Understanding Head Geometry and Dynamics in Federated Regression through a Natural Solution Selection Rule: An Unconstrained Feature Model Analysis

Excerpt

arXiv:2609.39464v1 Announce Type: new Abstract: In federated averaging, local objectives can admit multiple optimal heads, making the aggregate depend on which heads clients return. We study this ambiguity in federated multivariate regression with private backbones and a shared linear head, using an unconstrained feature model (UFM) that treats training-sample features as free variables. We introduce a natural selection rule: each client returns the optimal head closest to the broadcast head. We