# FedSOL: Stabilized Orthogonal Learning with Proximal Restrictions in Federated Learning

arXiv: https://arxiv.org/abs/2308.12532 · HTML: https://mlsanity.com/paper/2308.12532/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 57 of its 73 references that are in the map.
- First posted on arXiv 24 Aug 2023.

## Builds on (most cited first, 30 of 57)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [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)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [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)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Improved Regularization of Convolutional Neural Networks with Cutout](https://mlsanity.com/paper/1708.04552/) (2017)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Federated Learning with Non-IID Data](https://mlsanity.com/paper/1806.00582/) (2018)
- [Efficient Lifelong Learning with A-GEM](https://mlsanity.com/paper/1812.00420/) (2018)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [Model-Contrastive Federated Learning](https://mlsanity.com/paper/2103.16257/) (2021)
- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (2021)
- [Local SGD Converges Fast and Communicates Little](https://mlsanity.com/paper/1805.09767/) (2018)
- [Federated Optimization: Distributed Machine Learning for On-Device Intelligence](https://mlsanity.com/paper/1610.02527/) (2016)
- [Federated Learning with Matched Averaging](https://mlsanity.com/paper/2002.06440/) (2020)
- [Federated Learning Based on Dynamic Regularization](https://mlsanity.com/paper/2111.04263/) (2021)
- [Fantastic Generalization Measures and Where to Find Them](https://mlsanity.com/paper/1912.02178/) (2019)
- [Orthogonal Gradient Descent for Continual Learning](https://mlsanity.com/paper/1910.07104/) (2019)

## Built on by (most cited first, 14 of 14)

- [(FL)2: Overcoming Few Labels in Federated Semi-Supervised Learning](https://mlsanity.com/paper/2410.23227/) (2024)
- [Understanding Federated Learning from IID to Non-IID dataset: An Experimental Study](https://mlsanity.com/paper/2502.00182/) (2025)
- [FedDr+: Stabilizing Dot-regression with Global Feature Distillation for Federated Learning](https://mlsanity.com/paper/2406.02355/) (2024)
- [GC-Fed: Gradient Centralized Federated Learning with Partial Client Participation](https://mlsanity.com/paper/2503.13180/) (2025)
- [FedORGP: Guiding Heterogeneous Federated Learning with Orthogonality Regularization on Global Prototypes](https://mlsanity.com/paper/2502.16119/) (2025)
- [Task-Agnostic Federated Continual Learning via Replay-Free Gradient Projection](https://mlsanity.com/paper/2509.21606/) (2025)
- [Neighborhood and Global Perturbations Supported SAM in Federated Learning: From Local Tweaks To Global Awareness](https://mlsanity.com/paper/2408.14144/) (2024)
- [HeteRo-Select: Informativeness as the Participation Driver in Heterogeneous Federated Learning](https://mlsanity.com/paper/2508.06692/) (2025)
- [Federated Learning with Feedback Alignment](https://mlsanity.com/paper/2512.12762/) (2025)
- [MDiffFR: Modality-Guided Diffusion Generation for Cold-start Items in Federated Recommendation](https://mlsanity.com/paper/2512.24715/) (2025)
- [Class-wise Contribution Estimation via Logit Maximization for Federated Learning](https://mlsanity.com/paper/2605.18892/) (2026)
- [FedFFT: Taming Client Drift in Federated SAM via Spectral Perturbation Filtering](https://mlsanity.com/paper/2607.04170/) (2026)
- [FedADB: Class Anchor-Driven Dual-Branch Federated Learning for Mitigating Forgetting](https://mlsanity.com/paper/2608.15310/) (2026)
- [Federated Continual Learning as a Distributed Drift-Plus-Penalty Control Problem](https://mlsanity.com/paper/2608.21539/) (2026)

## Abstract (arXiv)

Federated Learning (FL) aggregates locally trained models from individual clients to construct a global model. While FL enables learning a model with data privacy, it often suffers from significant performance degradation when clients have heterogeneous data distributions. This data heterogeneity causes the model to forget the global knowledge acquired from previously sampled clients after being trained on local datasets. Although the introduction of proximal objectives in local updates helps to preserve global knowledge, it can also hinder local learning by interfering with local objectives. To address this problem, we propose a novel method, Federated Stabilized Orthogonal Learning (FedSOL), which adopts an orthogonal learning strategy to balance the two conflicting objectives. FedSOL is designed to identify gradients of local objectives that are inherently orthogonal to directions affecting the proximal objective. Specifically, FedSOL targets parameter regions where learning on the local objective is minimally influenced by proximal weight perturbations. Our experiments demonstrate that FedSOL consistently achieves state-of-the-art performance across various scenarios.