# Relational Pooling for Graph Representations

arXiv: https://arxiv.org/abs/1903.02541 · HTML: https://mlsanity.com/paper/1903.02541/

## Key facts

- Cited by 150 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Mar 2019.

## Built on by (most cited first, 30 of 150)

- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [Graph Neural Networks with Learnable Structural and Positional Representations](https://mlsanity.com/paper/2110.07875/) (2021)
- [Combinatorial optimization and reasoning with graph neural networks](https://mlsanity.com/paper/2102.09544/) (2021)
- [Weisfeiler and Lehman Go Cellular: CW Networks](https://mlsanity.com/paper/2106.12575/) (2021)
- [Identity-aware Graph Neural Networks](https://mlsanity.com/paper/2101.10320/) (2021)
- [Exphormer: Sparse Transformers for Graphs](https://mlsanity.com/paper/2303.06147/) (2023)
- [Frame Averaging for Invariant and Equivariant Network Design](https://mlsanity.com/paper/2110.03336/) (2021)
- [From Stars to Subgraphs: Uplifting Any GNN with Local Structure Awareness](https://mlsanity.com/paper/2110.03753/) (2021)
- [Equivariant Subgraph Aggregation Networks](https://mlsanity.com/paper/2110.02910/) (2021)
- [Learning Causally Invariant Representations for Out-of-Distribution Generalization on Graphs](https://mlsanity.com/paper/2202.05441/) (2022)
- [Nested Graph Neural Networks](https://mlsanity.com/paper/2110.13197/) (2021)
- [Scalars are universal: Equivariant machine learning, structured like classical physics](https://mlsanity.com/paper/2106.06610/) (2021)
- [Weisfeiler and Leman go Machine Learning: The Story so far](https://mlsanity.com/paper/2112.09992/) (2021)
- [A Unified Lottery Ticket Hypothesis for Graph Neural Networks](https://mlsanity.com/paper/2102.06790/) (2021)
- [Global Self-Attention as a Replacement for Graph Convolution](https://mlsanity.com/paper/2108.03348/) (2021)
- [Breaking the Limits of Message Passing Graph Neural Networks](https://mlsanity.com/paper/2106.04319/) (2021)
- [Equivariant and Stable Positional Encoding for More Powerful Graph Neural Networks](https://mlsanity.com/paper/2203.00199/) (2022)
- [A Generalization of ViT/MLP-Mixer to Graphs](https://mlsanity.com/paper/2212.13350/) (2022)
- [How Powerful are K-hop Message Passing Graph Neural Networks](https://mlsanity.com/paper/2205.13328/) (2022)
- [Graph Mamba: Towards Learning on Graphs with State Space Models](https://mlsanity.com/paper/2402.08678/) (2024)
- [Size-Invariant Graph Representations for Graph Classification Extrapolations](https://mlsanity.com/paper/2103.05045/) (2021)
- [Attending to Graph Transformers](https://mlsanity.com/paper/2302.04181/) (2023)
- [A Survey on Graph Representation Learning Methods](https://mlsanity.com/paper/2204.01855/) (2022)
- [Reconstruction for Powerful Graph Representations](https://mlsanity.com/paper/2110.00577/) (2021)
- [Theory of Graph Neural Networks: Representation and Learning](https://mlsanity.com/paper/2204.07697/) (2022)
- [CktGNN: Circuit Graph Neural Network for Electronic Design Automation](https://mlsanity.com/paper/2308.16406/) (2023)
- [Ordered Subgraph Aggregation Networks](https://mlsanity.com/paper/2206.11168/) (2022)
- [Boosting the Cycle Counting Power of Graph Neural Networks with I2-GNNs](https://mlsanity.com/paper/2210.13978/) (2022)
- [Graph Pooling for Graph Neural Networks: Progress, Challenges, and Opportunities](https://mlsanity.com/paper/2204.07321/) (2022)
- [KAGNNs: Kolmogorov-Arnold Networks meet Graph Learning](https://mlsanity.com/paper/2406.18380/) (2024)

## Abstract (arXiv)

This work generalizes graph neural networks (GNNs) beyond those based on the Weisfeiler-Lehman (WL) algorithm, graph Laplacians, and diffusions. Our approach, denoted Relational Pooling (RP), draws from the theory of finite partial exchangeability to provide a framework with maximal representation power for graphs. RP can work with existing graph representation models and, somewhat counterintuitively, can make them even more powerful than the original WL isomorphism test. Additionally, RP allows architectures like Recurrent Neural Networks and Convolutional Neural Networks to be used in a theoretically sound approach for graph classification. We demonstrate improved performance of RP-based graph representations over state-of-the-art methods on a number of tasks.