# Towards A Universal Graph Structural Encoder

arXiv: https://arxiv.org/abs/2504.10917 · HTML: https://mlsanity.com/paper/2504.10917/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 81 of its 115 references that are in the map.
- First posted on arXiv 15 Apr 2025.

## Builds on (most cited first, 30 of 81)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [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)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [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)
- [Image-based Recommendations on Styles and Substitutes](https://mlsanity.com/paper/1506.04757/) (2015)
- [Contrastive Multi-View Representation Learning on Graphs](https://mlsanity.com/paper/2006.05582/) (2020)
- [AudioLM: a Language Modeling Approach to Audio Generation](https://mlsanity.com/paper/2209.03143/) (2022)
- [Cluster-GCN: An Efficient Algorithm for Training Deep and Large Graph Convolutional Networks](https://mlsanity.com/paper/1905.07953/) (2019)
- [Ups and Downs: Modeling the Visual Evolution of Fashion Trends with One-Class Collaborative Filtering](https://mlsanity.com/paper/1602.01585/) (2016)
- [Rethinking Graph Transformers with Spectral Attention](https://mlsanity.com/paper/2106.03893/) (2021)
- [GCC: Graph Contrastive Coding for Graph Neural Network Pre-Training](https://mlsanity.com/paper/2006.09963/) (2020)
- [GraphMAE: Self-Supervised Masked Graph Autoencoders](https://mlsanity.com/paper/2205.10803/) (2022)
- [InfoGraph: Unsupervised and Semi-supervised Graph-Level Representation Learning via Mutual Information Maximization](https://mlsanity.com/paper/1908.01000/) (2019)
- [Residual Gated Graph ConvNets](https://mlsanity.com/paper/1711.07553/) (2017)

## Built on by (most cited first, 7 of 7)

- [MM-OpenFGL: A Comprehensive Benchmark for Multimodal Federated Graph Learning](https://mlsanity.com/paper/2601.22416/) (2026)
- [Toward Effective Multimodal Graph Foundation Model: A Divide-and-Conquer Based Approach](https://mlsanity.com/paper/2602.04116/) (2026)
- [Bridging Input Feature Spaces Towards Graph Foundation Models](https://mlsanity.com/paper/2605.04834/) (2026)
- [Rethinking Federated Graph Foundation Models: A Graph-Language Alignment-based Approach](https://mlsanity.com/paper/2601.21369/) (2026)
- [Two Facets of the Same Optimization Coin: Model Degradation and Representation Collapse in Graph Foundation Models](https://mlsanity.com/paper/2509.08401/) (2025)
- [SPR: Toward a Graph Foundation Model for Transferable Graph Cognition via Spectral Patterns and Relational Geometry](https://mlsanity.com/paper/2606.03315/) (2026)
- [Training Graph Foundation Models on The Web Graph](https://mlsanity.com/paper/2609.30894/) (2026)

## Abstract (arXiv)

Recent advancements in large-scale pre-training have shown the potential to learn generalizable representations for downstream tasks. In the graph domain, however, capturing and transferring structural information across different graph domains remains challenging, primarily due to the inherent differences in graph topological patterns across various contexts. For example, a social network's structure is fundamentally different from that of a product co-purchase graph. Additionally, most existing models struggle to capture the rich topological complexity of graph structures, leading to inadequate exploration of the graph embedding space. To address these challenges, we propose GFSE, a universal pre-trained graph encoder designed to capture transferable structural patterns across diverse domains such as the web graph, social networks, and citation networks. GFSE is the first cross-domain graph structural encoder pre-trained with multiple self-supervised learning objectives. Built on a Graph Transformer, GFSE incorporates attention mechanisms informed by graph structural information, enabling it to encode intricate multi-level and fine-grained topological features within complex graph structures. The pre-trained GFSE produces generic and theoretically expressive positional and structural encoding for graphs, which can be seamlessly integrated with various downstream graph feature encoders, including graph neural networks for vectorized features and Large Language Models (LLMs) for text-attributed graphs. Comprehensive experiments on synthetic and real-world datasets demonstrate GFSE's capability to significantly enhance the model's performance while requiring substantially less task-specific fine-tuning.