Multigraph Message Passing with Bi-Directional Multi-Edge Aggregations
H. \c{C}a\u{g}r{\i} Bilgi, Lydia Y. Chen, Kubilay Atasu
TL;DR
This paper introduces MEGA-GNN, a novel message passing framework for multigraphs that improves expressive power and permutation equivariance, leading to better performance on real-world graph learning tasks.
Contribution
The paper proposes MEGA-GNN, a new multigraph message passing method with a two-stage aggregation that enhances expressiveness and permutation equivariance.
Findings
MEGA-GNN outperforms existing methods by up to 13% on Anti-Money Laundering datasets.
MEGA-GNN achieves comparable accuracy to state-of-the-art on phishing classification.
The approach is permutation equivariant and universal with a strict total edge ordering.
Abstract
Graph Neural Networks (GNNs) have seen significant advances in recent years, yet their application to multigraphs, where parallel edges exist between the same pair of nodes, remains under-explored. Standard GNNs, designed for simple graphs, compute node representations by combining all connected edges at once, without distinguishing between edges from different neighbors. There are some GNN architectures proposed specifically for multigraphs, yet these architectures perform only node-level aggregation in their message passing layers, which limits their expressive power. Furthermore, these approaches either lack permutation equivariance when a strict total edge ordering is absent, or fail to preserve the topological structure of the multigraph. To address all these shortcomings, we propose MEGA-GNN, a unified framework for message passing on multigraphs that can effectively perform…
Peer Reviews
Decision·Submitted to ICLR 2025
- The use of two-stage aggregation and artificial nodes can effectively address the limitations of existing GNN models to capture information across parallel edges while preserving certain properties. - The MEGA-GNN framework shows good flexibility and performance in applications on financial transaction datasets. - The authors offer in-depth analysis and jusfiication for the proposed framework regarding properties of permutation equivariance, injectivity and universality.
- The techniques used in MEGA-GNN such as bi-directional message passing and multi-stage aggregation are already well established, and the technical challenges for multi-graph have also been largely addressed by hypergraph learning research, which limits the overall novelty. - The model is only evaluated on financial datasets, which raise questions about wheter multi-graph learning is applicabile for broad scenarios. - Some choices, such as specific aggregation functions and the role of artif
- The paper is clearly written and easy to follow with various figures demonstrating the ideas in the paper. - Novel Aggregation Mechanism: The two-stage approach addresses the limitation of traditional GNNs, enhancing expressivity by first aggregating parallel edges and then aggregating at the node level. - The paper provides proofs for permutation equivariance, injectivity, and universality. - Experimental Evaluation: The proposed method shows promising improvements in the included datasets. -
1- Scalability: Although multigraphs are well-suited to some applications, real-world graphs can be vast in scale. The two-stage aggregation with artificial nodes might pose computational challenges and memory overhead for large, densely connected multigraphs. Some discussion on scalability in practical settings or optimizations for large-scale data would be appreciated. 2- The paper shows that under a consistent ordering of edges the model is universal. However, for many real work scenarios, t
1. MEGA-GNN gives a solution to a gap of GNNs' effecitveness, by focusing on multigraphs rather than simple graphs, where multiple edges between nodes could be useful for many applications, such as financial fraud detection (as benchmarked in the paper). 2. The authors theoretically validate MEGA-GNN’s permutation equivariance, injectivity, and universality properties. 3. MEGA-GNN achieves state-of-the-art or comparable performance across various (synthetic and real-world0 datasets, particular
1. The proof for the universality property assumes that there is an ordering over the edges of the multigraph. This is not always the case for real-world setups, giving a small question-mark on what happens when the edge ordering is not consistent. 2. Although I find the utilization of financial transaction datasets quite interesting, I think it's not very diverse. I'd be very interested in seeing whether such a multigraph approach can be useful in other domains (e.g. knowledge graphs could pot
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Taxonomy
Topicsgraph theory and CDMA systems · Interconnection Networks and Systems · Wireless Communication Networks Research