Personalized Federated Learning with Residual Fisher Information for Medical Image Segmentation

Personalized Federated Learning (PFL) aims to train customized models for clients with highly heterogeneous data distributions while preserving data privacy. Existing approaches often rely on heuristics like clustering or model interpolation, which lack principled mechanisms for balancing heterogeneous client objectives. Serving $M$ clients with distinct data distributions is inherently a multi-objective optimization problem, where achieving optimal personalization ideally requires $M$ distinct models on the Pareto front. However, maintaining $M$ separate models poses significant scalability challenges in federated settings with hundreds or thousands of clients. To address this challenge, we reformulate PFL as a few-for-many optimization problem that maintains only $K$ shared server models ($K \ll M$) to collectively serve all $M$ clients. We prove that this framework achieves near-optimal personalization: the approximation error diminishes as $K$ increases and each client's model converges to each client's optimum as data grows. Building on this reformulation, we propose FedFew, a practical algorithm that jointly optimizes the $K$ server models through efficient gradient-based updates. Unlike clustering-based approaches that require manual client partitioning or interpolation-based methods that demand careful hyperparameter tuning, FedFew automatically discovers the optimal model diversity through its optimization process. Experiments across vision, NLP, and real-world medical imaging datasets demonstrate that FedFew, with just 3 models, consistently outperforms other state-of-the-art approaches. Code is available at https://github.com/pgg3/FedFew.

Federated learning enables collaborative model training without sharing raw data, but its performance can degrade substantially under heterogeneous client data distributions. A single global model often cannot satisfy diverse client requirements, so personalized federated learning has therefore been explored to improve client specific performance while preserving global generalization. Existing PFL methods often face a fundamental tradeoff in which stronger global sharing can undermine local specialization, whereas stronger local adaptation can lead to overfitting under limited data, label imbalance, and missing class scenarios. In this work, we propose PGFedSplit, a personalized federated learning framework that improves both personalization and global generalization under severe client heterogeneity. PGFedSplit adopts a split architecture and performs adaptive aggregation scheduling tailored to the roles of different model components, enabling stable knowledge sharing while maintaining client specific adaptation. Each client further leverages a mixture of locally extracted representations and synthetic representations generated from server side Gaussian statistics, improving robustness under label imbalance and missing class conditions. Extensive experiments on Fashion MNIST, CIFAR 10, CIFAR 100, and Tiny ImageNet demonstrate consistent improvements over state of the art PFL methods, with stable convergence and superior personalization in highly heterogeneous settings.

Federated learning enables collaborative model training across medical institutions without sharing raw data, but its performance is often limited by domain heterogeneity across clients. Existing approaches to address this challenge fall into two main paradigms: model-side personalization, which adapts model parameters to each client, and data-side harmonization, which reduces inter-client variation at the input level. Despite their widespread use, these strategies have not been systematically compared. In this work, we conduct a comprehensive study across six medical imaging settings-colon polyp, skin lesion, and breast tumor segmentation, and tuberculosis CXR, brain tumor, and breast tumor classification-covering diverse types of domain shift. We evaluate a broad set of state-of-the-art harmonization and personalization methods under a unified framework. Our results reveal a conditional trade-off driven by the nature of heterogeneity: harmonization is more effective when variation is primarily appearance-based (e.g., CXR classification), while personalization performs better when differences are structural (e.g., colon polyp segmentation). When inter-client variation is limited, both strategies perform similarly. These findings demonstrate that the effectiveness of adaptation in federated medical imaging depends on the type and magnitude of domain shift rather than the strategy alone. We provide practical guidelines for selecting between harmonization and personalization and highlight directions for future hybrid approaches that combine both paradigms. Code is available at https://github.com/ChamaniS/WhenToAdapt.