# Structure-Centric Graph Foundation Model via Geometric Bases

arXiv: https://arxiv.org/abs/2605.08689 · HTML: https://mlsanity.com/paper/2605.08689/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 51 of its 72 references that are in the map.
- First posted on arXiv 9 May 2026.

## Builds on (most cited first, 30 of 51)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [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)
- [Strategies for Pre-training Graph Neural Networks](https://mlsanity.com/paper/1905.12265/) (2019)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [GraphSAINT: Graph Sampling Based Inductive Learning Method](https://mlsanity.com/paper/1907.04931/) (2019)
- [GraphMAE: Self-Supervised Masked Graph Autoencoders](https://mlsanity.com/paper/2205.10803/) (2022)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [Graph Self-Supervised Learning: A Survey](https://mlsanity.com/paper/2103.00111/) (2021)
- [Can Language Models Solve Graph Problems in Natural Language?](https://mlsanity.com/paper/2305.10037/) (2023)
- [One for All: Towards Training One Graph Model for All Classification Tasks](https://mlsanity.com/paper/2310.00149/) (2023)
- [Language is All a Graph Needs](https://mlsanity.com/paper/2308.07134/) (2023)
- [Self-Supervised Learning of Graph Neural Networks: A Unified Review](https://mlsanity.com/paper/2102.10757/) (2021)
- [Optimal Transport for structured data with application on graphs](https://mlsanity.com/paper/1805.09114/) (2018)
- [All in One: Multi-task Prompting for Graph Neural Networks](https://mlsanity.com/paper/2307.01504/) (2023)
- [On the Properties of the Softmax Function with Application in Game Theory and Reinforcement Learning](https://mlsanity.com/paper/1704.00805/) (2017)
- [GraphMAE2: A Decoding-Enhanced Masked Self-Supervised Graph Learner](https://mlsanity.com/paper/2304.04779/) (2023)
- [Graph Foundation Models: Concepts, Opportunities and Challenges](https://mlsanity.com/paper/2310.11829/) (2023)

## Built on by (most cited first, 5 of 5)

- [SCGFM-ART: Amortized Relational Transport for Structure-Centric Graph Foundation Models](https://mlsanity.com/paper/2609.20419/) (2026)
- [SPR: Toward a Graph Foundation Model for Transferable Graph Cognition via Spectral Patterns and Relational Geometry](https://mlsanity.com/paper/2606.03315/) (2026)
- [What Makes Graph Unified? Principles and Generative Sliding-Window Transformer for Graph Foundation Models](https://mlsanity.com/paper/2607.27966/) (2026)
- [Preserving Geometric Integrity in Graph Prompting via Measure-Constrained Optimal Transport](https://mlsanity.com/paper/2609.23547/) (2026)
- [Spectral Reversal: Counteracting Singular Value Bias for Graph Prompting](https://mlsanity.com/paper/2609.32143/) (2026)

## Abstract (arXiv)

Graph foundation models (GFMs) seek transferable representations across graph domains but are limited by structural heterogeneity and incompatible node feature spaces. We propose Structure-Centric Graph Foundation Models (SCGFM), which treat graph topology as the primary source of transferable knowledge. Modeling graphs as metric measure spaces, SCGFM introduces learnable geometric bases that define a shared structural coordinate system. Graphs are aligned to these bases via Gromov-Wasserstein distances, yielding structure-aligned latent representations that accommodate heterogeneous graph topologies. To address feature incompatibility, SCGFM employs a structure-aware feature re-encoding mechanism that unifies node representations without assuming a fixed feature dimensionality or requiring dataset-specific preprocessing. Experiments on graph- and node-level tasks demonstrate strong in-domain and cross-domain generalization, outperforming existing GFM approaches.