# Row-wise Fusion Regularization: An Interpretable Personalized Federated Learning Framework in Large-Scale Scenarios

arXiv: https://arxiv.org/abs/2510.14413 · HTML: https://mlsanity.com/paper/2510.14413/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 20 references that are in the map.
- First posted on arXiv 16 Oct 2025.

## Builds on (most cited first, 7 of 7)

- [Federated Learning with Personalization Layers](https://mlsanity.com/paper/1912.00818/) (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)
- [Personalized Cross-Silo Federated Learning on Non-IID Data](https://mlsanity.com/paper/2007.03797/) (2020)
- [A concave pairwise fusion approach to subgroup analysis](https://mlsanity.com/paper/1508.07045/) (2015)
- [Tuning parameter selection in high dimensional penalized likelihood](https://mlsanity.com/paper/1605.03321/) (2016)
- [SOFAR: large-scale association network learning](https://mlsanity.com/paper/1704.08349/) (2017)

## Abstract (arXiv)

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.