Out-of-Distribution Generalization on Graphs

arXiv: https://arxiv.org/abs/2410.22228 · HTML: https://mlsanity.com/paper/2410.22228/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 48 references that are in the map.
- First posted on arXiv 29 Oct 2024.

## Builds on (most cited first, 30 of 34)

- [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)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [GNNExplainer: Generating Explanations for Graph Neural Networks](https://mlsanity.com/paper/1903.03894/) (2019)
- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [Linear Mode Connectivity and the Lottery Ticket Hypothesis](https://mlsanity.com/paper/1912.05671/) (2019)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [SWAD: Domain Generalization by Seeking Flat Minima](https://mlsanity.com/paper/2102.08604/) (2021)
- [Parameterized Explainer for Graph Neural Network](https://mlsanity.com/paper/2011.04573/) (2020)
- [Explainability in Graph Neural Networks: A Taxonomic Survey](https://mlsanity.com/paper/2012.15445/) (2020)
- [AllenNLP: A Deep Semantic Natural Language Processing Platform](https://mlsanity.com/paper/1803.07640/) (2018)
- [Essentially No Barriers in Neural Network Energy Landscape](https://mlsanity.com/paper/1803.00885/) (2018)
- [Uniform convergence may be unable to explain generalization in deep learning](https://mlsanity.com/paper/1902.04742/) (2019)
- [Graph Random Neural Network for Semi-Supervised Learning on Graphs](https://mlsanity.com/paper/2005.11079/) (2020)
- [Interpretable and Generalizable Graph Learning via Stochastic Attention Mechanism](https://mlsanity.com/paper/2201.12987/) (2022)
- [Understanding Attention and Generalization in Graph Neural Networks](https://mlsanity.com/paper/1905.02850/) (2019)
- [Handling Distribution Shifts on Graphs: An Invariance Perspective](https://mlsanity.com/paper/2202.02466/) (2022)
- [Domain Generalization via Conditional Invariant Representation](https://mlsanity.com/paper/1807.08479/) (2018)
- [Ensemble of Averages: Improving Model Selection and Boosting Performance in Domain Generalization](https://mlsanity.com/paper/2110.10832/) (2021)
- [Learning Causally Invariant Representations for Out-of-Distribution Generalization on Graphs](https://mlsanity.com/paper/2202.05441/) (2022)
- [Generative Causal Explanations for Graph Neural Networks](https://mlsanity.com/paper/2104.06643/) (2021)
- [Graph Information Bottleneck for Subgraph Recognition](https://mlsanity.com/paper/2010.05563/) (2020)
- [Debiasing Graph Neural Networks via Learning Disentangled Causal Substructure](https://mlsanity.com/paper/2209.14107/) (2022)
- [Loss Surface Simplexes for Mode Connecting Volumes and Fast Ensembling](https://mlsanity.com/paper/2102.13042/) (2021)

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

- [Stop Rewarding Hallucinated Steps: Faithfulness-Aware Step-Level Reinforcement Learning for Small Reasoning Models](https://mlsanity.com/paper/2602.05897/) (2026)
- [CLIR-Bench: Benchmarking Multimodal Question Answering over Irregular Clinical Time Series](https://mlsanity.com/paper/2607.09880/) (2026)
- [PISA: Prioritized Invariant Subgraph Aggregation for Out-of-Distribution Generalization on Graphs](https://mlsanity.com/paper/2511.22435/) (2025)
- [Multi-View Molecular Representation Learning with Hierarchical Graphs and Contextualized Fingerprints](https://mlsanity.com/paper/2609.15611/) (2026)

## Abstract (arXiv)

Out-of-distribution (OOD) generalization in Graph Neural Networks (GNNs) has gained significant attention due to its critical importance in graph-based predictions in real-world scenarios. Existing methods primarily focus on extracting a single causal subgraph from the input graph to achieve generalizable predictions. However, relying on a single subgraph can lead to susceptibility to spurious correlations and is insufficient for learning invariant patterns behind graph data. Moreover, in many real-world applications, such as molecular property prediction, multiple critical subgraphs may influence the target label property. To address these challenges, we propose a novel framework, SubGraph Aggregation (SuGAr), designed to learn a diverse set of subgraphs that are crucial for OOD generalization on graphs. Specifically, SuGAr employs a tailored subgraph sampler and diversity regularizer to extract a diverse set of invariant subgraphs. These invariant subgraphs are then aggregated by averaging their representations, which enriches the subgraph signals and enhances coverage of the underlying causal structures, thereby improving OOD generalization. Extensive experiments on both synthetic and real-world datasets demonstrate that ours outperforms state-of-the-art methods, achieving up to a 24% improvement in OOD generalization on graphs. To the best of our knowledge, this is the first work to study graph OOD generalization by learning multiple invariant subgraphs. code: https://github.com/Nanolbw/SuGAr