Depth-Adaptive Graph Neural Networks via Learnable Bakry-'Emery Curvature
This addresses the challenge of effective learning in graph neural networks for researchers and practitioners in graph-based machine learning, representing a novel method rather than an incremental improvement.
The paper tackles the problem of graph neural networks overlooking diffusion dynamics and task-specific dependencies by integrating Bakry-Émery curvature to capture both structural and task-driven aspects of information propagation, resulting in consistent performance improvements across diverse graph learning tasks on benchmark datasets.
Graph Neural Networks (GNNs) have demonstrated strong representation learning capabilities for graph-based tasks. Recent advances on GNNs leverage geometric properties, such as curvature, to enhance its representation capabilities by modeling complex connectivity patterns and information flow within graphs. However, most existing approaches focus solely on discrete graph topology, overlooking diffusion dynamics and task-specific dependencies essential for effective learning. To address this, we propose integrating Bakry-Émery curvature, which captures both structural and task-driven aspects of information propagation. We develop an efficient, learnable approximation strategy, making curvature computation scalable for large graphs. Furthermore, we introduce an adaptive depth mechanism that dynamically adjusts message-passing layers per vertex based on its curvature, ensuring efficient propagation. Our theoretical analysis establishes a link between curvature and feature distinctiveness, showing that high-curvature vertices require fewer layers, while low-curvature ones benefit from deeper propagation. Extensive experiments on benchmark datasets validate the effectiveness of our approach, showing consistent performance improvements across diverse graph learning tasks.