mlsanityData to 7 Oct 2026

Stability of Aggregation Graph Neural Networks

arXiv 2207.03678 ↗First posted 8 Jul 2022cs.LGcited by 7

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Abstract (arXiv)

In this paper we study the stability properties of aggregation graph neural networks (Agg-GNNs) considering perturbations of the underlying graph. An Agg-GNN is a hybrid architecture where information is defined on the nodes of a graph, but it is processed block-wise by Euclidean CNNs on the nodes after several diffusions on the graph shift operator. We derive stability bounds for the mapping operator associated to a generic Agg-GNN, and we specify conditions under which such operators can be stable to deformations. We prove that the stability bounds are defined by the properties of the filters in the first layer of the CNN that acts on each node. Additionally, we show that there is a close relationship between the number of aggregations, the filter's selectivity, and the size of the stability constants. We also conclude that in Agg-GNNs the selectivity of the mapping operators is tied to the properties of the filters only in the first layer of the CNN stage. This shows a substantial difference with respect to the stability properties of selection GNNs, where the selectivity of the filters in all layers is constrained by their stability. We provide numerical evidence corroborating the results derived, testing the behavior of Agg-GNNs in real life application scenarios considering perturbations of different magnitude.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 14 of its 38 references that are in the map. First posted on arXiv 8 Jul 2022.

Builds on

14 of 38 references.

References · 14

  1. 2017Graph Signal Processing: Overview, Challenges and Applicationscited by 409
  2. 2019Stability Properties of Graph Neural Networkscited by 125
  3. 2018Convolutional Neural Network Architectures for Signals Supported on Graphscited by 94
  4. 2020Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networkscited by 73
  5. 2019Learning Decentralized Controllers for Robot Swarms with Graph Neural Networkscited by 62
  6. 2015A Mathematical Theory of Deep Convolutional Neural Networks for Feature Extractioncited by 46
  7. 2018Graph Convolutional Neural Networks via Scatteringcited by 46
  8. 2019On the Transferability of Spectral Graph Filterscited by 27
  9. 2020On the Stability of Graph Convolutional Neural Networks under Edge Rewiringcited by 25
  10. 2021Learning Decentralized Wireless Resource Allocations with Graph Neural Networkscited by 24
  11. 2020Algebraic Neural Networks: Stability to Deformationscited by 22
  12. 2015Sampling of graph signals with successive local aggregationscited by 19
2 more
  1. 2020Graphon Pooling in Graph Neural Networkscited by 11
  2. 2020Stability of Algebraic Neural Networks to Small Perturbationscited by 8

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Cited by year

Citing papers per year: 2023: 2; 2024: 3; 2025: 2.

7 papers.

  1. 2023Convolutional Learning on Simplicial Complexescited by 26
  2. 2024Sampling and Uniqueness Sets in Graphon Signal Processingcited by 5
  3. 2024Higher-Order GNNs Meet Efficiency: Sparse Sobolev Graph Neural Networkscited by 1
  4. 2023Non Commutative Convolutional Signal Models in Neural Networks: Stability to Small Deformationscited by 0
  5. 2024Alleviating Over-Smoothing via Aggregation over Compact Manifoldscited by 0
  6. 2025On the Stability of Graph Convolutional Neural Networks: A Probabilistic Perspectivecited by 0
  7. 2025Denoised Recommendation Model with Collaborative Signal Decouplingcited by 0