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

arXiv: https://arxiv.org/abs/2603.21601 · HTML: https://mlsanity.com/paper/2603.21601/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 77 references that are in the map.
- First posted on arXiv 23 Mar 2026.

## Builds on (most cited first, 30 of 54)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [One for All: Towards Training One Graph Model for All Classification Tasks](https://mlsanity.com/paper/2310.00149/) (2023)
- [GraphGPT: Graph Instruction Tuning for Large Language Models](https://mlsanity.com/paper/2310.13023/) (2023)
- [Language is All a Graph Needs](https://mlsanity.com/paper/2308.07134/) (2023)
- [LLaGA: Large Language and Graph Assistant](https://mlsanity.com/paper/2402.08170/) (2024)
- [Understanding World or Predicting Future? A Comprehensive Survey of World Models](https://mlsanity.com/paper/2411.14499/) (2024)
- [GraphText: Graph Reasoning in Text Space](https://mlsanity.com/paper/2310.01089/) (2023)
- [All in One and One for All: A Simple yet Effective Method towards Cross-domain Graph Pretraining](https://mlsanity.com/paper/2402.09834/) (2024)
- [GFT: Graph Foundation Model with Transferable Tree Vocabulary](https://mlsanity.com/paper/2411.06070/) (2024)
- [Graph-ToolFormer: To Empower LLMs with Graph Reasoning Ability via Prompt Augmented by ChatGPT](https://mlsanity.com/paper/2304.11116/) (2023)
- [OpenGraph: Towards Open Graph Foundation Models](https://mlsanity.com/paper/2403.01121/) (2024)
- [GraphTranslator: Aligning Graph Model to Large Language Model for Open-ended Tasks](https://mlsanity.com/paper/2402.07197/) (2024)
- [SAMGPT: Text-free Graph Foundation Model for Multi-domain Pre-training and Cross-domain Adaptation](https://mlsanity.com/paper/2502.05424/) (2025)
- [GraphCLIP: Enhancing Transferability in Graph Foundation Models for Text-Attributed Graphs](https://mlsanity.com/paper/2410.10329/) (2024)
- [AnyGraph: Graph Foundation Model in the Wild](https://mlsanity.com/paper/2408.10700/) (2024)
- [Can we Soft Prompt LLMs for Graph Learning Tasks?](https://mlsanity.com/paper/2402.10359/) (2024)
- [Hyperbolic Variational Graph Neural Network for Modeling Dynamic Graphs](https://mlsanity.com/paper/2104.02228/) (2021)
- [Text-Free Multi-domain Graph Pre-training: Toward Graph Foundation Models](https://mlsanity.com/paper/2405.13934/) (2024)
- [Multi-Domain Graph Foundation Models: Robust Knowledge Transfer via Topology Alignment](https://mlsanity.com/paper/2502.02017/) (2025)
- [Fully-inductive Node Classification on Arbitrary Graphs](https://mlsanity.com/paper/2405.20445/) (2024)
- [On the Scalability of GNNs for Molecular Graphs](https://mlsanity.com/paper/2404.11568/) (2024)
- [RiemannGFM: Learning a Graph Foundation Model from Riemannian Geometry](https://mlsanity.com/paper/2502.03251/) (2025)
- [Self-Supervised Continual Graph Learning in Adaptive Riemannian Spaces](https://mlsanity.com/paper/2211.17068/) (2022)
- [Towards Graph Foundation Models: Learning Generalities Across Graphs via Task-Trees](https://mlsanity.com/paper/2412.16441/) (2024)

## Built on by (most cited first, 1 of 1)

- [PermuFormer: Multi-Task Pretraining for Permutation Representation in Algebraic Combinatorics](https://mlsanity.com/paper/2609.25438/) (2026)

## Abstract (arXiv)

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 foundational principles for GFM. Reimagining with Riemannian geometry, we introduce a blue sky idea-Riemannian Foundation Model (RFM)-that opens a new pathway for capturing complex structural patterns and uncovering cross-domain generalities. RFM emphasizes intrinsic graph geometry and embodies endogenous capacities for structural inference and generation, moving beyond mere representation-space switching. Accordingly, we outline a progressive agenda that begins with universal structural understanding through intrinsic geometry, and then rebuilds LLM with a Riemannian engine for general-purpose graph modeling and beyond. Thus, RFM enables a paradigm shift from designing graph models to solving graph-structured applications with RFM agents, unlocking the next-generation graph intelligence.