[2603.21601] Riemannian Geometry Speaks Louder Than Words: From Graph Foundation Model to Next-Generation Graph Intelligence

Computer Science > Machine Learning arXiv:2603.21601 (cs) [Submitted on 23 Mar 2026] Title:Riemannian Geometry Speaks Louder Than Words: From Graph Foundation Model to Next-Generation Graph Intelligence Authors:Philip S. Yu, Li Sun View a PDF of the paper titled Riemannian Geometry Speaks Louder Than Words: From Graph Foundation Model to Next-Generation Graph Intelligence, by Philip S. Yu and 1 other authors View PDF HTML (experimental) Abstract:Graphs provide a natural description of the complex relationships among objects, and play a pivotal role in communications, transportation, social computing, the life sciences, etc. Currently, there is strong agreement that Graph Foundation Models (GFMs) are essential for advancing graph learning, yet considerable disagreement persists on how to build a powerful, general-purpose GFM analogous to Large Language Models (LLMs). Graph Neural Networks (GNNs) exhibit limitations in memory retention and principled interpretability when confronted with multi-domain pretraining and adaptation. The challenge of graph serialization hinders the direct application of LLMs, as the words struggle to capture the structural complexity and diversity inherent in graphs. In contrast, Riemannian geometry offers an elegant mathematical framework for modeling structures, while remaining compatible with graph semantic learning, even with LLMs. In this paper, we argue that, for graphs, Riemannian geometry speaks louder than words, and lay out the foundatio...