ATLAS: Adaptive Topology-based Learning at Scale for Homophilic and Heterophilic Graphs

Graph neural networks (GNNs) excel on homophilic graphs where connected nodes share labels, but struggle with heterophilic graphs where edges do not imply similarity. Moreover, iterative message passing limits scalability due to neighborhood expansion overhead. We introduce ATLAS (Adaptive Topology-based Learning at Scale), a propagation-free framework that encodes graph structure through multi-resolution community features rather than message passing. We first prove that community refinement involves a fundamental trade-off: finer partitions increase label-community mutual information but also increase entropy. We formalize when refinement improves normalized mutual information, explaining why intermediate granularities are often most predictive. ATLAS employs modularity-guided adaptive search to automatically identify informative community scales, which are one-hot encoded, projected into learnable embeddings, and concatenated with node attributes for MLP classification. This enables standard mini-batch training and adjacency-free inference after one-time preprocessing. Across 13 benchmarks including million-node graphs, ATLAS achieves competitive or superior accuracy, up to 20-point gains over GCN on heterophilic datasets and 12-point gains over MLPs on homophilic graphs. By treating topology as explicit features, ATLAS adapts intelligently: leveraging structure when informative, remaining robust when weakly aligned, and avoiding propagation when structure misleads, providing both scalable performance and interpretable structural insights.