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

arXiv: https://arxiv.org/abs/2505.15191 · HTML: https://mlsanity.com/paper/2505.15191/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 45 references that are in the map.
- First posted on arXiv 21 May 2025.

## Builds on (most cited first, 25 of 25)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Adversarial Training for Free!](https://mlsanity.com/paper/1904.12843/) (2019)
- [MACE: Mass Concept Erasure in Diffusion Models](https://mlsanity.com/paper/2403.06135/) (2024)
- [TF-ICON: Diffusion-Based Training-Free Cross-Domain Image Composition](https://mlsanity.com/paper/2307.12493/) (2023)
- [Disentangling Adversarial Robustness and Generalization](https://mlsanity.com/paper/1812.00740/) (2018)
- [ODTrack: Online Dense Temporal Token Learning for Visual Tracking](https://mlsanity.com/paper/2401.01686/) (2024)
- [Robust Watermarking Using Generative Priors Against Image Editing: From Benchmarking to Advances](https://mlsanity.com/paper/2410.18775/) (2024)
- [EraseAnything: Enabling Concept Erasure in Rectified Flow Transformers](https://mlsanity.com/paper/2412.20413/) (2024)
- [Towards Unified Token Learning for Vision-Language Tracking](https://mlsanity.com/paper/2308.14103/) (2023)
- [Set You Straight: Auto-Steering Denoising Trajectories to Sidestep Unwanted Concepts](https://mlsanity.com/paper/2504.12782/) (2025)
- [Person Re-identification Method Based on Color Attack and Joint Defence](https://mlsanity.com/paper/2111.09571/) (2021)
- [RainMamba: Enhanced Locality Learning with State Space Models for Video Deraining](https://mlsanity.com/paper/2407.21773/) (2024)
- [Cross-Modality Perturbation Synergy Attack for Person Re-identification](https://mlsanity.com/paper/2401.10090/) (2024)
- [Eliminate Deviation with Deviation for Data Augmentation and a General Multi-modal Data Learning Method](https://mlsanity.com/paper/2101.08533/) (2021)
- [Exploring Color Invariance through Image-Level Ensemble Learning](https://mlsanity.com/paper/2401.10512/) (2024)
- [Beyond Augmentation: Empowering Model Robustness under Extreme Capture Environments](https://mlsanity.com/paper/2407.13640/) (2024)
- [Exploiting Multi-Label Correlation in Label Distribution Learning](https://mlsanity.com/paper/2308.01742/) (2023)
- [Beyond Dropout: Robust Convolutional Neural Networks Based on Local Feature Masking](https://mlsanity.com/paper/2407.13646/) (2024)
- [Adversarial Learning for Neural PDE Solvers with Sparse Data](https://mlsanity.com/paper/2409.02431/) (2024)
- [Cross-Modality Attack Boosted by Gradient-Evolutionary Multiform Optimization](https://mlsanity.com/paper/2409.17977/) (2024)
- [Inaccurate Label Distribution Learning](https://mlsanity.com/paper/2302.13000/) (2023)
- [Cross-Task Attack: A Self-Supervision Generative Framework Based on Attention Shift](https://mlsanity.com/paper/2407.13700/) (2024)
- [Label Distribution Learning with Biased Annotations by Learning Multi-Label Representation](https://mlsanity.com/paper/2502.01170/) (2025)

## Built on by (most cited first, 1 of 1)

- [Manifold-Constrained Adversarial Training for Long-Tailed Robustness via Geometric Alignment](https://mlsanity.com/paper/2605.02183/) (2026)

## Abstract (arXiv)

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.