# Test-Time Adaptation with Principal Component Analysis

arXiv: https://arxiv.org/abs/2209.05779 · HTML: https://mlsanity.com/paper/2209.05779/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 29 references that are in the map.
- First posted on arXiv 13 Sep 2022.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Unsupervised Domain Adaptation by Backpropagation](https://mlsanity.com/paper/1409.7495/) (2014)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Adversarial Discriminative Domain Adaptation](https://mlsanity.com/paper/1702.05464/) (2017)
- [CyCADA: Cycle-Consistent Adversarial Domain Adaptation](https://mlsanity.com/paper/1711.03213/) (2017)
- [Do We Really Need to Access the Source Data? Source Hypothesis Transfer for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2002.08546/) (2020)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [RobustBench: a standardized adversarial robustness benchmark](https://mlsanity.com/paper/2010.09670/) (2020)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [Improving robustness against common corruptions by covariate shift adaptation](https://mlsanity.com/paper/2006.16971/) (2020)
- [Evaluating Prediction-Time Batch Normalization for Robustness under Covariate Shift](https://mlsanity.com/paper/2006.10963/) (2020)
- [Learning Discrete Representations via Information Maximizing Self-Augmented Training](https://mlsanity.com/paper/1702.08720/) (2017)
- [Correlation Alignment for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1612.01939/) (2016)
- [Unsupervised Domain Adaptation through Self-Supervision](https://mlsanity.com/paper/1909.11825/) (2019)
- [Test-Time Adaptation to Distribution Shift by Confidence Maximization and Input Transformation](https://mlsanity.com/paper/2106.14999/) (2021)

## Built on by (most cited first, 2 of 2)

- [A Comprehensive Survey on Test-Time Adaptation under Distribution Shifts](https://mlsanity.com/paper/2303.15361/) (2023)
- [Hierarchical Adaptive networks with Task vectors for Test-Time Adaptation](https://mlsanity.com/paper/2508.09223/) (2025)

## Abstract (arXiv)

Machine Learning models are prone to fail when test data are different from training data, a situation often encountered in real applications known as distribution shift. While still valid, the training-time knowledge becomes less effective, requiring a test-time adaptation to maintain high performance. Following approaches that assume batch-norm layer and use their statistics for adaptation, we propose a Test-Time Adaptation with Principal Component Analysis (TTAwPCA), which presumes a fitted PCA and adapts at test time a spectral filter based on the singular values of the PCA for robustness to corruptions. TTAwPCA combines three components: the output of a given layer is decomposed using a Principal Component Analysis (PCA), filtered by a penalization of its singular values, and reconstructed with the PCA inverse transform. This generic enhancement adds fewer parameters than current methods. Experiments on CIFAR-10-C and CIFAR- 100-C demonstrate the effectiveness and limits of our method using a unique filter of 2000 parameters.