Geometric Graph Learning Network for Node Classification

Graph attention improves neighbor discrimination, but it remains limited by local receptive fields and by a strong dependence on the input topology, which is often unreliable on heterophilous graphs. We propose Geometric Graph Learning Network (G2LNet), a structure-learning framework that infers message-passing probabilities from an explicit geometric topology learned in latent Euclidean or hyperbolic spaces. G2LNet combines (i) a geometric mapping module, (ii) distance- or inner-product-based relation operators with perceptual connectivity to control the influence of the given graph, and (iii) end-to-end constraint objectives enforcing stability, sparsity, and (optional) symmetry of the learned topology. This design yields unified local, non-local, and graph-free neighborhoods, enabling systematic analysis of when non-local aggregation helps. Experiments on node classification across nine publicly available benchmark datasets demonstrate that G2LNet’s controlled variant consistently achieves higher accuracy than representative strong baseline models–both local and non-local–on most datasets. This establishes a robust alternative for smaller scale node classification tasks.