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

TL;DR

GAMA tackles domain adaptation under deep geometric misalignment by marrying structured, tangent-space perturbations with explicit geodesic-based manifold alignment. It introduces a four-part training objective that enforces on-manifold consistency, off-manifold robustness, and cross-domain geometric alignment, guided by a manifold-geometry model and PCA-based tangent estimation. Theoretical analysis shows tightened generalization bounds via geometry-aware regularization and reduced manifold divergence, while experiments on DomainNet, VisDA-2017, and Office-Home demonstrate superior accuracy, robustness, and alignment compared with strong baselines in both unsupervised and few-shot settings. This geometry-centric framework offers robust, transferable representations for real-world domain shifts and lays groundwork for extensions to multimodal and SciML applications.

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.