# Test-time Correlation Alignment

arXiv: https://arxiv.org/abs/2505.00533 · HTML: https://mlsanity.com/paper/2505.00533/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 61 references that are in the map.
- First posted on arXiv 1 May 2025.

## Builds on (most cited first, 30 of 38)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [Domain Generalization: A Survey](https://mlsanity.com/paper/2103.02503/) (2021)
- [Deep Visual Domain Adaptation: A Survey](https://mlsanity.com/paper/1802.03601/) (2018)
- [Efficient Test-Time Model Adaptation without Forgetting](https://mlsanity.com/paper/2204.02610/) (2022)
- [Improving robustness against common corruptions by covariate shift adaptation](https://mlsanity.com/paper/2006.16971/) (2020)
- [Towards Stable Test-Time Adaptation in Dynamic Wild World](https://mlsanity.com/paper/2302.12400/) (2023)
- [Return of Frustratingly Easy Domain Adaptation](https://mlsanity.com/paper/1511.05547/) (2015)
- [A Comprehensive Survey on Test-Time Adaptation under Distribution Shifts](https://mlsanity.com/paper/2303.15361/) (2023)
- [Robust Test-Time Adaptation in Dynamic Scenarios](https://mlsanity.com/paper/2303.13899/) (2023)
- [Correlation Alignment for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1612.01939/) (2016)
- [Entropy is not Enough for Test-Time Adaptation: From the Perspective of Disentangled Factors](https://mlsanity.com/paper/2403.07366/) (2024)
- [Test-Time Adaptation via Conjugate Pseudo-labels](https://mlsanity.com/paper/2207.09640/) (2022)
- [Rethinking Importance Weighting for Deep Learning under Distribution Shift](https://mlsanity.com/paper/2006.04662/) (2020)
- [Test-Time Training on Nearest Neighbors for Large Language Models](https://mlsanity.com/paper/2305.18466/) (2023)
- [Test-Time Model Adaptation with Only Forward Passes](https://mlsanity.com/paper/2404.01650/) (2024)
- [Transfer Learning for Nonparametric Classification: Minimax Rate and Adaptive Classifier](https://mlsanity.com/paper/1906.02903/) (2019)
- [Correlation-aware Adversarial Domain Adaptation and Generalization](https://mlsanity.com/paper/1911.12983/) (2019)
- [MT3: Meta Test-Time Training for Self-Supervised Test-Time Adaption](https://mlsanity.com/paper/2103.16201/) (2021)
- [Test-Time Adaptation via Self-Training with Nearest Neighbor Information](https://mlsanity.com/paper/2207.10792/) (2022)
- [SoTTA: Robust Test-Time Adaptation on Noisy Data Streams](https://mlsanity.com/paper/2310.10074/) (2023)
- [AdaNPC: Exploring Non-Parametric Classifier for Test-Time Adaptation](https://mlsanity.com/paper/2304.12566/) (2023)
- [Feature Alignment and Uniformity for Test Time Adaptation](https://mlsanity.com/paper/2303.10902/) (2023)
- [Towards Real-World Test-Time Adaptation: Tri-Net Self-Training with Balanced Normalization](https://mlsanity.com/paper/2309.14949/) (2023)

## Built on by (most cited first, 4 of 4)

- [FRET: Feature Redundancy Elimination for Test Time Adaptation](https://mlsanity.com/paper/2505.10641/) (2025)
- [HD-TTA: Hypothesis-Driven Test-Time Adaptation for Safer Brain Tumor Segmentation](https://mlsanity.com/paper/2602.19454/) (2026)
- [MixTTA: Low-Rank Cross-Channel Mixing for Reliable Test-Time Adaptation](https://mlsanity.com/paper/2606.28142/) (2026)
- [On the Limits of Representation-Based Test-Time Adaptation for Multimodal LLMs](https://mlsanity.com/paper/2610.19892/) (2026)

## Abstract (arXiv)

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%.