New entropic curvature solves GNN oversmoothing and oversquashing in one framework

Graph Neural Networks (GNNs) struggle with oversmoothing—where node features become indistinguishable across layers—and oversquashing, where topological bottlenecks block long-range information flow. Existing curvature methods like Ollivier-Ricci and Forman only capture local edge-level comparisons, failing to model global propagation. In a new arXiv preprint, Rachid Caich and Yassine Abbahaddou introduce Entropic Curvature, a global transport-based curvature that extends the Lott-Sturm-Villani framework to graphs via displacement convexity of entropy along Wasserstein geodesics. They define a tractable Weak Entropic Curvature proxy and derive three theoretical results: a Poincare-type inequality that bounds oversmoothing, a transport-entropy generalization bound, and a striking expansion paradox proving that sparsity, strong spectral expansion, and positive entropic curvature cannot coexist in large graphs. This paradox elegantly reframes oversmoothing and oversquashing as opposite ends of a single curvature spectrum.

Translating theory into practice, the authors propose three mechanisms: E-Gate (a curvature-aware message aggregator), ENT (structural positional encoding), and Midpoint-Completion Rewiring (MCR) that actively rewires edges to improve curvature. These are benchmarked against SDRF, FoSR, BORF, LCP, and Graph Ricci Flow on six node-classification datasets and graph-classification tasks. The results show consistent gains, particularly in preventing oversmoothing while maintaining long-range dependencies. For ML engineers, this provides a principled, theoretically grounded toolkit to improve GNN performance without ad‑hoc fixes. The components can be dropped into existing architectures, making this a directly actionable advance for anyone building deep graph models.