Permutation Equivariant Neural Controlled Differential Equations for Dynamic Graph Representation Learning

2025-06-25

AI Summary

Dynamic graphs exhibit coupled evolution of node features and topological structure, whose complex temporal dynamics are poorly captured by existing Graph Neural Continuous-Time Dynamic Models (e.g., Neural CDEs), which suffer from excessive parameter counts and limited generalization. To address this, we propose Permutation-Equivariant Neural Graph Differential Equations (PE-NGDE), extending the Neural CDE framework to graph-structured data. Leveraging group equivariance theory, PE-NGDE constrains the learned dynamics to the space of permutation-equivariant functions, drastically reducing parameters while preserving expressive power. The method enables continuous, differentiable, and symmetry-preserving joint modeling of graph topology and node states. Extensive experiments on synthetic dynamical systems and real-world dynamic graphs demonstrate that PE-NGDE consistently outperforms state-of-the-art methods in both interpolation and extrapolation settings, achieving superior accuracy, training efficiency, and generalization.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Dynamic graphs exhibit complex temporal dynamics due to the interplay between evolving node features and changing network structures. Recently, Graph Neural Controlled Differential Equations (Graph Neural CDEs) successfully adapted Neural CDEs from paths on Euclidean domains to paths on graph domains. Building on this foundation, we introduce Permutation Equivariant Neural Graph CDEs, which project Graph Neural CDEs onto permutation equivariant function spaces. This significantly reduces the model's parameter count without compromising representational power, resulting in more efficient training and improved generalisation. We empirically demonstrate the advantages of our approach through experiments on simulated dynamical systems and real-world tasks, showing improved performance in both interpolation and extrapolation scenarios.

Problem

• Model dynamic graphs with temporal node and structure changes
• Enhance Graph Neural CDEs with permutation equivariance
• Reduce parameters while maintaining performance and generalization

Innovation

• Permutation Equivariant Neural Graph CDEs
• Reduced parameter count without losing power
• Improved efficiency and generalization