# Generalization of Graph Neural Networks is Robust to Model Mismatch

arXiv: https://arxiv.org/abs/2408.13878 · HTML: https://mlsanity.com/paper/2408.13878/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 65 references that are in the map.
- First posted on arXiv 25 Aug 2024.

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

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Graph Neural Networks in Recommender Systems: A Survey](https://mlsanity.com/paper/2011.02260/) (2020)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Generalization and Representational Limits of Graph Neural Networks](https://mlsanity.com/paper/2002.06157/) (2020)
- [Generalization in Deep Learning](https://mlsanity.com/paper/1710.05468/) (2017)
- [From Local Structures to Size Generalization in Graph Neural Networks](https://mlsanity.com/paper/2010.08853/) (2020)
- [Graphon Neural Networks and the Transferability of Graph Neural Networks](https://mlsanity.com/paper/2006.03548/) (2020)
- [Convolutional Neural Network Architectures for Signals Supported on Graphs](https://mlsanity.com/paper/1805.00165/) (2018)
- [Transfer Learning of Graph Neural Networks with Ego-graph Information Maximization](https://mlsanity.com/paper/2009.05204/) (2020)
- [Transferability of Spectral Graph Convolutional Neural Networks](https://mlsanity.com/paper/1907.12972/) (2019)
- [A PAC-Bayesian Approach to Generalization Bounds for Graph Neural Networks](https://mlsanity.com/paper/2012.07690/) (2020)
- [Stability and Generalization of Graph Convolutional Neural Networks](https://mlsanity.com/paper/1905.01004/) (2019)
- [OOD-GNN: Out-of-Distribution Generalized Graph Neural Network](https://mlsanity.com/paper/2112.03806/) (2021)
- [Convergence and Stability of Graph Convolutional Networks on Large Random Graphs](https://mlsanity.com/paper/2006.01868/) (2020)
- [Generalizing Graph Neural Networks on Out-Of-Distribution Graphs](https://mlsanity.com/paper/2111.10657/) (2021)
- [Graph Convolution for Semi-Supervised Classification: Improved Linear Separability and Out-of-Distribution Generalization](https://mlsanity.com/paper/2102.06966/) (2021)
- [Subgroup Generalization and Fairness of Graph Neural Networks](https://mlsanity.com/paper/2106.15535/) (2021)
- [Generalization Analysis of Message Passing Neural Networks on Large Random Graphs](https://mlsanity.com/paper/2202.00645/) (2022)
- [Transferability of Graph Neural Networks: an Extended Graphon Approach](https://mlsanity.com/paper/2109.10096/) (2021)
- [Learning Theory Can (Sometimes) Explain Generalisation in Graph Neural Networks](https://mlsanity.com/paper/2112.03968/) (2021)
- [CoCo: A Coupled Contrastive Framework for Unsupervised Domain Adaptive Graph Classification](https://mlsanity.com/paper/2306.04979/) (2023)
- [Transferability Properties of Graph Neural Networks](https://mlsanity.com/paper/2112.04629/) (2021)
- [Generalization in Graph Neural Networks: Improved PAC-Bayesian Bounds on Graph Diffusion](https://mlsanity.com/paper/2302.04451/) (2023)
- [A graphon-signal analysis of graph neural networks](https://mlsanity.com/paper/2305.15987/) (2023)
- [A User Guide to Low-Pass Graph Signal Processing and its Applications](https://mlsanity.com/paper/2008.01305/) (2020)
- [Learning by Transference: Training Graph Neural Networks on Growing Graphs](https://mlsanity.com/paper/2106.03693/) (2021)
- [Intrinsic Geometric Information Transfer Learning on Multiple Graph-Structured Datasets](https://mlsanity.com/paper/1611.04687/) (2016)
- [Limits, approximation and size transferability for GNNs on sparse graphs via graphops](https://mlsanity.com/paper/2306.04495/) (2023)

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

- [Generalization Error Analysis for Selective State-Space Models Through the Lens of Attention](https://mlsanity.com/paper/2502.01473/) (2025)
- [Distributed Link Sparsification for Scalable Scheduling Using Graph Neural Networks (Journal Version)](https://mlsanity.com/paper/2509.05447/) (2025)
- [Graph Learning Should Move Beyond Restrictive Views of Spectral and Message-Passing GNNs](https://mlsanity.com/paper/2602.10031/) (2026)
- [Rethinking Generalization in Graph Neural Networks: A Structural Complexity Perspective](https://mlsanity.com/paper/2605.13597/) (2026)

## Abstract (arXiv)

Graph neural networks (GNNs) have demonstrated their effectiveness in various tasks supported by their generalization capabilities. However, the current analysis of GNN generalization relies on the assumption that training and testing data are independent and identically distributed (i.i.d). This imposes limitations on the cases where a model mismatch exists when generating testing data. In this paper, we examine GNNs that operate on geometric graphs generated from manifold models, explicitly focusing on scenarios where there is a mismatch between manifold models generating training and testing data. Our analysis reveals the robustness of the GNN generalization in the presence of such model mismatch. This indicates that GNNs trained on graphs generated from a manifold can still generalize well to unseen nodes and graphs generated from a mismatched manifold. We attribute this mismatch to both node feature perturbations and edge perturbations within the generated graph. Our findings indicate that the generalization gap decreases as the number of nodes grows in the training graph while increasing with larger manifold dimension as well as larger mismatch. Importantly, we observe a trade-off between the generalization of GNNs and the capability to discriminate high-frequency components when facing a model mismatch. The most important practical consequence of this analysis is to shed light on the filter design of generalizable GNNs robust to model mismatch. We verify our theoretical findings with experiments on multiple real-world datasets.