# FlatLand: Personalized Graph Federated Learning via Tailored Lorentz Space

arXiv: https://arxiv.org/abs/2608.21096 · HTML: https://mlsanity.com/paper/2608.21096/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 69 references that are in the map.
- First posted on arXiv 21 Aug 2026.

## Builds on (most cited first, 30 of 47)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [Adaptive Federated Optimization](https://mlsanity.com/paper/2003.00295/) (2020)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Ditto: Fair and Robust Federated Learning Through Personalization](https://mlsanity.com/paper/2012.04221/) (2020)
- [Personalized Federated Learning with Moreau Envelopes](https://mlsanity.com/paper/2006.08848/) (2020)
- [Federated Learning with Personalization Layers](https://mlsanity.com/paper/1912.00818/) (2019)
- [Exploiting Shared Representations for Personalized Federated Learning](https://mlsanity.com/paper/2102.07078/) (2021)
- [Towards Personalized Federated Learning](https://mlsanity.com/paper/2103.00710/) (2021)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Adaptive Personalized Federated Learning](https://mlsanity.com/paper/2003.13461/) (2020)
- [Three Approaches for Personalization with Applications to Federated Learning](https://mlsanity.com/paper/2002.10619/) (2020)
- [Personalized Cross-Silo Federated Learning on Non-IID Data](https://mlsanity.com/paper/2007.03797/) (2020)
- [Improving Federated Learning Personalization via Model Agnostic Meta Learning](https://mlsanity.com/paper/1909.12488/) (2019)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [Federated Learning of a Mixture of Global and Local Models](https://mlsanity.com/paper/2002.05516/) (2020)
- [Personalized Federated Learning with First Order Model Optimization](https://mlsanity.com/paper/2012.08565/) (2020)
- [Federated Evaluation of On-device Personalization](https://mlsanity.com/paper/1910.10252/) (2019)
- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [Subgraph Federated Learning with Missing Neighbor Generation](https://mlsanity.com/paper/2106.13430/) (2021)
- [Federated Graph Classification over Non-IID Graphs](https://mlsanity.com/paper/2106.13423/) (2021)
- [Fully Hyperbolic Neural Networks](https://mlsanity.com/paper/2105.14686/) (2021)
- [Hyperbolic Image Segmentation](https://mlsanity.com/paper/2203.05898/) (2022)

## Built on by (most cited first, 2 of 2)

- [Memory Has Geometry: Non-Uniform Geometric Memory for Long-Horizon Personalized AI](https://mlsanity.com/paper/2609.17969/) (2026)
- [Hyperbolic Multimodal Continual Learning: A Closest-Admissible Solution](https://mlsanity.com/paper/2609.29329/) (2026)

## Abstract (arXiv)

Federated learning enables privacy-preserving collaborative training, but highly heterogeneous client data remain challenging, especially in graph federated learning where clients possess structurally diverse graphs. Existing personalized federated learning (PFL) methods ignore the intrinsic geometric properties of diverse graph structures. We propose FlatLand, a novel personalized federated learning method that embeds different clients' data in tailored Lorentz space of hyperbolic geometry. Our key insight is that hyperbolic geometry naturally accommodates the intrinsic negative curvature prevalent in real-world graphs, while the time-like dimension in Lorentz space provides a principled way to encode client-specific heterogeneity. We develop a parameter decoupling strategy that separates heterogeneous information (captured in time-like parameters) from common knowledge (preserved in space-like parameters), enabling direct aggregation without requiring client similarity estimation and extra calculation modules. Empirical results on diverse federated graph learning tasks demonstrate that FlatLand achieves superior performance, particularly in low-dimensional settings.