# SPR: Toward a Graph Foundation Model for Transferable Graph Cognition via Spectral Patterns and Relational Geometry

arXiv: https://arxiv.org/abs/2606.03315 · HTML: https://mlsanity.com/paper/2606.03315/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 33 of its 41 references that are in the map.
- First posted on arXiv 2 Jun 2026.

## Builds on (most cited first, 30 of 33)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [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)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (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)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Deep Graph Contrastive Representation Learning](https://mlsanity.com/paper/2006.04131/) (2020)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [One for All: Towards Training One Graph Model for All Classification Tasks](https://mlsanity.com/paper/2310.00149/) (2023)
- [Optimal Transport for structured data with application on graphs](https://mlsanity.com/paper/1805.09114/) (2018)
- [GraphPrompt: Unifying Pre-Training and Downstream Tasks for Graph Neural Networks](https://mlsanity.com/paper/2302.08043/) (2023)
- [GraphMAE2: A Decoding-Enhanced Masked Self-Supervised Graph Learner](https://mlsanity.com/paper/2304.04779/) (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)
- [UniGraph: Learning a Unified Cross-Domain Foundation Model for Text-Attributed Graphs](https://mlsanity.com/paper/2402.13630/) (2024)
- [SAMGPT: Text-free Graph Foundation Model for Multi-domain Pre-training and Cross-domain Adaptation](https://mlsanity.com/paper/2502.05424/) (2025)
- [Graph Foundation Models: A Comprehensive Survey](https://mlsanity.com/paper/2505.15116/) (2025)
- [Fully-inductive Node Classification on Arbitrary Graphs](https://mlsanity.com/paper/2405.20445/) (2024)
- [RiemannGFM: Learning a Graph Foundation Model from Riemannian Geometry](https://mlsanity.com/paper/2502.03251/) (2025)
- [Towards Graph Foundation Models: Learning Generalities Across Graphs via Task-Trees](https://mlsanity.com/paper/2412.16441/) (2024)
- [Spectral Invariant Learning for Dynamic Graphs under Distribution Shifts](https://mlsanity.com/paper/2403.05026/) (2024)
- [Flock: A Knowledge Graph Foundation Model via Learning on Random Walks](https://mlsanity.com/paper/2510.01510/) (2025)
- [Towards A Universal Graph Structural Encoder](https://mlsanity.com/paper/2504.10917/) (2025)
- [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)

## Abstract (arXiv)

Recently, Graph Foundation Models (GFMs) have attracted increasing attention for their potential to learn unified and generalizable knowledge across diverse graphs, thereby supporting a wide range of graph scenarios. However, unlike natural language and images, graphs lack an intuitive and unified form for perceiving and organizing transferable knowledge. Therefore, despite many initial explorations, a key problem remains unresolved: the transferable cognitive mechanism for graphs. Existing GFMs usually rely on intuitively defined mechanisms to encode transferable graph patterns, such as handcrafted structural templates (e.g., cycles and trees), fixed propagation mechanisms, and predefined random-walk patterns. These mechanisms are often prescriptive and rigid, limiting their ability to flexibly characterize diverse graph patterns across domains. This motivates the exploration of a more flexible, graph-native, and transferable cognitive mechanism. To this end, we analyze graphs from the spectral perspective and propose SPR. SPR decomposes graph information into Chebyshev polynomial bases and learns shared spectral responses, enabling unified yet adaptive cognition of continuously varying spectral patterns across graphs. We further model cross-graph relational geometry to distill recurring pairwise organization from multiple graphs, providing a shared relational reference for transferring such graph cognition across domains. Extensive experiments across diverse graphs and downstream scenarios demonstrate that SPR enables effective and transferable graph cognition.