H-KAN: Hyperbolic Kuramoto Attention Networks for Hierarchical Representation Learning

Deep neural networks in Euclidean space face geometric limitations for hierarchical data.We introduce H-KAN (Hyperbolic Kuramoto Attention Networks), coupling hyper-bolic geometry with oscillatory synchronization dynamics. H-KAN embeds neural cellularautomata in the Poincaré disk, achieving exponential volume growth for hierarchical struc-tures. Temporal binding is achieved through H-AKOrN with geodesic-modulated coupling.Geodesic attention integrates features based on semantic similarity and hyperbolic distance.Topological regularization via persistent homology encourages structurally coherent repre-sentations.