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

TL;DR

GAMA introduces a geometry-aware framework for manifold alignment in domain adaptation, utilizing structured adversarial perturbations guided by geometric information to improve robustness and cross-domain alignment.

Contribution

It presents a novel structured adversarial perturbation approach that explicitly aligns manifolds using geometric information, enhancing robustness and generalization in domain adaptation.

Findings

GAMA outperforms existing methods on DomainNet, VisDA, and Office-Home datasets.

It improves robustness to off-manifold deviations.

It achieves superior manifold alignment and generalization in unsupervised and few-shot settings.

Abstract

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.