Deep neural networks often degrade under distribution shifts. Although domain adaptation offers a solution, privacy constraints often prevent access to source data, making Test-Time Adaptation (TTA, which adapts using only unlabeled test data) increasingly attractive. However, current TTA methods still face practical challenges: (1) a primary focus on instance-wise alignment, overlooking CORrelation ALignment (CORAL) due to missing source correlations; (2) complex backpropagation operations for model updating, resulting in overhead computation and (3) domain forgetting. To address these challenges, we provide a theoretical analysis to investigate the feasibility of Test-time Correlation Alignment (TCA), demonstrating that correlation alignment between high-certainty instances and test instances can enhance test performances with a theoretical guarantee. Based on this, we propose two simple yet effective algorithms: LinearTCA and LinearTCA+. LinearTCA applies a simple linear transformation to achieve both instance and correlation alignment without additional model updates, while LinearTCA+ serves as a plug-and-play module that can easily boost existing TTA methods. Extensive experiments validate our theoretical insights and show that TCA methods significantly outperforms baselines across various tasks, benchmarks and backbones. Notably, LinearTCA achieves higher accuracy with only 4% GPU memory and 0.6% computation time compared to the best TTA baseline. It also outperforms existing methods on CLIP over 1.86%.

Many recent machine learning tasks focus to develop models that can generalize to unseen distributions. Domain generalization (DG) has become one of the key topics in various fields. Several literatures show that DG can be arbitrarily hard without exploiting target domain information. To address this issue, test-time adaptive (TTA) methods are proposed. Existing TTA methods require offline target data or extra sophisticated optimization procedures during the inference stage. In this work, we adopt Non-Parametric Classifier to perform the test-time Adaptation (AdaNPC). In particular, we construct a memory that contains the feature and label pairs from training domains. During inference, given a test instance, AdaNPC first recalls K closed samples from the memory to vote for the prediction, and then the test feature and predicted label are added to the memory. In this way, the sample distribution in the memory can be gradually changed from the training distribution towards the test distribution with very little extra computation cost. We theoretically justify the rationality behind the proposed method. Besides, we test our model on extensive numerical experiments. AdaNPC significantly outperforms competitive baselines on various DG benchmarks. In particular, when the adaptation target is a series of domains, the adaptation accuracy of AdaNPC is 50% higher than advanced TTA methods. The code is available at https://github.com/yfzhang114/AdaNPC.