Rachid Caich

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature

Entropic Curvature is introduced, a global, transport-based curvature obtained by extending the Lott-Sturm-Villani framework to graphs through the displacement convexity of entropy along Wasserstein geodesics, and an expansion paradox proving that sparsity, strong spectral expansion, and positive entropic curvature cannot coexist in large graphs is proved.