# From Euclidean to Graph-Structured Data: A Survey of Collaborative Learning

arXiv: https://arxiv.org/abs/2609.02984 · HTML: https://mlsanity.com/paper/2609.02984/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 459 references that are in the map.
- First posted on arXiv 2 Sep 2026.

## Builds on (most cited first, 30 of 32)

- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Federated Learning with Non-IID Data](https://mlsanity.com/paper/1806.00582/) (2018)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Federated Learning with Personalization Layers](https://mlsanity.com/paper/1912.00818/) (2019)
- [iDLG: Improved Deep Leakage from Gradients](https://mlsanity.com/paper/2001.02610/) (2020)
- [Adaptive Personalized Federated Learning](https://mlsanity.com/paper/2003.13461/) (2020)
- [Think Locally, Act Globally: Federated Learning with Local and Global Representations](https://mlsanity.com/paper/2001.01523/) (2020)
- [Three Approaches for Personalization with Applications to Federated Learning](https://mlsanity.com/paper/2002.10619/) (2020)
- [Personalized Federated Learning: A Meta-Learning Approach](https://mlsanity.com/paper/2002.07948/) (2020)
- [Improving Federated Learning Personalization via Model Agnostic Meta Learning](https://mlsanity.com/paper/1909.12488/) (2019)
- [Client Selection in Federated Learning: Convergence Analysis and Power-of-Choice Selection Strategies](https://mlsanity.com/paper/2010.01243/) (2020)
- [Discovering Invariant Rationales for Graph Neural Networks](https://mlsanity.com/paper/2201.12872/) (2022)
- [Threats to Federated Learning: A Survey](https://mlsanity.com/paper/2003.02133/) (2020)
- [Protection Against Reconstruction and Its Applications in Private Federated Learning](https://mlsanity.com/paper/1812.00984/) (2018)
- [FedGNN: Federated Graph Neural Network for Privacy-Preserving Recommendation](https://mlsanity.com/paper/2102.04925/) (2021)
- [Topological Deep Learning: Going Beyond Graph Data](https://mlsanity.com/paper/2206.00606/) (2022)
- [Graph Foundation Models: A Comprehensive Survey](https://mlsanity.com/paper/2505.15116/) (2025)
- [Federated Graph Learning -- A Position Paper](https://mlsanity.com/paper/2105.11099/) (2021)
- [Federated User Representation Learning](https://mlsanity.com/paper/1909.12535/) (2019)
- [Achieving Personalized Federated Learning with Sparse Local Models](https://mlsanity.com/paper/2201.11380/) (2022)
- [On Node Features for Graph Neural Networks](https://mlsanity.com/paper/1911.08795/) (2019)
- [A Vertical Federated Learning Framework for Graph Convolutional Network](https://mlsanity.com/paper/2106.11593/) (2021)
- [A Survey of Deep Graph Learning under Distribution Shifts: from Graph Out-of-Distribution Generalization to Adaptation](https://mlsanity.com/paper/2410.19265/) (2024)
- [Graph Neural Networks for Decentralized Multi-Robot Submodular Action Selection](https://mlsanity.com/paper/2105.08601/) (2021)
- [Should Graph Neural Networks Use Features, Edges, Or Both?](https://mlsanity.com/paper/2103.06857/) (2021)
- [Future Directions in the Theory of Graph Machine Learning](https://mlsanity.com/paper/2402.02287/) (2024)
- [Towards Communication-Efficient Decentralized Federated Graph Learning over Non-IID Data](https://mlsanity.com/paper/2509.08409/) (2025)
- [Graph Representational Learning: When Does More Expressivity Hurt Generalization?](https://mlsanity.com/paper/2505.11298/) (2025)
- [A dual approach for federated learning](https://mlsanity.com/paper/2201.11183/) (2022)
- [FedSheafHN: Personalized Federated Learning on Graph-structured Data](https://mlsanity.com/paper/2405.16056/) (2024)

## Abstract (arXiv)

The conventional approach to machine learning, that is, collecting data, training models, and performing inference in a single location, faces fundamental limitations, including scalability and privacy, that restrict its applicability. To address these challenges, recent research has explored collaborative learning approaches, including federated learning and decentralized learning, where individual agents perform training and inference locally, with limited collaboration. Most collaborative learning research focuses on Euclidean data with regular, grid-like structure (e.g., images, text). However, these approaches fail to capture the relational patterns in many real-world applications, best represented by graphs. Learning on graphs relies on message-passing mechanisms to propagate information between connected nodes, making it conceptually well-suited for collaborative environments where agents must exchange information. Yet, the opportunities and challenges of learning on graph-structured data in collaborative settings remain largely underexplored. This survey provides a comprehensive investigation of collaborative learning from Euclidean to graph-structured data, aiming to consolidate this emerging field. We begin by reviewing its foundational principles for Euclidean data, organizing them along three core dimensions: learning effectiveness, efficiency, and privacy preservation. We then extend the discussion to graph-structured data, introducing a taxonomy of graph distribution scenarios, characterizing associated statistical heterogeneities, and developing standardized problem formulations and algorithmic frameworks. Finally, we systematically identify open challenges and promising research directions.