Geodesic-SVDD Latent Mixup for One-Shot Distributed Tabular Learning

Distributed Learning on structured data is a key and widely adopted approach in privacy-sensitive sectors, ranging from financial fraud prevention to federated healthcare diagnostics. While Gradient Boosted Decision Trees are widely used in centralized settings due to their efficiency, they are incompatible with standard gradient-based federated learning protocols because of their non-differentiability. Conversely, standard deep classifiers that are amenable to federated optimization often suffer from catastrophic forgetting under label distribution skew. In this work, to address these gaps we propose Geodesic-SVDD, a framework for Distributed Spherical Prototype Learning that recasts each client's task as one-class density estimation on the hypersphere, so that local models can be aggregated as probabilistic manifolds in a single round. Specifically, for each client, we employ a Residual Spherical Encoder and Geodesic Latent Mixup that enforces strict hyperspherical constraints ($\|φ(x)\| \equiv 1$), preventing the manifold collapse observed in linear approximations. Furthermore, leveraging this insight, we propose a novel One-Shot "Product of Experts" protocol that enables privacy-preserving aggregation without iterative synchronization. Finally, we mechanistically analyze the trade-off between interpolation strategies, demonstrating that while linear mixup offers an enticing computational shortcut, it destabilizes optimization gradients by orders of magnitude ($10^9\times$). Across five tabular benchmarks and four levels of label skew, Geodesic-SVDD attains the highest mean AUROC among seven federated methods, outperforms federated tree ensembles by up to 21 AUROC points on Covertype, and its One-Shot variant matches centralized Deep SVDD under IID and mild skew with a single communication round.