Graph Pooling via Ricci Flow

• DOI: 10.48550/arxiv.2407.04236
• Publication Date: 2024-07-04
• Authors: Amy Feng; Melanie Weber
• Keywords: Pooling; Ricci Flow

Graph Machine Learning often involves the clustering of nodes based on similarity structure encoded in graph's topology and nodes' attributes. On homophilous graphs, integration pooling layers has been shown to enhance performance Neural Networks by accounting for inherent multi-scale structure. Here, similar are grouped together coarsen graph reduce input size subsequent deeper architectures. In both settings, underlying approach can be implemented via operators, which rely classical tools from Theory. this work, we introduce a operator (ORC-Pool), utilizes characterization geometry Ollivier's discrete Ricci curvature an associated geometric flow. Previous flow approaches have great promise across several domains, but construction unable account node However, many ML applications, such information is vital downstream tasks. ORC-Pool extends attributed allowing coarsening into as layer.