Unsupervised Domain Adaptation for Multitask Image Analysis in Realistic Context with Extreme Label Shift; Application to the CTAO first Large Sized Telescope

Test-time adaptation (TTA) aims to align a model to shifting test domains using only unlabeled streaming data. Most existing methods implicitly infer a single global domain distribution, ignoring the multidimensional and sample-specific nature of real-world domain shifts, leading to fragile adaptation. We propose DOME, an effective domain encoder that explicitly models each sample's domain in a zero-shot manner. DOME leverages vision-language pretraining to extract dense, continuous representations, parameterizes domains as distributional variables, and introduces a momentum-updated sparse domain bank for disentangled supervision. By injecting these explicit domain cues into downstream models, even a basic entropy-minimization TTA strategy achieves state-of-the-art performance across ImageNet-C, ImageNet-R, and ImageNet-Sketch, outperforming complex TTA approaches. Our results demonstrate that robust adaptation stems not from intricate adaptation algorithms, but from explicit, structured domain representation.

Domain shift remains a major obstacle to the reliable deployment of machine learning models in high-stakes environments such as healthcare. While Domain adaptation aims to mitigate these effects, existing approaches suffer from limited expressiveness of latent representations and a reliance on handcrafted, static augmentations. In this work, we address these limitations by proposing a novel deep learning architecture for Unsupervised Domain Adaptation (UDA), specifically optimized for medical image segmentation. Our framework, ADualVUOT, integrates a dual-encoder Variational Autoencoder (VAE) with Continuous Normalizing Flows (CNFs) to increase modeling flexibility and posterior expressiveness. To achieve domain alignment, we leverage Unbalanced Optimal Transport (UOT) through the Gaussian-Gromov-Wasserstein (GGW) distance, which handles structural and topological discrepancies between domains. Furthermore, we incorporate an adversarial augmentation scheme to synthesize worst-case compositions, thus enhancing model robustness. Extensive experiments on medical imaging benchmarks show significant gains over prior OT-based approaches.

Semi-supervised domain adaptation (SSDA) seeks to achieve accurate predictions in a target domain with limited labeled target data by exploiting abundant source and unlabeled target data. We study this problem under structural causal models (SCMs), which provide a statistical framework to describe distribution shifts between source and target domains as interventions in the data-generating process rather than ad hoc changes in model parameters. The central phenomenon is that, under low-dimensional interventions, source and unlabeled target data can help identify the high-dimensional shared structure, leaving only a low-dimensional target-specific correction to be learned from limited labeled target data. We formalize this principle for three canonical intervention models and propose the corresponding SSDA methods FT-DIP, FT-OLS-Src and FT-CIP. Under each intervention model, we demonstrate how extending an unsupervised domain adaptation (UDA) method to SSDA can achieve minimax-optimal target performance with limited target labels, with the labeled-target sample complexity scaling with the intervention dimension rather than the ambient dimension. When the distribution shift is underspecified, we propose the Multi-Adaptive-Start Fine-Tuning (MASFT) algorithm, which fine-tunes from multiple adaptive starts and selects among them using a small target validation set, incurring only logarithmic overhead in the number of starts. We validate the effectiveness of our proposed methods through simulated and real data experiments.