A Large-Dimensional Analysis of Least-Squares Federated Learning via Generalized Total Variation Minimization
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Institution: Aalto University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222223671