# GraphGLOW: Universal and Generalizable Structure Learning for Graph Neural Networks

arXiv: https://arxiv.org/abs/2306.11264 · HTML: https://mlsanity.com/paper/2306.11264/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 56 references that are in the map.
- First posted on arXiv 20 Jun 2023.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Show, Attend and Tell: Neural Image Caption Generation with Visual Attention](https://mlsanity.com/paper/1502.03044/) (2015)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Domain Generalization via Invariant Feature Representation](https://mlsanity.com/paper/1301.2115/) (2013)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Graph Neural Network for Traffic Forecasting: A Survey](https://mlsanity.com/paper/2101.11174/) (2021)
- [Probabilistic Model-Agnostic Meta-Learning](https://mlsanity.com/paper/1806.02817/) (2018)
- [Learning Discrete Structures for Graph Neural Networks](https://mlsanity.com/paper/1903.11960/) (2019)
- [Iterative Deep Graph Learning for Graph Neural Networks: Better and Robust Node Embeddings](https://mlsanity.com/paper/2006.13009/) (2020)
- [NodeFormer: A Scalable Graph Structure Learning Transformer for Node Classification](https://mlsanity.com/paper/2306.08385/) (2023)
- [Graph Neural Networks with Heterophily](https://mlsanity.com/paper/2009.13566/) (2020)
- [Is Homophily a Necessity for Graph Neural Networks?](https://mlsanity.com/paper/2106.06134/) (2021)
- [Graph Information Bottleneck](https://mlsanity.com/paper/2010.12811/) (2020)
- [Handling Distribution Shifts on Graphs: An Invariance Perspective](https://mlsanity.com/paper/2202.02466/) (2022)
- [Adaptive Graph Convolutional Neural Networks](https://mlsanity.com/paper/1801.03226/) (2018)
- [How to learn a graph from smooth signals](https://mlsanity.com/paper/1601.02513/) (2016)
- [Causal Attention for Interpretable and Generalizable Graph Classification](https://mlsanity.com/paper/2112.15089/) (2021)
- [Bayesian graph convolutional neural networks for semi-supervised classification](https://mlsanity.com/paper/1811.11103/) (2018)
- [Shift-Robust GNNs: Overcoming the Limitations of Localized Graph Training Data](https://mlsanity.com/paper/2108.01099/) (2021)
- [DIFFormer: Scalable (Graph) Transformers Induced by Energy Constrained Diffusion](https://mlsanity.com/paper/2301.09474/) (2023)
- [Size-Invariant Graph Representations for Graph Classification Extrapolations](https://mlsanity.com/paper/2103.05045/) (2021)

## Built on by (most cited first, 12 of 12)

- [Graph Prompt Learning: A Comprehensive Survey and Beyond](https://mlsanity.com/paper/2311.16534/) (2023)
- [A Survey of Deep Graph Learning under Distribution Shifts: from Graph Out-of-Distribution Generalization to Adaptation](https://mlsanity.com/paper/2410.19265/) (2024)
- [Towards Dynamic Message Passing on Graphs](https://mlsanity.com/paper/2410.23686/) (2024)
- [Bridged-GNN: Knowledge Bridge Learning for Effective Knowledge Transfer](https://mlsanity.com/paper/2308.09499/) (2023)
- [Beyond Generalization: A Survey of Out-Of-Distribution Adaptation on Graphs](https://mlsanity.com/paper/2402.11153/) (2024)
- [View Space: Learning Representation across Arbitrary Graphs](https://mlsanity.com/paper/2512.11561/) (2025)
- [MLDGG: Meta-Learning for Domain Generalization on Graphs](https://mlsanity.com/paper/2411.12913/) (2024)
- [GeoMix: Towards Geometry-Aware Data Augmentation](https://mlsanity.com/paper/2407.10681/) (2024)
- [A Unified Graph Selective Prompt Learning for Graph Neural Networks](https://mlsanity.com/paper/2406.10498/) (2024)
- [Heterogeneous Graph Structure Learning through the Lens of Data-generating Processes](https://mlsanity.com/paper/2503.08760/) (2025)
- [FedHERO: A Federated Learning Approach for Node Classification Task on Heterophilic Graphs](https://mlsanity.com/paper/2504.21206/) (2025)
- [Training Robust Graph Neural Networks by Modeling Noise Dependencies](https://mlsanity.com/paper/2502.19670/) (2025)

## Abstract (arXiv)

Graph structure learning is a well-established problem that aims at optimizing graph structures adaptive to specific graph datasets to help message passing neural networks (i.e., GNNs) to yield effective and robust node embeddings. However, the common limitation of existing models lies in the underlying textitclosed-world assumption: the testing graph is the same as the training graph. This premise requires independently training the structure learning model from scratch for each graph dataset, which leads to prohibitive computation costs and potential risks for serious over-fitting. To mitigate these issues, this paper explores a new direction that moves forward to learn a universal structure learning model that can generalize across graph datasets in an open world. We first introduce the mathematical definition of this novel problem setting, and describe the model formulation from a probabilistic data-generative aspect. Then we devise a general framework that coordinates a single graph-shared structure learner and multiple graph-specific GNNs to capture the generalizable patterns of optimal message-passing topology across datasets. The well-trained structure learner can directly produce adaptive structures for unseen target graphs without any fine-tuning. Across diverse datasets and various challenging cross-graph generalization protocols, our experiments show that even without training on target graphs, the proposed model i) significantly outperforms expressive GNNs trained on input (non-optimized) topology, and ii) surprisingly performs on par with state-of-the-art models that independently optimize adaptive structures for specific target graphs, with notably orders-of-magnitude acceleration for training on the target graph.