Federated Learning with Energy-Based Structured Probabilistic Inference

Federated learning usually aggregates client updates using dataset size or gradient-level criteria, while overlooking internal signals about how each client model is organizing its input space during training. We introduce FedOUI, a simple aggregation rule based on the Overfitting-Underfitting Indicator (OUI), an activation-based and label-free metric. Each participating client sends its local update together with a OUI value computed on a fixed probe batch, and the server estimates the round-wise OUI distribution to assign lower weights to structurally atypical clients through a smooth reweighting rule. We evaluate FedOUI on CIFAR-10 under strong non-IID partitioning and noisy-client conditions, comparing it with FedAvg, FedProx, and a gradient-alignment baseline. The clearest gains appear under strong heterogeneity, where OUI-based weighting improves aggregation quality while remaining lightweight and interpretable. These results show that internal activation structure can provide useful information for federated aggregation beyond client size and gradient geometry.

The aggregation of conflicting client updates remains a fundamental bottleneck in federated learning (FL) under heterogeneous data distributions. Naive averaging can produce a global update that improves the global objective while conflicting with specific clients, causing degradation for those clients. In this work, we propose CRAFT (Conflict-Resolved Aggregation for Federated Training), a new aggregation framework that treats the global update as a geometric correction problem. We formulate aggregation as finding the update closest to a reference direction while satisfying conflict-free alignment constraints. We derive a closed-form expression for the constrained optimization problem, avoiding the computational overhead of iterative solvers. Furthermore, we use a layer-wise adaptation to address conflicts at varying feature granularities. We provide a theoretical analysis showing that CRAFT promotes a common-descent structure and mitigates conflicts through its projection geometry. Extensive experiments on heterogeneous benchmarks demonstrate that CRAFT improves the accuracy of the global model while reducing performance disparity across clients compared with state-of-the-art baselines. The source code for CRAFT is available at https://github.com/tum-pbs/CRAFT.

Federated Learning (FL) facilitates collaborative model training across decentralized clients while preserving data privacy by avoiding raw data exchange. Despite its potential, FL performance is often compromised by data heterogeneity across clients. To address this, Clustered Federated Learning (CFL) groups clients with similar data distributions to improve model performance, but constrained by intra-cluster heterogeneity. Conversely, Personalized Federated Learning (PFL) tailors models to individual clients, but usually neglects the underlying structural similarities among clients. In this work, we investigate a probabilistic mixture (PM) scenario, where each client's local data distribution is modeled as a convex combination of several shared inherent distributions. To effectively model this structure, we propose FedGMI, a framework that utilizes Variational Autoencoders (VAEs) as generative density estimators to represent these inherent distributions and infer the mixture components of clients' local data distributions. This approach enables structured personalization without sacrificing the benefits of collaborative learning. Extensive experiments demonstrate that FedGMI effectively characterizes and discriminate the inherent distributions, as well as accurately estimates mixture proportions. Furthermore, FedGMI maintains robust performance even under communication cost constraints.