Demystifying Higher-Order Graph Neural Networks

2024-06-18

arXiv.org

AI Summary

High-order graph neural networks (HOGNNs) suffer from architectural and definitional ambiguity regarding “high-order,” impeding systematic analysis, fair comparison, and principled model selection. Method: We propose the first unified taxonomy and design blueprint for HOGNNs, systematically deconstructing diverse high-order modeling paradigms—including hypergraphs, simplicial complexes, and tensors—and their architectural distinctions; distilling task-aware selection principles for scenarios such as node/hyperedge prediction and homophily modeling; and uncovering fundamental trade-offs among scalability, expressive power, and computational efficiency. Contributions: (1) An interpretable, cross-paradigm model comparison framework; (2) A ready-to-use, task-oriented model selection guide; and (3) A benchmarking analysis paradigm supporting standardized evaluation and future research. This work establishes a foundation for transitioning HOGNN development from empirical exploration to systematic, principle-driven design.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Higher-order graph neural networks (HOGNNs) and the related architectures from Topological Deep Learning are an important class of GNN models that harness polyadic relations between vertices beyond plain edges. They have been used to eliminate issues such as over-smoothing or over-squashing, to significantly enhance the accuracy of GNN predictions, to improve the expressiveness of GNN architectures, and for numerous other goals. A plethora of HOGNN models have been introduced, and they come with diverse neural architectures, and even with different notions of what the"higher-order"means. This richness makes it very challenging to appropriately analyze and compare HOGNN models, and to decide in what scenario to use specific ones. To alleviate this, we first design an in-depth taxonomy and a blueprint for HOGNNs. This facilitates designing models that maximize performance. Then, we use our taxonomy to analyze and compare the available HOGNN models. The outcomes of our analysis are synthesized in a set of insights that help to select the most beneficial GNN model in a given scenario, and a comprehensive list of challenges and opportunities for further research into more powerful HOGNNs.

Problem

• Classifying diverse higher-order graph neural network architectures
• Comparing HOGNN models across different scenarios and applications
• Providing guidance for selecting optimal GNN models in specific contexts

Innovation

• Developed taxonomy and blueprint for HOGNNs
• Analyzed available models using designed taxonomy
• Provided insights for optimal model selection