mlsanityData to 14 Oct 2026

Graph neural networks and non-commuting operators

arXiv 2411.04265 ↗First posted 6 Nov 2024stat.ML cs.AI cs.LGcited by 5

Not on the map. Why?

Abstract (arXiv)

Graph neural networks (GNNs) provide state-of-the-art results in a wide variety of tasks which typically involve predicting features at the vertices of a graph. They are built from layers of graph convolutions which serve as a powerful inductive bias for describing the flow of information among the vertices. Often, more than one data modality is available. This work considers a setting in which several graphs have the same vertex set and a common vertex-level learning task. This generalizes standard GNN models to GNNs with several graph operators that do not commute. We may call this model graph-tuple neural networks (GtNN). In this work, we develop the mathematical theory to address the stability and transferability of GtNNs using properties of non-commuting non-expansive operators. We develop a limit theory of graphon-tuple neural networks and use it to prove a universal transferability theorem that guarantees that all graph-tuple neural networks are transferable on convergent graph-tuple sequences. In particular, there is no non-transferable energy under the convergence we consider here. Our theoretical results extend well-known transferability theorems for GNNs to the case of several simultaneous graphs (GtNNs) and provide a strict improvement on what is currently known even in the GNN case. We illustrate our theoretical results with simple experiments on synthetic and real-world data. To this end, we derive a training procedure that provably enforces the stability of the resulting model.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 40 of its 50 references that are in the map. First posted on arXiv 6 Nov 2024.

Builds on

40 of 50 references.

References · 40

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28 more
  1. 2019Stability Properties of Graph Neural Networkscited by 127
  2. 2023Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systemscited by 121
  3. 2020Graphon Neural Networks and the Transferability of Graph Neural Networkscited by 118
  4. 2018Convolutional Neural Network Architectures for Signals Supported on Graphscited by 95
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  6. 2020A PAC-Bayesian Approach to Generalization Bounds for Graph Neural Networkscited by 85
  7. 2020Graph Neural Networks: Architectures, Stability and Transferabilitycited by 80
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  11. 2021Transferability Properties of Graph Neural Networkscited by 43
  12. 2020On the Stability of Graph Convolutional Neural Networks under Edge Rewiringcited by 25
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  14. 2020Algebraic Neural Networks: Stability to Deformationscited by 22
  15. 2023Limits, approximation and size transferability for GNNs on sparse graphs via graphopscited by 18
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  17. 2023Approximately Equivariant Graph Networkscited by 16
  18. 2021Training Stable Graph Neural Networks Through Constrained Learningcited by 12
  19. 2022From Local to Global: Spectral-Inspired Graph Neural Networkscited by 11
  20. 2022Convergence of Invariant Graph Networkscited by 9
  21. 2023Convergence of Message Passing Graph Neural Networks with Generic Aggregation On Large Random Graphscited by 9
  22. 2023Any-dimensional equivariant neural networkscited by 9
  23. 2021Convolutional Filtering and Neural Networks with Non Commutative Algebrascited by 8
  24. 2024Learning on Large Graphs using Intersecting Communitiescited by 8
  25. 2022Learning with Multigraph Convolutional Filterscited by 5
  26. 2022A Spectral Analysis of Graph Neural Networks on Dense and Sparse Graphscited by 5
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  28. 2021On random walks and switched random walks on homogeneous spacescited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 2; 2026: 3.

5 papers.

  1. 2025Towards Coordinate- and Dimension-Agnostic Machine Learning for Partial Differential Equationscited by 2
  2. 2025Multi-View Graph Learning with Graph-Tuplecited by 0
  3. 2026Graph Learning Should Move Beyond Restrictive Views of Spectral and Message-Passing GNNscited by 0
  4. 2026PGD-NO: A Neural Operator with Precomputed Geometry Decomposition for 3D Million-scale Physics Simulationscited by 0
  5. 2026Warm-starting PDE solvers with any-dimensional machine learningcited by 0