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

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.

GAMA++: Disentangled Geometric Alignment with Adaptive Contrastive Perturbation for Reliable Domain Transfer

Despite progress in geometry-aware domain adaptation, current methods such as GAMA still suffer from two unresolved issues: (1) insufficient disentanglement of task-relevant and task-irrelevant manifold dimensions, and (2) rigid perturbation schemes that ignore per-class alignment asymmetries. To address this, we propose GAMA++, a novel framework that introduces (i) latent space disentanglement to isolate label-consistent manifold directions from nuisance factors, and (ii) an adaptive contrastive perturbation strategy that tailors both on- and off-manifold exploration to class-specific manifold curvature and alignment discrepancy. We further propose a cross-domain contrastive consistency loss that encourages local semantic clusters to align while preserving intra-domain diversity. Our method achieves state-of-the-art results on DomainNet, Office-Home, and VisDA benchmarks under both standard and few-shot settings, with notable improvements in class-level alignment fidelity and boundary robustness. GAMA++ sets a new standard for semantic geometry alignment in transfer learning.

GAMA: Geometry-Aware Manifold Alignment via Structured Adversarial Perturbations for Robust Domain Adaptation

Domain adaptation remains a challenge when there is significant manifold discrepancy between source and target domains. Although recent methods leverage manifold-aware adversarial perturbations to perform data augmentation, they often neglect precise manifold alignment and systematic exploration of structured perturbations. To address this, we propose GAMA (Geometry-Aware Manifold Alignment), a structured framework that achieves explicit manifold alignment via adversarial perturbation guided by geometric information. GAMA systematically employs tangent space exploration and manifold-constrained adversarial optimization, simultaneously enhancing semantic consistency, robustness to off-manifold deviations, and cross-domain alignment. Theoretical analysis shows that GAMA tightens the generalization bound via structured regularization and explicit alignment. Empirical results on DomainNet, VisDA, and Office-Home demonstrate that GAMA consistently outperforms existing adversarial and adaptation methods in both unsupervised and few-shot settings, exhibiting superior robustness, generalization, and manifold alignment capability.