Topologic Attention Networks: Attending to Direct and Indirect Neighbors through Gaussian Belief Propagation

Graph Neural Networks rely on local message passing, which limits their ability to model long-range dependencies in graphs. Existing approaches extend this range through continuous-time dynamics or dense self-attention, but both suffer from high computational cost and limited scalability. We propose Topologic Attention Networks, a new framework that applies topologic attention, a probabilistic mechanism that learns how information should flow through both direct and indirect connections in a graph. Unlike conventional attention that depends on explicit pairwise interactions, topologic attention emerges from the learned information propagation of the graph, enabling unified reasoning over local and global relationships. This method achieves provides state-of-the-art performance across all measured baseline models. Our implementation is available at https://github.com/Marshall-Rosenhoover/Topologic-Attention-Networks.