Geometrically Regularized Transfer Learning with On-Manifold and Off-Manifold Perturbation

Hana Satou; Alan Mitkiy; Emma Collins; Finn Kingston

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arXiv · 2505.15191

Geometrically Regularized Transfer Learning with On-Manifold and Off-Manifold Perturbation

Hana Satou·Alan Mitkiy·Emma Collins·Finn Kingston

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Abstract

Transfer learning under domain shift remains a fundamental challenge due to the divergence between source and target data manifolds. In this paper, we propose MAADA (Manifold-Aware Adversarial Data Augmentation), a novel framework that decomposes adversarial perturbations into on-manifold and off-manifold components to simultaneously capture semantic variation and model brittleness. We theoretically demonstrate that enforcing on-manifold consistency reduces hypothesis complexity and improves generalization, while off-manifold regularization smooths decision boundaries in low-density regions. Moreover, we introduce a geometry-aware alignment loss that minimizes geodesic discrepancy between source and target manifolds. Experiments on DomainNet, VisDA, and Office-Home show that MAADA consistently outperforms existing adversarial and adaptation methods in both unsupervised and few-shot settings, demonstrating superior structural robustness and cross-domain generalization.

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Hana Satou, Alan Mitkiy, Emma Collins, Finn Kingston. 2025-05-21. Geometrically Regularized Transfer Learning with On-Manifold and Off-Manifold Perturbation. https://arxiv.org/abs/2505.15191

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