Row‐Wise Fusion Regularization: An Interpretable Personalized Federated Learning Framework in Large‐Scale Scenarios

ABSTRACT We study personalized federated learning for multivariate responses where client models are heterogeneous yet share variable‐level structure. Existing entry‐wise penalties ignore cross‐response dependence, while matrix‐wise fusion over‐couples clients. We propose a Sparse Row‐wise Fusion (SROF) regularizer that clusters row vectors across clients and induces within‐row sparsity, and we develop RowFed , a communication‐efficient federated algorithm that embeds SROF into a linearized ADMM framework with privacy‐preserving partial participation. Theoretically, we establish an oracle property for SROF—achieving correct variable‐level group recovery with asymptotic normality—and prove convergence of RowFed to a stationary solution. Under random client participation, the iterate gap contracts at a rate that improves with participation probability. Empirically, simulations in heterogeneous regimes show that RowFed consistently lowers estimation and prediction error and strengthens variable‐level cluster recovery over NonFed, FedAvg and a personalized matrix‐fusion baseline. A real‐data study further corroborates these gains while preserving interpretability. Together, our results position row‐wise fusion as an effective and transparent paradigm for large‐scale personalized federated multivariate learning, bridging the gap between entry‐wise and matrix‐wise formulations.