# Federated Classification in Hyperbolic Spaces via Secure Aggregation of Convex Hulls

arXiv: https://arxiv.org/abs/2308.06895 · HTML: https://mlsanity.com/paper/2308.06895/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 45 of its 100 references that are in the map.
- First posted on arXiv 14 Aug 2023.

## Builds on (most cited first, 30 of 45)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [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)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [Federated Learning with Non-IID Data](https://mlsanity.com/paper/1806.00582/) (2018)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [The Future of Digital Health with Federated Learning](https://mlsanity.com/paper/2003.08119/) (2020)
- [Learning from Noisy Labels with Deep Neural Networks: A Survey](https://mlsanity.com/paper/2007.08199/) (2020)
- [Clustered Federated Learning: Model-Agnostic Distributed Multi-Task Optimization under Privacy Constraints](https://mlsanity.com/paper/1910.01991/) (2019)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Differential Privacy Has Disparate Impact on Model Accuracy](https://mlsanity.com/paper/1905.12101/) (2019)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Low-Dimensional Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2005.00545/) (2020)
- [Poincar'e GloVe: Hyperbolic Word Embeddings](https://mlsanity.com/paper/1810.06546/) (2018)
- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [Distilled One-Shot Federated Learning](https://mlsanity.com/paper/2009.07999/) (2020)
- [Mixed-curvature Variational Autoencoders](https://mlsanity.com/paper/1911.08411/) (2019)
- [Practical One-Shot Federated Learning for Cross-Silo Setting](https://mlsanity.com/paper/2010.01017/) (2020)
- [Embedding Text in Hyperbolic Spaces](https://mlsanity.com/paper/1806.04313/) (2018)
- [Hyperbolic Graph Attention Network](https://mlsanity.com/paper/1912.03046/) (2019)
- [From Trees to Continuous Embeddings and Back: Hyperbolic Hierarchical Clustering](https://mlsanity.com/paper/2010.00402/) (2020)
- [Large-Margin Classification in Hyperbolic Space](https://mlsanity.com/paper/1806.00437/) (2018)
- [Modeling Scale-free Graphs with Hyperbolic Geometry for Knowledge-aware Recommendation](https://mlsanity.com/paper/2108.06468/) (2021)
- [Tree! I am no Tree! I am a Low Dimensional Hyperbolic Embedding](https://mlsanity.com/paper/2005.03847/) (2020)
- [Coded Computing for Low-Latency Federated Learning over Wireless Edge Networks](https://mlsanity.com/paper/2011.06223/) (2020)
- [Hyperbolic Interaction Model For Hierarchical Multi-Label Classification](https://mlsanity.com/paper/1905.10802/) (2019)
- [One-Shot Federated Learning: Theoretical Limits and Algorithms to Achieve Them](https://mlsanity.com/paper/1905.04634/) (2019)

## Abstract (arXiv)

Hierarchical and tree-like data sets arise in many applications, including language processing, graph data mining, phylogeny and genomics. It is known that tree-like data cannot be embedded into Euclidean spaces of finite dimension with small distortion. This problem can be mitigated through the use of hyperbolic spaces. When such data also has to be processed in a distributed and privatized setting, it becomes necessary to work with new federated learning methods tailored to hyperbolic spaces. As an initial step towards the development of the field of federated learning in hyperbolic spaces, we propose the first known approach to federated classification in hyperbolic spaces. Our contributions are as follows. First, we develop distributed versions of convex SVM classifiers for Poincar'e discs. In this setting, the information conveyed from clients to the global classifier are convex hulls of clusters present in individual client data. Second, to avoid label switching issues, we introduce a number-theoretic approach for label recovery based on the so-called integer Bh sequences. Third, we compute the complexity of the convex hulls in hyperbolic spaces to assess the extent of data leakage; at the same time, in order to limit communication cost for the hulls, we propose a new quantization method for the Poincar'e disc coupled with Reed-Solomon-like encoding. Fourth, at the server level, we introduce a new approach for aggregating convex hulls of the clients based on balanced graph partitioning. We test our method on a collection of diverse data sets, including hierarchical single-cell RNA-seq data from different patients distributed across different repositories that have stringent privacy constraints. The classification accuracy of our method is up to ~ 11% better than its Euclidean counterpart, demonstrating the importance of privacy-preserving learning in hyperbolic spaces.