# SphereFed: Hyperspherical Federated Learning

arXiv: https://arxiv.org/abs/2207.09413 · HTML: https://mlsanity.com/paper/2207.09413/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 72 of its 97 references that are in the map.
- First posted on arXiv 19 Jul 2022.

## Builds on (most cited first, 30 of 72)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [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)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [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)
- [Adaptive Federated Optimization](https://mlsanity.com/paper/2003.00295/) (2020)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [Measuring the Effects of Non-Identical Data Distribution for Federated Visual Classification](https://mlsanity.com/paper/1909.06335/) (2019)
- [Decoupling Representation and Classifier for Long-Tailed Recognition](https://mlsanity.com/paper/1910.09217/) (2019)
- [Model-Contrastive Federated Learning](https://mlsanity.com/paper/2103.16257/) (2021)
- [SphereFace: Deep Hypersphere Embedding for Face Recognition](https://mlsanity.com/paper/1704.08063/) (2017)
- [Federated Multi-Task Learning](https://mlsanity.com/paper/1705.10467/) (2017)
- [Federated Learning on Non-IID Data Silos: An Experimental Study](https://mlsanity.com/paper/2102.02079/) (2021)
- [Federated Learning Based on Dynamic Regularization](https://mlsanity.com/paper/2111.04263/) (2021)
- [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)
- [FedMD: Heterogenous Federated Learning via Model Distillation](https://mlsanity.com/paper/1910.03581/) (2019)
- [Data-Free Knowledge Distillation for Heterogeneous Federated Learning](https://mlsanity.com/paper/2105.10056/) (2021)
- [Rapid Learning or Feature Reuse? Towards Understanding the Effectiveness of MAML](https://mlsanity.com/paper/1909.09157/) (2019)
- [HeteroFL: Computation and Communication Efficient Federated Learning for Heterogeneous Clients](https://mlsanity.com/paper/2010.01264/) (2020)

## Built on by (most cited first, 19 of 19)

- [L-DAWA: Layer-wise Divergence Aware Weight Aggregation in Federated Self-Supervised Visual Representation Learning](https://mlsanity.com/paper/2307.07393/) (2023)
- [Learning to Generate Image Embeddings with User-level Differential Privacy](https://mlsanity.com/paper/2211.10844/) (2022)
- [FedImpro: Measuring and Improving Client Update in Federated Learning](https://mlsanity.com/paper/2402.07011/) (2024)
- [ProtoFL: Unsupervised Federated Learning via Prototypical Distillation](https://mlsanity.com/paper/2307.12450/) (2023)
- [FuseFL: One-Shot Federated Learning through the Lens of Causality with Progressive Model Fusion](https://mlsanity.com/paper/2410.20380/) (2024)
- [FedLoGe: Joint Local and Generic Federated Learning under Long-tailed Data](https://mlsanity.com/paper/2401.08977/) (2024)
- [HyperFed: Hyperbolic Prototypes Exploration with Consistent Aggregation for Non-IID Data in Federated Learning](https://mlsanity.com/paper/2307.14384/) (2023)
- [FedFN: Feature Normalization for Alleviating Data Heterogeneity Problem in Federated Learning](https://mlsanity.com/paper/2311.13267/) (2023)
- [Unlocking Visual Secrets: Inverting Features with Diffusion Priors for Image Reconstruction](https://mlsanity.com/paper/2412.10448/) (2024)
- [Neural Collapse Inspired Federated Learning with Non-iid Data](https://mlsanity.com/paper/2303.16066/) (2023)
- [Covariances for Free: Exploiting Mean Distributions for Training-free Federated Learning](https://mlsanity.com/paper/2412.14326/) (2024)
- [Joint Local Relational Augmentation and Global Nash Equilibrium for Federated Learning with Non-IID Data](https://mlsanity.com/paper/2308.11646/) (2023)
- [FedSSC: Shared Supervised-Contrastive Federated Learning](https://mlsanity.com/paper/2301.05797/) (2023)
- [FedDr+: Stabilizing Dot-regression with Global Feature Distillation for Federated Learning](https://mlsanity.com/paper/2406.02355/) (2024)
- [FOCoOp: Enhancing Out-of-Distribution Robustness in Federated Prompt Learning for Vision-Language Models](https://mlsanity.com/paper/2506.16218/) (2025)
- [Neural Collapse-Inspired Multi-Label Federated Learning under Label-Distribution Skew](https://mlsanity.com/paper/2509.12544/) (2025)
- [FedRE: A Representation Entanglement Framework for Model-Heterogeneous Federated Learning](https://mlsanity.com/paper/2511.22265/) (2025)
- [FedHarmony: Harmonizing Heterogeneous Label Correlations in Federated Multi-Label Learning](https://mlsanity.com/paper/2604.28024/) (2026)
- [From Data Heterogeneity to Convergence: A Data-Centric Review of Federated Learning](https://mlsanity.com/paper/2606.10595/) (2026)

## Abstract (arXiv)

Federated Learning aims at training a global model from multiple decentralized devices (i.e. clients) without exchanging their private local data. A key challenge is the handling of non-i.i.d. (independent identically distributed) data across multiple clients that may induce disparities of their local features. We introduce the Hyperspherical Federated Learning (SphereFed) framework to address the non-i.i.d. issue by constraining learned representations of data points to be on a unit hypersphere shared by clients. Specifically, all clients learn their local representations by minimizing the loss with respect to a fixed classifier whose weights span the unit hypersphere. After federated training in improving the global model, this classifier is further calibrated with a closed-form solution by minimizing a mean squared loss. We show that the calibration solution can be computed efficiently and distributedly without direct access of local data. Extensive experiments indicate that our SphereFed approach is able to improve the accuracy of multiple existing federated learning algorithms by a considerable margin (up to 6% on challenging datasets) with enhanced computation and communication efficiency across datasets and model architectures.