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

Andrea Moleri; Christian Internò; Markus Olhofer; Barbara Hammer; Ali Raza

cs.LGOct 24, 2026

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

Authors: Andrea Moleri, Christian Internò, Markus Olhofer, Barbara Hammer, Ali Raza

Organizations: Honda Research Institute Europe · University of Milan-Bicocca · Bielefeld University

Abstract

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.

Figures & tables

Panel of Figure 1 — Fig. 1: The Geodesic-SVDD Framework. (Top) Local clients utilize a Residual Spherical Encoder to map sparse tabular features onto the unit hypersphere $\mathbb{S}^{d-1}$ . We contrast our Geodesic Mixup (which maintains unit norm via SLERP) against Linear Mixup (which collapses the manifold norm). (Bottom) The architecture supports two protocols: privacy-preserving One-Shot aggregation via Product of Experts (PoE) and iterative Federated Averaging.

Fig. 2: Performance Profile (Covertype,

\alpha=0.01

). A radar chart comparison of Geodesic-SVDD against the federated baselines; centralized k-NN (IID) is shown for reference. Our method maintains balanced precision and recall, whereas Fed-XGB and FedAvg (SM) fall below

0.60

recall.

Fig. 3: Resilience to Non-IID Label Skew. Performance (AUC) across five benchmarks with increasing non-IID partition skew. Centralized references are trained on pooled IID data and drawn as flat lines.

Fig. 4: Critical Difference Diagram (Friedman–Nemenyi,

\alpha=0.05

). Average AUROC ranks over 20 scenarios (lower is better). Both Geodesic-SVDD variants rank in the top three; only Fed-XGB is significantly worse (

CD=2.01

Dataset	Method	IID (Uniform)					Dirichlet ( $\alpha=0.5$ ) [Mild]
Dataset	Method	AUC	Acc	Prec	Rec	F1	AUC	Acc	Prec	Rec	F1
Iris	Centralized SVDD	90.10 $\pm$ 11.0	82.70 $\pm$ 14.8	91.80 $\pm$ 13.7	83.20 $\pm$ 15.3	86.00 $\pm$ 12.3	– Centralized Baselines –
	Centralized k-NN	96.00 $\pm$ 4.00	88.00 $\pm$ 8.00	97.00 $\pm$ 4.00	87.00 $\pm$ 6.00	91.00 $\pm$ 6.00
	FedAvg (FE)	90.40 $\pm$ 10.1	82.00 $\pm$ 13.6	91.10 $\pm$ 8.40	82.70 $\pm$ 12.1	85.50 $\pm$ 11.6	91.30 $\pm$ 8.80	82.40 $\pm$ 13.6	93.40 $\pm$ 5.20	81.10 $\pm$ 15.4	84.90 $\pm$ 12.9
	FedAvg (No SM)	98.32 $\pm$ 1.85	93.33 $\pm$ 4.84	96.71 $\pm$ 2.37	93.15 $\pm$ 6.16	94.58 $\pm$ 4.21	98.20 $\pm$ 1.89	92.44 $\pm$ 5.29	96.74 $\pm$ 2.34	91.86 $\pm$ 6.74	93.73 $\pm$ 4.83
	FedAvg (SM)	96.84 $\pm$ 2.50	88.89 $\pm$ 6.45	95.31 $\pm$ 3.54	87.77 $\pm$ 6.34	90.91 $\pm$ 5.27	96.08 $\pm$ 2.85	87.56 $\pm$ 7.39	96.79 $\pm$ 2.41	84.42 $\pm$ 8.81	89.56 $\pm$ 6.22

TABLE I: Comparative Performance (Part I): IID and Mild Non-IID Scenarios. Mean

\pm

Std. Dev. (in %). Best federated result per column in bold , second best underlined ; centralized baselines are not ranked. Teal rows indicate our method.

Dataset	Method	Dirichlet ( $\alpha=0.1$ ) [Moderate]					Dirichlet ( $\alpha=0.01$ ) [Extreme]
Dataset	Method	AUC	Acc	Prec	Rec	F1	AUC	Acc	Prec	Rec	F1
Iris	Centralized SVDD	– Centralized Baselines –					– Centralized Baselines –
	Centralized k-NN
	FedAvg (FE)	90.70 $\pm$ 9.50	82.40 $\pm$ 13.3	91.90 $\pm$ 7.50	82.20 $\pm$ 12.9	85.00 $\pm$ 12.4	90.10 $\pm$ 10.4	82.90 $\pm$ 13.4	94.10 $\pm$ 5.70	81.60 $\pm$ 13.5	85.20 $\pm$ 12.5
	FedAvg (No SM)	98.32 $\pm$ 1.64	92.89 $\pm$ 4.69	96.27 $\pm$ 3.11	92.92 $\pm$ 4.57	94.34 $\pm$ 3.92	97.36 $\pm$ 2.91	90.89 $\pm$ 7.41	93.93 $\pm$ 5.77	92.53 $\pm$ 5.80	92.77 $\pm$ 6.16
	FedAvg (SM)	95.81 $\pm$ 3.29	87.78 $\pm$ 7.25	96.56 $\pm$ 2.47	85.15 $\pm$ 8.32	89.83 $\pm$ 5.93	96.30 $\pm$ 2.98	86.67 $\pm$ 8.02	96.52 $\pm$ 2.64	83.45 $\pm$ 9.37	88.78 $\pm$ 6.68

TABLE II: Comparative Performance (Part II): Moderate and Extreme Non-IID Scenarios. Same format as Table I : best federated result per column in bold , second best underlined .

Downstream Performance (Covertype, One-Shot)
Metric	Interpolation Method		Status
Metric	Linear (LERP)	Geodesic (SLERP)	Status
AUROC Score ( $\uparrow$ )	$0.920\pm 0.08$	$\mathbf{0.921\pm 0.08}$	Parity
Accuracy ( $\uparrow$ )	$0.851\pm 0.10$	$\mathbf{0.856\pm 0.10}$	Parity
F1-Score ( $\uparrow$ )	$0.880\pm 0.11$	$\mathbf{0.882\pm 0.12}$	Parity
Geometric Integrity & Stability

TABLE III: Comparison of Linear (LERP) vs. Geodesic (SLERP) .

\uparrow

Higher is better,

\downarrow

Lower is better.

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