# A Large-Dimensional Analysis of Least-Squares Federated Learning via Generalized Total Variation Minimization

arXiv: https://arxiv.org/abs/2610.20075 · HTML: https://mlsanity.com/paper/2610.20075/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 40 references that are in the map.
- First posted on arXiv 14 Oct 2026.

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

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Multi-Task Learning](https://mlsanity.com/paper/1705.10467/) (2017)
- [Ditto: Fair and Robust Federated Learning Through Personalization](https://mlsanity.com/paper/2012.04221/) (2020)
- [Personalized Federated Learning with Moreau Envelopes](https://mlsanity.com/paper/2006.08848/) (2020)
- [Exploiting Shared Representations for Personalized Federated Learning](https://mlsanity.com/paper/2102.07078/) (2021)
- [Surprises in High-Dimensional Ridgeless Least Squares Interpolation](https://mlsanity.com/paper/1903.08560/) (2019)
- [An Efficient Framework for Clustered Federated Learning](https://mlsanity.com/paper/2006.04088/) (2020)
- [Clustered Federated Learning: Model-Agnostic Distributed Multi-Task Optimization under Privacy Constraints](https://mlsanity.com/paper/1910.01991/) (2019)
- [Can Decentralized Algorithms Outperform Centralized Algorithms? A Case Study for Decentralized Parallel Stochastic Gradient Descent](https://mlsanity.com/paper/1705.09056/) (2017)
- [Towards Personalized Federated Learning](https://mlsanity.com/paper/2103.00710/) (2021)
- [A Unified Theory of Decentralized SGD with Changing Topology and Local Updates](https://mlsanity.com/paper/2003.10422/) (2020)
- [Three Approaches for Personalization with Applications to Federated Learning](https://mlsanity.com/paper/2002.10619/) (2020)
- [Federated Learning of a Mixture of Global and Local Models](https://mlsanity.com/paper/2002.05516/) (2020)
- [Federated Multi-Task Learning under a Mixture of Distributions](https://mlsanity.com/paper/2108.10252/) (2021)
- [High-Dimensional Asymptotics of Prediction: Ridge Regression and Classification](https://mlsanity.com/paper/1507.03003/) (2015)
- [Lower Bounds and Optimal Algorithms for Personalized Federated Learning](https://mlsanity.com/paper/2010.02372/) (2020)
- [Decentralized Collaborative Learning of Personalized Models over Networks](https://mlsanity.com/paper/1610.05202/) (2016)
- [Learning Gaussian Mixtures with Generalised Linear Models: Precise Asymptotics in High-dimensions](https://mlsanity.com/paper/2106.03791/) (2021)
- [Network Lasso: Clustering and Optimization in Large Graphs](https://mlsanity.com/paper/1507.00280/) (2015)
- [Fully Decentralized Joint Learning of Personalized Models and Collaboration Graphs](https://mlsanity.com/paper/1901.08460/) (2019)
- [On the Optimality of Averaging in Distributed Statistical Learning](https://mlsanity.com/paper/1407.2724/) (2014)
- [High Dimensional Classification via Regularized and Unregularized Empirical Risk Minimization: Precise Error and Optimal Loss](https://mlsanity.com/paper/1905.13742/) (2019)
- [Federated Asymptotics: a model to compare federated learning algorithms](https://mlsanity.com/paper/2108.07313/) (2021)
- [A Large Dimensional Analysis of Least Squares Support Vector Machines](https://mlsanity.com/paper/1701.02967/) (2017)
- [A Fixed-Point of View on Gradient Methods for Big Data](https://mlsanity.com/paper/1706.09880/) (2017)
- [Federated Learning: From Theory to Practice](https://mlsanity.com/paper/2505.19183/) (2025)

## Abstract (arXiv)

Federated learning over decentralized networks inherently trades off the suppression of local finite-sample noise through collaboration against the bias that collaboration introduces between heterogeneous nodes. We study this tension by performing a large-dimensional analysis of Generalized Total Variation Minimization with least-squares models. Using tools from random matrix theory, we show that Lipschitz observations of the global GTVMin solution concentrate in large dimensions, universally for any underlying network structure. We provide exact analytic expressions for the asymptotically precise performance under both i.i.d. and non-i.i.d. Gaussian mixture distributions on a fixed network. For the latter, these expressions quantify how regularization balances local adaptation against collaboration. Our theoretical results are confirmed by experiments on synthetic and real-world data.