# Widening the Network Mitigates the Impact of Data Heterogeneity on FedAvg

arXiv: https://arxiv.org/abs/2508.12576 · HTML: https://mlsanity.com/paper/2508.12576/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 36 references that are in the map.
- First posted on arXiv 18 Aug 2025.

## Builds on (most cited first, 28 of 28)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (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)
- [Model-Contrastive Federated Learning](https://mlsanity.com/paper/2103.16257/) (2021)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [Personalized Federated Learning with Moreau Envelopes](https://mlsanity.com/paper/2006.08848/) (2020)
- [FedBN: Federated Learning on Non-IID Features via Local Batch Normalization](https://mlsanity.com/paper/2102.07623/) (2021)
- [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)
- [In Search of the Real Inductive Bias: On the Role of Implicit Regularization in Deep Learning](https://mlsanity.com/paper/1412.6614/) (2014)
- [Client Selection in Federated Learning: Convergence Analysis and Power-of-Choice Selection Strategies](https://mlsanity.com/paper/2010.01243/) (2020)
- [FedPD: A Federated Learning Framework with Optimal Rates and Adaptivity to Non-IID Data](https://mlsanity.com/paper/2005.11418/) (2020)
- [Towards Understanding the Role of Over-Parametrization in Generalization of Neural Networks](https://mlsanity.com/paper/1805.12076/) (2018)
- [Stochastic Controlled Averaging for Federated Learning with Communication Compression](https://mlsanity.com/paper/2308.08165/) (2023)
- [First Analysis of Local GD on Heterogeneous Data](https://mlsanity.com/paper/1909.04715/) (2019)
- [Active Federated Learning](https://mlsanity.com/paper/1909.12641/) (2019)
- [Fed-CBS: A Heterogeneity-Aware Client Sampling Mechanism for Federated Learning via Class-Imbalance Reduction](https://mlsanity.com/paper/2209.15245/) (2022)
- [TCT: Convexifying Federated Learning using Bootstrapped Neural Tangent Kernels](https://mlsanity.com/paper/2207.06343/) (2022)
- [Fed-ensemble: Improving Generalization through Model Ensembling in Federated Learning](https://mlsanity.com/paper/2107.10663/) (2021)
- [The asymptotic spectrum of the Hessian of DNN throughout training](https://mlsanity.com/paper/1910.02875/) (2019)
- [The Effect of Network Width on Stochastic Gradient Descent and Generalization: an Empirical Study](https://mlsanity.com/paper/1905.03776/) (2019)
- [Neural Tangent Kernel Empowered Federated Learning](https://mlsanity.com/paper/2110.03681/) (2021)
- [Local SGD Optimizes Overparameterized Neural Networks in Polynomial Time](https://mlsanity.com/paper/2107.10868/) (2021)

## Built on by (most cited first, 2 of 2)

- [FedSLoP: Memory-Efficient Federated Learning with Low-Rank Gradient Projection](https://mlsanity.com/paper/2604.24012/) (2026)
- [Subspace Optimization for Efficient Federated Learning under Heterogeneous Data](https://mlsanity.com/paper/2604.25467/) (2026)

## Abstract (arXiv)

Federated learning (FL) enables decentralized clients to train a model collaboratively without sharing local data. A key distinction between FL and centralized learning is that clients' data are non-independent and identically distributed, which poses significant challenges in training a global model that generalizes well across heterogeneous local data distributions. In this paper, we analyze the convergence of overparameterized FedAvg with gradient descent (GD). We prove that the impact of data heterogeneity diminishes as the width of neural networks increases, ultimately vanishing when the width approaches infinity. In the infinite-width regime, we further prove that both the global and local models in FedAvg behave as linear models, and that FedAvg achieves the same generalization performance as centralized learning with the same number of GD iterations. Extensive experiments validate our theoretical findings across various network architectures, loss functions, and optimization methods.