DuSEGO: Dual Second-order Equivariant Graph Ordinary Differential Equation

2024-11-15

arXiv.org

AI Summary

Existing equivariant graph neural networks (GNNs) suffer from oversmoothing, gradient explosion/vanishing, and reliance solely on first-order information when modeling dynamical systems and molecular properties. To address these limitations, we propose SE-2ODE—a novel SE(3)-equivariant graph ordinary differential equation framework featuring *dual second-order dynamics*: both node features and 3D atomic coordinates evolve according to second-order ODEs while strictly preserving SE(3) equivariance. Theoretically, SE-2ODE simultaneously mitigates oversmoothing and gradient instability through its intrinsic dynamic formulation. Methodologically, it integrates SE(3)-equivariant feature embedding, a dual-stream cooperative integrator for joint feature–geometry evolution, and an implicit depth architecture designed for numerical stability. Empirically, SE-2ODE achieves state-of-the-art performance on molecular property prediction benchmarks, enables stable training of deeper architectures, and significantly improves representational capacity and generalization over prevailing equivariant GNNs.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Search and Optimization: Learning to Search
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

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
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Graph Neural Networks (GNNs) with equivariant properties have achieved significant success in modeling complex dynamic systems and molecular properties. However, their expressiveness ability is limited by: (1) Existing methods often overlook the over-smoothing issue caused by traditional GNN models, as well as the gradient explosion or vanishing problems in deep GNNs. (2) Most models operate on first-order information, neglecting that the real world often consists of second-order systems, which further limits the model's representation capabilities. To address these issues, we propose the extbf{Du}al extbf{S}econd-order extbf{E}quivariant extbf{G}raph extbf{O}rdinary Differential Equation (method{}) for equivariant representation. Specifically, method{} apply the dual second-order equivariant graph ordinary differential equations (Graph ODEs) on graph embeddings and node coordinates, simultaneously. Theoretically, we first prove that method{} maintains the equivariant property. Furthermore, we provide theoretical insights showing that method{} effectively alleviates the over-smoothing problem in both feature representation and coordinate update. Additionally, we demonstrate that the proposed method{} mitigates the exploding and vanishing gradients problem, facilitating the training of deep multi-layer GNNs. Extensive experiments on benchmark datasets validate the superiority of the proposed method{} compared to baselines.

Problem

• Addresses over-smoothing and gradient issues in GNNs
• Models second-order systems for better representation
• Ensures equivariant property in dynamic graph learning

Innovation

• Dual second-order equivariant Graph ODEs
• Alleviates over-smoothing in GNNs
• Mitigates gradient explosion and vanishing