Title: FedMC: Federated Manifold Calibration
Primary area: alignment, fairness, safety, privacy, and societal considerations
Keywords: Federated Learning, Distribution Calibrations, Geometric Knowledge

Abstract: Data heterogeneity in Federated Learning (FL) leads to significant bias in local training. While recent efforts to introduce distributional statistics as priors have shown progress, they universally rely on a flawed global linearity assumption, failing to capture the nonlinear manifold structures prevalent in real-world data. This model-reality mismatch causes the calibration process to generate out-of-distribution (OOD) samples, which fundamentally misleads the model. To address this, we introduce a paradigm shift. We propose Federated Manifold Calibration (FedMC), a novel framework that learns and leverages the local, nonlinear geometry of data. FedMC employs local kernel PCA on the client side to learn fine-grained local geometries, and constructs a global "geometry dictionary" on the server side to aggregate and distribute this knowledge. Clients then utilize this dictionary to perform context-aware, on-manifold calibration. We validate our proposed method by integrating it with a wide range of existing FL algorithms. Experimental results show that by explicitly modeling nonlinear manifolds, FedMC consistently and significantly enhances the performance of these state-of-the-art methods across multiple benchmarks.