An Introduction to Graph Neural Networks from a Distributed Computing Perspective

Papp, Pál András; Wattenhofer, Roger

doi:10.1007/978-3-030-94876-4_2

Cited by 9 publications

(10 citation statements)

References 10 publications

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“…A recent class of expressive GNNs called Subgraph GNNs, model graphs as collections of subgraphs (Frasca et al 2022;Zhao et al 2021). Papp et al (2021) drop random nodes from the input and run the GNN multiple times, gathering more information with each run. Zhang and Li (2021) instead extract subgraphs around each node and run the GNN on these.…”

Section: Related Workmentioning

confidence: 99%

Provably Powerful Graph Neural Networks for Directed Multigraphs

Egressy,

Von Niederhäusern,

Blanuša

et al. 2024

AAAI

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This paper analyses a set of simple adaptations that transform standard message-passing Graph Neural Networks (GNN) into provably powerful directed multigraph neural networks. The adaptations include multigraph port numbering, ego IDs, and reverse message passing. We prove that the combination of these theoretically enables the detection of any directed subgraph pattern. To validate the effectiveness of our proposed adaptations in practice, we conduct experiments on synthetic subgraph detection tasks, which demonstrate outstanding performance with almost perfect results. Moreover, we apply our proposed adaptations to two financial crime analysis tasks. We observe dramatic improvements in detecting money laundering transactions, improving the minority-class F1 score of a standard message-passing GNN by up to 30%, and closely matching or outperforming tree-based and GNN baselines. Similarly impressive results are observed on a real-world phishing detection dataset, boosting three standard GNNs’ F1 scores by around 15% and outperforming all baselines. An extended version with appendices can be found on arXiv: https://arxiv.org/abs/2306.11586.

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Section: Related Workmentioning

confidence: 99%

Provably Powerful Graph Neural Networks for Directed Multigraphs

Egressy,

Von Niederhäusern,

Blanuša

et al. 2024

AAAI

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“…Subgraph GNNs are an emerging class of higher-order GNNs that compute a feature representation for each subgraph-node pair. The earliest idea of subgraph GNNs may track back to Cotta et al (2021); Papp et al (2021), which proposed to use node-deleted subgraphs and performed message-passing on each subgraph separately without cross-graph interaction. Papp and Wattenhofer (2022) argued to use node marking instead of node deletion for better expressive power.…”

Section: Related Workmentioning

confidence: 99%

A Complete Expressiveness Hierarchy for Subgraph GNNs via Subgraph Weisfeiler-Lehman Tests

Zhang¹,

Feng²,

Du³

et al. 2023

Preprint

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Recently, subgraph GNNs have emerged as an important direction for developing expressive graph neural networks (GNNs). While numerous architectures have been proposed, so far there is still a limited understanding of how various design paradigms differ in terms of expressive power, nor is it clear what design principle achieves maximal expressiveness with minimal architectural complexity. Targeting these fundamental questions, this paper conducts a systematic study of general node-based subgraph GNNs through the lens of Subgraph Weisfeiler-Lehman Tests (SWL). Our central result is to build a complete hierarchy of SWL with strictly growing expressivity. Concretely, we prove that any node-based subgraph GNN falls into one of the six SWL equivalence classes, among which SSWL achieves the maximal expressive power. We also study how these equivalence classes differ in terms of their practical expressiveness such as encoding graph distance and biconnectivity. In addition, we give a tight expressivity upper bound of all SWL algorithms by establishing a close relation with localized versions of Folklore WL tests (FWL). Overall, our results provide insights into the power of existing subgraph GNNs, guide the design of new architectures, and point out their limitations by revealing an inherent gap with the 2-FWL test. Finally, experiments on the ZINC benchmark demonstrate that SSWL-inspired subgraph GNNs can significantly outperform prior architectures despite great simplicity.

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“…Subgraph GNNs are a recent family of GNNs (Cotta et al, 2021;Bevilacqua et al, 2022) that process multiple subgraphs in parallel and aggregate the results. It was recently suggested that instead of using different subgraphs, one can simply use the same graph with different input functions, such as node indicators (Papp & Wattenhofer, 2022). Our suggestion to use multiple RFP trajectories can be seen as a novel method for choosing a small and effective number of input functions.…”

Section: Architecturesmentioning

confidence: 99%

Graph Positional Encoding via Random Feature Propagation

Eliasof¹,

Frasca²,

Beatrice³

et al. 2023

Preprint

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Two main families of node feature augmentation schemes have been explored for enhancing GNNs: random features and spectral positional encoding. Surprisingly, however, there is still no clear understanding of the relation between these two augmentation schemes. Here we propose a novel family of positional encoding schemes which draws a link between the above two approaches and improves over both. The new approach, named Random Feature Propagation (RFP), is inspired by the power iteration method and its generalizations. It concatenates several intermediate steps of an iterative algorithm for computing the dominant eigenvectors of a propagation matrix, starting from random node features. Notably, these propagation steps are based on graph-dependent propagation operators that can be either predefined or learned. We explore the theoretical and empirical benefits of RFP. First, we provide theoretical justifications for using random features, for incorporating early propagation steps, and for using multiple random initializations. Then, we empirically demonstrate that RFP significantly outperforms both spectral PE and random features in multiple node classification and graph classification benchmarks.

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An Introduction to Graph Neural Networks from a Distributed Computing Perspective

Cited by 9 publications

References 10 publications

Provably Powerful Graph Neural Networks for Directed Multigraphs

Provably Powerful Graph Neural Networks for Directed Multigraphs

A Complete Expressiveness Hierarchy for Subgraph GNNs via Subgraph Weisfeiler-Lehman Tests

Graph Positional Encoding via Random Feature Propagation

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