Personalized federated learning, Row-wise fusion regularization, Multivariate modeling, Sparse estimation

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.

SD-GS: Structured Deformable 3D Gaussians for Efficient Dynamic Scene Reconstruction

Current 4D Gaussian frameworks for dynamic scene reconstruction deliver impressive visual fidelity and rendering speed, however, the inherent trade-off between storage costs and the ability to characterize complex physical motions significantly limits the practical application of these methods. To tackle these problems, we propose SD-GS, a compact and efficient dynamic Gaussian splatting framework for complex dynamic scene reconstruction, featuring two key contributions. First, we introduce a deformable anchor grid, a hierarchical and memory-efficient scene representation where each anchor point derives multiple 3D Gaussians in its local spatiotemporal region and serves as the geometric backbone of the 3D scene. Second, to enhance modeling capability for complex motions, we present a deformation-aware densification strategy that adaptively grows anchors in under-reconstructed high-dynamic regions while reducing redundancy in static areas, achieving superior visual quality with fewer anchors. Experimental results demonstrate that, compared to state-of-the-art methods, SD-GS achieves an average of 60\% reduction in model size and an average of 100\% improvement in FPS, significantly enhancing computational efficiency while maintaining or even surpassing visual quality.