A Large-Dimensional Analysis of Least-Squares Federated Learning via Generalized Total Variation Minimization
Abstract
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.
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BibTeX
@misc{schnoor2026largedimensional,
title = {{A Large-Dimensional Analysis of Least-Squares Federated Learning via Generalized Total Variation Minimization}},
author = {Ekkehard Schnoor and Malik Tiomoko and Alexander Jung},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20075},
eprint = {2610.20075},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20075},
}
RIS
TY - UNPB
TI - A Large-Dimensional Analysis of Least-Squares Federated Learning via Generalized Total Variation Minimization
AU - Ekkehard Schnoor
AU - Malik Tiomoko
AU - Alexander Jung
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20075
UR - https://arxiv.org/abs/2610.20075
AB - 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.
ER -