# Mode Connectivity and Data Heterogeneity of Federated Learning

arXiv: https://arxiv.org/abs/2309.16923 · HTML: https://mlsanity.com/paper/2309.16923/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 35 references that are in the map.
- First posted on arXiv 29 Sep 2023.

## Builds on (most cited first, 21 of 21)

- [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)
- [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 with Non-IID Data](https://mlsanity.com/paper/1806.00582/) (2018)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [A Mean Field View of the Landscape of Two-Layers Neural Networks](https://mlsanity.com/paper/1804.06561/) (2018)
- [Bayesian Nonparametric Federated Learning of Neural Networks](https://mlsanity.com/paper/1905.12022/) (2019)
- [Essentially No Barriers in Neural Network Energy Landscape](https://mlsanity.com/paper/1803.00885/) (2018)
- [The Role of Permutation Invariance in Linear Mode Connectivity of Neural Networks](https://mlsanity.com/paper/2110.06296/) (2021)
- [No Fear of Heterogeneity: Classifier Calibration for Federated Learning with Non-IID Data](https://mlsanity.com/paper/2106.05001/) (2021)
- [Mean-field theory of two-layers neural networks: dimension-free bounds and kernel limit](https://mlsanity.com/paper/1902.06015/) (2019)
- [Topology and Geometry of Half-Rectified Network Optimization](https://mlsanity.com/paper/1611.01540/) (2016)
- [A Rigorous Framework for the Mean Field Limit of Multilayer Neural Networks](https://mlsanity.com/paper/2001.11443/) (2020)
- [Explaining Landscape Connectivity of Low-cost Solutions for Multilayer Nets](https://mlsanity.com/paper/1906.06247/) (2019)
- [FedFA: Federated Learning with Feature Anchors to Align Features and Classifiers for Heterogeneous Data](https://mlsanity.com/paper/2211.09299/) (2022)
- [Landscape Connectivity and Dropout Stability of SGD Solutions for Over-parameterized Neural Networks](https://mlsanity.com/paper/1912.10095/) (2019)
- [A Survey of What to Share in Federated Learning: Perspectives on Model Utility, Privacy Leakage, and Communication Efficiency](https://mlsanity.com/paper/2307.10655/) (2023)
- [Understanding and Improving Model Averaging in Federated Learning on Heterogeneous Data](https://mlsanity.com/paper/2305.07845/) (2023)

## Built on by (most cited first, 3 of 3)

- [Proving Linear Mode Connectivity of Neural Networks via Optimal Transport](https://mlsanity.com/paper/2310.19103/) (2023)
- [Aggregation on Learnable Manifolds for Asynchronous Federated Optimization](https://mlsanity.com/paper/2503.14396/) (2025)
- [FedGuCci: Making Local Models More Connected in Landscape for Federated Learning](https://mlsanity.com/paper/2402.18949/) (2024)

## Abstract (arXiv)

Federated learning (FL) enables multiple clients to train a model while keeping their data private collaboratively. Previous studies have shown that data heterogeneity between clients leads to drifts across client updates. However, there are few studies on the relationship between client and global modes, making it unclear where these updates end up drifting. We perform empirical and theoretical studies on this relationship by utilizing mode connectivity, which measures performance change (i.e., connectivity) along parametric paths between different modes. Empirically, reducing data heterogeneity makes the connectivity on different paths more similar, forming more low-error overlaps between client and global modes. We also find that a barrier to connectivity occurs when linearly connecting two global modes, while it disappears with considering non-linear mode connectivity. Theoretically, we establish a quantitative bound on the global-mode connectivity using mean-field theory or dropout stability. The bound demonstrates that the connectivity improves when reducing data heterogeneity and widening trained models. Numerical results further corroborate our analytical findings.