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.

On the Mechanisms of Adversarial Data Augmentation for Robust and Adaptive Transfer Learning

Transfer learning across domains with distribution shift remains a fundamental challenge in building robust and adaptable machine learning systems. While adversarial perturbations are traditionally viewed as threats that expose model vulnerabilities, recent studies suggest that they can also serve as constructive tools for data augmentation. In this work, we systematically investigate the role of adversarial data augmentation (ADA) in enhancing both robustness and adaptivity in transfer learning settings. We analyze how adversarial examples, when used strategically during training, improve domain generalization by enriching decision boundaries and reducing overfitting to source-domain-specific features. We further propose a unified framework that integrates ADA with consistency regularization and domain-invariant representation learning. Extensive experiments across multiple benchmark datasets -- including VisDA, DomainNet, and Office-Home -- demonstrate that our method consistently improves target-domain performance under both unsupervised and few-shot domain adaptation settings. Our results highlight a constructive perspective of adversarial learning, transforming perturbation from a destructive attack into a regularizing force for cross-domain transferability.

Fusing Physics-Driven Strategies and Cross-Modal Adversarial Learning: Toward Multi-Domain Applications

The convergence of cross-modal adversarial learning and physics-driven methods represents a cutting-edge direction for tackling challenges in complex multi-modal tasks and scientific computing. This review focuses on systematically analyzing how these two approaches can be synergistically integrated to enhance performance and robustness across diverse application domains. By addressing key obstacles such as modality discrepancies, limited data availability, and insufficient model robustness, this paper highlights the role of physics-based optimization frameworks in facilitating efficient and interpretable adversarial perturbation generation. The review also explores significant advancements in cross-modal adversarial learning, including applications in tasks such as image cross-modal retrieval (e.g., infrared and RGB matching), scientific computing (e.g., solving partial differential equations), and optimization under physical consistency constraints in vision systems. By examining theoretical foundations and experimental outcomes, this study demonstrates the potential of combining these approaches to handle complex scenarios and improve the security of multi-modal systems. Finally, we outline future directions, proposing a novel framework that unifies physical principles with adversarial optimization, providing a pathway for researchers to develop robust and adaptable cross-modal learning methods with both theoretical and practical significance.