# Improving Generalization in Federated Learning by Seeking Flat Minima

arXiv: https://arxiv.org/abs/2203.11834 · HTML: https://mlsanity.com/paper/2203.11834/

## Key facts

- Cited by 98 papers in the map (data through 14 Oct 2026).
- Builds on 68 of its 93 references that are in the map.
- First posted on arXiv 22 Mar 2022.

## Builds on (most cited first, 30 of 68)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (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)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization](https://mlsanity.com/paper/2006.16241/) (2020)
- [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)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [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)
- [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)
- [Adaptive Federated Optimization](https://mlsanity.com/paper/2003.00295/) (2020)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Measuring the Effects of Non-Identical Data Distribution for Federated Visual Classification](https://mlsanity.com/paper/1909.06335/) (2019)
- [Model-Contrastive Federated Learning](https://mlsanity.com/paper/2103.16257/) (2021)
- [Ensemble Distillation for Robust Model Fusion in Federated Learning](https://mlsanity.com/paper/2006.07242/) (2020)
- [Federated Multi-Task Learning](https://mlsanity.com/paper/1705.10467/) (2017)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)

## Built on by (most cited first, 30 of 98)

- [Generalized Federated Learning via Sharpness Aware Minimization](https://mlsanity.com/paper/2206.02618/) (2022)
- [FedCLIP: Fast Generalization and Personalization for CLIP in Federated Learning](https://mlsanity.com/paper/2302.13485/) (2023)
- [Revisiting Weighted Aggregation in Federated Learning with Neural Networks](https://mlsanity.com/paper/2302.10911/) (2023)
- [FedSpeed: Larger Local Interval, Less Communication Round, and Higher Generalization Accuracy](https://mlsanity.com/paper/2302.10429/) (2023)
- [Dynamic Regularized Sharpness Aware Minimization in Federated Learning: Approaching Global Consistency and Smooth Landscape](https://mlsanity.com/paper/2305.11584/) (2023)
- [Improving the Model Consistency of Decentralized Federated Learning](https://mlsanity.com/paper/2302.04083/) (2023)
- [Learning Across Domains and Devices: Style-Driven Source-Free Domain Adaptation in Clustered Federated Learning](https://mlsanity.com/paper/2210.02326/) (2022)
- [Cross-Silo Prototypical Calibration for Federated Learning with Non-IID Data](https://mlsanity.com/paper/2308.03457/) (2023)
- [Make Landscape Flatter in Differentially Private Federated Learning](https://mlsanity.com/paper/2303.11242/) (2023)
- [L-DAWA: Layer-wise Divergence Aware Weight Aggregation in Federated Self-Supervised Visual Representation Learning](https://mlsanity.com/paper/2307.07393/) (2023)
- [Locally Estimated Global Perturbations are Better than Local Perturbations for Federated Sharpness-aware Minimization](https://mlsanity.com/paper/2405.18890/) (2024)
- [Federated Unlearning: A Survey on Methods, Design Guidelines, and Evaluation Metrics](https://mlsanity.com/paper/2401.05146/) (2024)
- [Enhancing One-Shot Federated Learning Through Data and Ensemble Co-Boosting](https://mlsanity.com/paper/2402.15070/) (2024)
- [FedSWA: Improving Generalization in Federated Learning with Highly Heterogeneous Data via Momentum-Based Stochastic Controlled Weight Averaging](https://mlsanity.com/paper/2507.20016/) (2025)
- [Understanding How Consistency Works in Federated Learning via Stage-wise Relaxed Initialization](https://mlsanity.com/paper/2306.05706/) (2023)
- [Beyond Losses Reweighting: Empowering Multi-Task Learning via the Generalization Perspective](https://mlsanity.com/paper/2211.13723/) (2022)
- [FedSOL: Stabilized Orthogonal Learning with Proximal Restrictions in Federated Learning](https://mlsanity.com/paper/2308.12532/) (2023)
- [Is Aggregation the Only Choice? Federated Learning via Layer-wise Model Recombination](https://mlsanity.com/paper/2305.10730/) (2023)
- [Flat Seeking Bayesian Neural Networks](https://mlsanity.com/paper/2302.02713/) (2023)
- [Accelerating Heterogeneous Federated Learning with Closed-form Classifiers](https://mlsanity.com/paper/2406.01116/) (2024)
- [Multi-Dataset Co-Training with Sharpness-Aware Optimization for Audio Anti-spoofing](https://mlsanity.com/paper/2305.19953/) (2023)
- [Semantic Self-adaptation: Enhancing Generalization with a Single Sample](https://mlsanity.com/paper/2208.05788/) (2022)
- [Federated Survival Forests](https://mlsanity.com/paper/2302.02807/) (2023)
- [Towards More Suitable Personalization in Federated Learning via Decentralized Partial Model Training](https://mlsanity.com/paper/2305.15157/) (2023)
- [Beyond Local Sharpness: Communication-Efficient Global Sharpness-aware Minimization for Federated Learning](https://mlsanity.com/paper/2412.03752/) (2024)
- [Understanding and Improving Model Averaging in Federated Learning on Heterogeneous Data](https://mlsanity.com/paper/2305.07845/) (2023)
- [Taxonomy Adaptive Cross-Domain Adaptation in Medical Imaging via Optimization Trajectory Distillation](https://mlsanity.com/paper/2307.14709/) (2023)
- [Window-based Model Averaging Improves Generalization in Heterogeneous Federated Learning](https://mlsanity.com/paper/2310.01366/) (2023)
- [Federated Motor Imagery Classification for Privacy-Preserving Brain-Computer Interfaces](https://mlsanity.com/paper/2412.01079/) (2024)
- [FedNSAM:Consistency of Local and Global Flatness for Federated Learning](https://mlsanity.com/paper/2602.23827/) (2026)

## Abstract (arXiv)

Models trained in federated settings often suffer from degraded performances and fail at generalizing, especially when facing heterogeneous scenarios. In this work, we investigate such behavior through the lens of geometry of the loss and Hessian eigenspectrum, linking the model's lack of generalization capacity to the sharpness of the solution. Motivated by prior studies connecting the sharpness of the loss surface and the generalization gap, we show that i) training clients locally with Sharpness-Aware Minimization (SAM) or its adaptive version (ASAM) and ii) averaging stochastic weights (SWA) on the server-side can substantially improve generalization in Federated Learning and help bridging the gap with centralized models. By seeking parameters in neighborhoods having uniform low loss, the model converges towards flatter minima and its generalization significantly improves in both homogeneous and heterogeneous scenarios. Empirical results demonstrate the effectiveness of those optimizers across a variety of benchmark vision datasets (e.g. CIFAR10/100, Landmarks-User-160k, IDDA) and tasks (large scale classification, semantic segmentation, domain generalization).