Scalable Implicit Graphon Learning

Ali Azizpour, Nicolas Zilberstein, Santiago Segarra
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:3952-3960, 2025.

Abstract

Graphons are continuous models that represent the structure of graphs and allow the generation of graphs of varying sizes. We propose Scalable Implicit Graphon Learning (SIGL), a scalable method that combines implicit neural representations (INRs) and graph neural networks (GNNs) to estimate a graphon from observed graphs. Unlike existing methods, which face important limitations like fixed resolution and scalability issues, SIGL learns a continuous graphon at arbitrary resolutions. GNNs are used to determine the correct node ordering, improving graph alignment. Furthermore, we characterize the asymptotic consistency of our estimator, showing that more expressive INRs and GNNs lead to consistent estimators. We evaluate SIGL in synthetic and real-world graphs, showing that it outperforms existing methods and scales effectively to larger graphs, making it ideal for tasks like graph data augmentation.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-azizpour25a, title = {Scalable Implicit Graphon Learning}, author = {Azizpour, Ali and Zilberstein, Nicolas and Segarra, Santiago}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {3952--3960}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/azizpour25a/azizpour25a.pdf}, url = {https://proceedings.mlr.press/v258/azizpour25a.html}, abstract = {Graphons are continuous models that represent the structure of graphs and allow the generation of graphs of varying sizes. We propose Scalable Implicit Graphon Learning (SIGL), a scalable method that combines implicit neural representations (INRs) and graph neural networks (GNNs) to estimate a graphon from observed graphs. Unlike existing methods, which face important limitations like fixed resolution and scalability issues, SIGL learns a continuous graphon at arbitrary resolutions. GNNs are used to determine the correct node ordering, improving graph alignment. Furthermore, we characterize the asymptotic consistency of our estimator, showing that more expressive INRs and GNNs lead to consistent estimators. We evaluate SIGL in synthetic and real-world graphs, showing that it outperforms existing methods and scales effectively to larger graphs, making it ideal for tasks like graph data augmentation.} }
Endnote
%0 Conference Paper %T Scalable Implicit Graphon Learning %A Ali Azizpour %A Nicolas Zilberstein %A Santiago Segarra %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-azizpour25a %I PMLR %P 3952--3960 %U https://proceedings.mlr.press/v258/azizpour25a.html %V 258 %X Graphons are continuous models that represent the structure of graphs and allow the generation of graphs of varying sizes. We propose Scalable Implicit Graphon Learning (SIGL), a scalable method that combines implicit neural representations (INRs) and graph neural networks (GNNs) to estimate a graphon from observed graphs. Unlike existing methods, which face important limitations like fixed resolution and scalability issues, SIGL learns a continuous graphon at arbitrary resolutions. GNNs are used to determine the correct node ordering, improving graph alignment. Furthermore, we characterize the asymptotic consistency of our estimator, showing that more expressive INRs and GNNs lead to consistent estimators. We evaluate SIGL in synthetic and real-world graphs, showing that it outperforms existing methods and scales effectively to larger graphs, making it ideal for tasks like graph data augmentation.
APA
Azizpour, A., Zilberstein, N. & Segarra, S.. (2025). Scalable Implicit Graphon Learning. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:3952-3960 Available from https://proceedings.mlr.press/v258/azizpour25a.html.

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