FedCADC: Curvature-Aware Direction Consistency for Globally Flat Federated Learning

Despite the success of federated learning (FL), improving global generalization under heterogeneous client data remains challenging. To improve the generalization of FL, recent methods seek flatter minima by applying sharpness-aware optimization during local training. However, differences in local curvature and update directions can make locally flat solutions inconsistent after aggregation, such that local flatness does not necessarily translate into global flatness. To address this issue, we propose Federated Learning with Curvature-Aware Direction Consistency (FedCADC). FedCADC uses a curvature-aware constraint to suppress local updates toward perturbation-sensitive regions and a direction-consistency constraint to align local trajectories with the global optimization trend. Their weights are adaptively adjusted according to the optimization geometry of each mini-batch. Our theoretical analysis characterizes the optimization, generalization, and flatness discrepancy of FedCADC. Experiments on CIFAR-10 and CIFAR-100 demonstrate that FedCADC achieves higher accuracy in most heterogeneous settings and generally finds flatter global solutions than recent advanced FL methods.