# Graphon Pooling in Graph Neural Networks

arXiv: https://arxiv.org/abs/2003.01795 · HTML: https://mlsanity.com/paper/2003.01795/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Mar 2020.

## Built on by (most cited first, 11 of 11)

- [GSP-KalmanNet: Tracking Graph Signals via Neural-Aided Kalman Filtering](https://mlsanity.com/paper/2311.16602/) (2023)
- [Graphon Pooling for Reducing Dimensionality of Signals and Convolutional Operators on Graphs](https://mlsanity.com/paper/2212.08171/) (2022)
- [Stability of Aggregation Graph Neural Networks](https://mlsanity.com/paper/2207.03678/) (2022)
- [Learning with Multigraph Convolutional Filters](https://mlsanity.com/paper/2210.16272/) (2022)
- [Sampling and Uniqueness Sets in Graphon Signal Processing](https://mlsanity.com/paper/2401.06279/) (2024)
- [Transferability of Graph Neural Networks using Graphon and Sampling Theories](https://mlsanity.com/paper/2307.13206/) (2023)
- [Convolutional Filtering with RKHS Algebras](https://mlsanity.com/paper/2411.01341/) (2024)
- [RKHS Representation of Algebraic Convolutional Filters with Integral Operators](https://mlsanity.com/paper/2602.19094/) (2026)
- [Tuning the Geometry of Graph Neural Networks](https://mlsanity.com/paper/2207.05887/) (2022)
- [Non Commutative Convolutional Signal Models in Neural Networks: Stability to Small Deformations](https://mlsanity.com/paper/2310.03879/) (2023)
- [Fundamental Limits of Transferability and Equivariance in Algebraic Signal Models I: Finite Dimensions](https://mlsanity.com/paper/2609.36106/) (2026)

## Abstract (arXiv)

Graph neural networks (GNNs) have been used effectively in different applications involving the processing of signals on irregular structures modeled by graphs. Relying on the use of shift-invariant graph filters, GNNs extend the operation of convolution to graphs. However, the operations of pooling and sampling are still not clearly defined and the approaches proposed in the literature either modify the graph structure in a way that does not preserve its spectral properties, or require defining a policy for selecting which nodes to keep. In this work, we propose a new strategy for pooling and sampling on GNNs using graphons which preserves the spectral properties of the graph. To do so, we consider the graph layers in a GNN as elements of a sequence of graphs that converge to a graphon. In this way we have no ambiguity in the node labeling when mapping signals from one layer to the other and a spectral representation that is consistent throughout the layers. We evaluate this strategy in a synthetic and a real-world numerical experiment where we show that graphon pooling GNNs are less prone to overfitting and improve upon other pooling techniques, especially when the dimensionality reduction ratios between layers is large.