Subspace Optimization for Backpropagation-Free Continual Test-Time Adaptation

Deep neural nets achieve remarkable performance when training and test data share the same distribution, but this assumption frequently breaks in real-world deployment, where data undergoes continual distributional shifts. Continual Test-Time Adaptation (CTTA) addresses this challenge by adapting pretrained models to non-stationary target distributions on-the-fly, without access to source data or labeled targets, while mitigating two critical failure modes: catastrophic forgetting of source knowledge and error accumulation from noisy pseudo-labels over extended time horizons. In this comprehensive survey, we formally define the CTTA problem, analyze the diverse continual domain shift patterns that characterize different evaluation protocols, and propose a hierarchical taxonomy that categorizes existing methods into three families: optimization-based strategies (entropy minimization, pseudo-labeling, parameter restoration), parameter-efficient methods (normalization layer adaptation, adaptive parameter selection), and architecture-based approaches (teacher-student frameworks, adapters, visual prompting, masked modeling). We systematically review representative methods within each category and present comparative benchmarks and experimental results across standard evaluation settings. Finally, we discuss the limitations of current approaches and highlight emerging research directions, including the adaptation of foundation models and black-box systems, thereby providing a roadmap for future research in robust continual test-time adaptation.

Test-Time Adaptation (TTA) is essential for enabling deep learning models to handle real-world data distribution shifts. However, current approaches face significant limitations: backpropagation-based methods are not suitable for low-end deployment devices, due to their high computation and memory requirements, as well as their tendency to modify model weights during adaptation; while traditional backpropagation-free techniques exhibit constrained adaptation capabilities. In this work, we propose Forward-Only Zeroth-Order Optimization (FOZO), a novel and practical backpropagation-free paradigm for TTA. FOZO leverages a memory-efficient zeroth-order prompt optimization, which is led by objectives optimizing both intermediate feature statistics and prediction entropy. To ensure efficient and stable adaptation over the out-of-distribution data stream, we introduce a dynamically decaying perturbation scale during zeroth-order gradient estimation and theoretically prove its convergence under the TTA data stream assumption. Extensive continual adaptation experiments on ImageNet-C, ImageNet-R, and ImageNet-Sketch demonstrate FOZO's superior performance, achieving 59.52% Top-1 accuracy on ImageNet-C (5K, level 5) and outperforming main gradient-based methods and SOTA forward-only FOA (58.13%). Furthermore, FOZO exhibits strong generalization on quantized (INT8) models. These findings demonstrate that FOZO is a highly competitive solution for TTA deployment in resource-limited scenarios.

In many real-world scenarios, encountering continual shifts in domain during inference is very common. Consequently, continual test-time adaptation (CTTA) techniques leveraging a teacher-student framework have gained prominence, allowing models to adapt continuously even after deployment. In such a framework, a weight-averaged mean teacher is used to produce pseudo-labels from test data for self-training. The mean teacher gets updated as an exponential moving average of the student parameters using a high value of momentum that is kept fixed even if different distributions of test data are encountered. To combat the resulting drift of the model, we propose a novel controlled teacher adaptation methodology that dynamically sets a proper momentum value depending on the quality of the incoming data. Additionally, we estimate class prototypes from the source pretrained model to help align the target data as they come in. Importantly, our method does not require access to source data or its statistics at any stage of the pipeline, making it truly source-free. We perform extensive experiments on benchmark datasets to demonstrate that our approach outperforms different state-of-the-art adaptation frameworks, many of which require access to source data.