When few labeled target data suffice: a theory of semi-supervised domain adaptation via fine-tuning from multiple adaptive starts
Authors: Wooseok Ha, Yuansi Chen
Organizations: Department of Mathematical Sciences, KAIST · Department of Mathematics, ETH Zürich
Abstract
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.
Source-free domain adaptation (SFDA) adapts a source-trained model to an unlabeled target domain without source data, a practical setting under privacy or storage constraints. Yet its self-generated supervision can reinforce source bias under substantial domain shifts. Pretrained vision-language models (VLMs) offer complementary semantic knowledge, but the relative reliability of the source model and VLM varies across target samples. Existing cross-model guidance does not explicitly account for this variation and may overwrite valid source-derived evidence under conflict, a failure we term source-derived evidence forgetting. We formulate VLM-guided SFDA as a sample-wise reliability-allocation problem and propose Consensus-Driven Shift Modulation (COSMO). COSMO replaces expert-to-expert guidance with co-adaptation through an anchored shared consensus. It first forms a sample-specific initial consensus that favors the more concentrated prediction. During adaptation, COSMO re-aggregates both branches' evolving evidence and regulates how far the resulting consensus moves from its initial anchor based on consensus uncertainty and training progress. This keeps the shared supervision anchored yet adaptive. Across four benchmarks, COSMO achieves state-of-the-art performance under matched VLM backbones. Further analyses indicate that it better balances the retention of valid source-derived evidence with the absorption of complementary VLM evidence.
Autonomous systems (AS) often rely on Deep Neural Network (DNN) classifiers to operate in complex and dynamically changing environments. However, during operation, these classifiers may encounter domains that differ from those seen during development, causing performance degradation under distribution shift. Removing systems from operation for labelled data collection and retraining is often impractical, particularly when adaptation must occur quickly and at scale. This paper introduces DIRA-SS, a self-supervised extension of Dynamic Incremental Regularised Adaptation (DIRA) that enables online domain adaptation using only a small number of unlabelled target-domain samples. DIRA-SS augments an existing classifier with an auxiliary retraining branch and adapts the shared feature representation through a rotation-prediction task, while elastic weight consolidation regularises important source-domain parameters to reduce destructive updates. This allows the model to benefit from transfer learning without requiring classification labels during operation. We evaluate DIRA-SS on CIFAR-10C, CIFAR-100C, and ImageNet-C using ResNet architectures under severe common corruptions. The results show that DIRA-SS substantially improves performance over the non-adapted source model, achieves accuracy close to the supervised DIRA method, and outperforms existing unsupervised test-time adaptation baselines on ImageNet-C when using only 100 target-domain samples.
Correlation alignment and the maximum mean discrepancy are two widely used distribution-matching frameworks for unsupervised domain adaptation (UDA). However, high variance in these losses has been shown to undermine their effectiveness in minibatch optimisation settings. Furthermore, the losses lack finite-sum structure, which renders them incompatible with classical stochastic variance reduction (SVR) methods. This paper proposes Paired Sampling for Domain Adaptation (PSDA), a novel SVR technique tailored to such objectives. PSDA pairs observations both within and across domains, to form quadruplets that are always sampled together during training. The pairings are designed to minimise expected gradient variance, and reduce to solving a set of linear assignment problems. Our simulations demonstrate reduced variance compared to related methods, and experiments on three domain shift datasets show improved target domain accuracy.