# RiemannGFM: Learning a Graph Foundation Model from Riemannian Geometry

arXiv: https://arxiv.org/abs/2502.03251 · HTML: https://mlsanity.com/paper/2502.03251/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 59 references that are in the map.
- First posted on arXiv 5 Feb 2025.

## Builds on (most cited first, 30 of 45)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [A Survey on Evaluation of Large Language Models](https://mlsanity.com/paper/2307.03109/) (2023)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [GraphSAINT: Graph Sampling Based Inductive Learning Method](https://mlsanity.com/paper/1907.04931/) (2019)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Wiki-CS: A Wikipedia-Based Benchmark for Graph Neural Networks](https://mlsanity.com/paper/2007.02901/) (2020)
- [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)
- [struc2vec: Learning Node Representations from Structural Identity](https://mlsanity.com/paper/1704.03165/) (2017)
- [LLaGA: Large Language and Graph Assistant](https://mlsanity.com/paper/2402.08170/) (2024)
- [GraphMAE2: A Decoding-Enhanced Masked Self-Supervised Graph Learner](https://mlsanity.com/paper/2304.04779/) (2023)
- [PRODIGY: Enabling In-context Learning Over Graphs](https://mlsanity.com/paper/2305.12600/) (2023)
- [Position: Graph Foundation Models are Already Here](https://mlsanity.com/paper/2402.02216/) (2024)
- [All in One and One for All: A Simple yet Effective Method towards Cross-domain Graph Pretraining](https://mlsanity.com/paper/2402.09834/) (2024)
- [OpenGraph: Towards Open Graph Foundation Models](https://mlsanity.com/paper/2403.01121/) (2024)
- [Lorentzian Graph Convolutional Networks](https://mlsanity.com/paper/2104.07477/) (2021)
- [AnyGraph: Graph Foundation Model in the Wild](https://mlsanity.com/paper/2408.10700/) (2024)
- [Hyperbolic Variational Graph Neural Network for Modeling Dynamic Graphs](https://mlsanity.com/paper/2104.02228/) (2021)

## Built on by (most cited first, 30 of 35)

- [LLM as GNN: Graph Vocabulary Learning for Text-Attributed Graph Foundation Models](https://mlsanity.com/paper/2503.03313/) (2025)
- [Towards Effective Federated Graph Foundation Model via Mitigating Knowledge Entanglement](https://mlsanity.com/paper/2505.12684/) (2025)
- [Deeper with Riemannian Geometry: Overcoming Oversmoothing and Oversquashing for Graph Foundation Models](https://mlsanity.com/paper/2510.17457/) (2025)
- [Toward Effective Multimodal Graph Foundation Model: A Divide-and-Conquer Based Approach](https://mlsanity.com/paper/2602.04116/) (2026)
- [Multi-Domain Riemannian Graph Gluing for Building Graph Foundation Models](https://mlsanity.com/paper/2603.00618/) (2026)
- [Structure-Centric Graph Foundation Model via Geometric Bases](https://mlsanity.com/paper/2605.08689/) (2026)
- [Hyperbolic Continuous Structural Entropy for Hierarchical Clustering](https://mlsanity.com/paper/2512.00524/) (2025)
- [Learning Graph Foundation Models on Riemannian Graph-of-Graphs](https://mlsanity.com/paper/2605.09993/) (2026)
- [A Survey of Cross-domain Graph Learning: Progress and Future Directions](https://mlsanity.com/paper/2503.11086/) (2025)
- [GILT: An LLM-Free, Tuning-Free Graph Foundational Model for In-Context Learning](https://mlsanity.com/paper/2510.04567/) (2025)
- [Heterophily-Agnostic Hypergraph Neural Networks with Riemannian Local Exchanger](https://mlsanity.com/paper/2603.00599/) (2026)
- [Towards Non-Euclidean Foundation Models: Advancing AI Beyond Euclidean Frameworks](https://mlsanity.com/paper/2505.14417/) (2025)
- [Grounding Intelligence in Movement](https://mlsanity.com/paper/2507.02771/) (2025)
- [Towards LLM-Empowered Knowledge Tracing via LLM-Student Hierarchical Behavior Alignment in Hyperbolic Space](https://mlsanity.com/paper/2602.22879/) (2026)
- [Riemannian Geometry Speaks Louder Than Words: From Graph Foundation Model to Next-Generation Graph Intelligence](https://mlsanity.com/paper/2603.21601/) (2026)
- [Decoupled and Divergence-Conditioned Prompt for Multi-domain Dynamic Graph Foundation Models](https://mlsanity.com/paper/2605.13540/) (2026)
- [GFMate: Empowering Graph Foundation Models with Test-time Prompt Tuning](https://mlsanity.com/paper/2605.14809/) (2026)
- [Beyond Feature and Structure Alignment: Learning Transferable Propagation Knowledge for Graph Foundation Models](https://mlsanity.com/paper/2607.28980/) (2026)
- [SCGFM-ART: Amortized Relational Transport for Structure-Centric Graph Foundation Models](https://mlsanity.com/paper/2609.20419/) (2026)
- [Two Facets of the Same Optimization Coin: Model Degradation and Representation Collapse in Graph Foundation Models](https://mlsanity.com/paper/2509.08401/) (2025)
- [GraphShaper: Geometry-aware Alignment for Improving Transfer Learning in Text-Attributed Graphs](https://mlsanity.com/paper/2510.12085/) (2025)
- [Out-of-Distribution Generalization in Graph Foundation Models](https://mlsanity.com/paper/2601.21067/) (2026)
- [GraphVec: Cross-Domain Graph Vectorization for Graph-Level Representation Learning](https://mlsanity.com/paper/2602.04244/) (2026)
- [Learning to Explore: Policy-Guided Outlier Synthesis for Graph Out-of-Distribution Detection](https://mlsanity.com/paper/2603.00602/) (2026)
- [LLM+Graph@VLDB'2025 Workshop Summary](https://mlsanity.com/paper/2604.02861/) (2026)
- [A Unified Graph Language Model for Multi-Domain Multi-Task Graph Alignment Instruction Tuning](https://mlsanity.com/paper/2605.12197/) (2026)
- [Are Common Substructures Transferable? Riemannian Graph Foundation Model with Neural Vector Bundles](https://mlsanity.com/paper/2606.03270/) (2026)
- [SPR: Toward a Graph Foundation Model for Transferable Graph Cognition via Spectral Patterns and Relational Geometry](https://mlsanity.com/paper/2606.03315/) (2026)
- [CHARM: A Multimodal Graph Foundation Model with Hierarchical Context Modeling for Zero-Shot Transfer](https://mlsanity.com/paper/2607.26023/) (2026)
- [AgentGFM: A Graph Foundation Model with Node-Agent Information-Flow Control](https://mlsanity.com/paper/2607.26533/) (2026)

## Abstract (arXiv)

The foundation model has heralded a new era in artificial intelligence, pretraining a single model to offer cross-domain transferability on different datasets. Graph neural networks excel at learning graph data, the omnipresent non-Euclidean structure, but often lack the generalization capacity. Hence, graph foundation model is drawing increasing attention, and recent efforts have been made to leverage Large Language Models. On the one hand, existing studies primarily focus on text-attributed graphs, while a wider range of real graphs do not contain fruitful textual attributes. On the other hand, the sequential graph description tailored for the Large Language Model neglects the structural complexity, which is a predominant characteristic of the graph. Such limitations motivate an important question: Can we go beyond Large Language Models, and pretrain a universal model to learn the structural knowledge for any graph? The answer in the language or vision domain is a shared vocabulary. We observe the fact that there also exist shared substructures underlying graph domain, and thereby open a new opportunity of graph foundation model with structural vocabulary. The key innovation is the discovery of a simple yet effective structural vocabulary of trees and cycles, and we explore its inherent connection to Riemannian geometry. Herein, we present a universal pretraining model, RiemannGFM. Concretely, we first construct a novel product bundle to incorporate the diverse geometries of the vocabulary. Then, on this constructed space, we stack Riemannian layers where the structural vocabulary, regardless of specific graph, is learned in Riemannian manifold offering cross-domain transferability. Extensive experiments show the effectiveness of RiemannGFM on a diversity of real graphs.