# Test-time Batch Statistics Calibration for Covariate Shift

arXiv: https://arxiv.org/abs/2110.04065 · HTML: https://mlsanity.com/paper/2110.04065/

## Key facts

- Cited by 50 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 73 references that are in the map.
- First posted on arXiv 6 Oct 2021.

## Builds on (most cited first, 30 of 47)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [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)
- [Rethinking Atrous Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1706.05587/) (2017)
- [Arbitrary Style Transfer in Real-time with Adaptive Instance Normalization](https://mlsanity.com/paper/1703.06868/) (2017)
- [ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness](https://mlsanity.com/paper/1811.12231/) (2018)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [Learning Transferable Features with Deep Adaptation Networks](https://mlsanity.com/paper/1502.02791/) (2015)
- [BDD100K: A Diverse Driving Dataset for Heterogeneous Multitask Learning](https://mlsanity.com/paper/1805.04687/) (2018)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [Do We Really Need to Access the Source Data? Source Hypothesis Transfer for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2002.08546/) (2020)
- [Playing for Data: Ground Truth from Computer Games](https://mlsanity.com/paper/1608.02192/) (2016)
- [Learning to Generalize: Meta-Learning for Domain Generalization](https://mlsanity.com/paper/1710.03463/) (2017)
- [RobustBench: a standardized adversarial robustness benchmark](https://mlsanity.com/paper/2010.09670/) (2020)
- [Learning to Adapt Structured Output Space for Semantic Segmentation](https://mlsanity.com/paper/1802.10349/) (2018)
- [Domain Generalization with MixStyle](https://mlsanity.com/paper/2104.02008/) (2021)
- [Generalizing to Unseen Domains via Adversarial Data Augmentation](https://mlsanity.com/paper/1805.12018/) (2018)
- [Domain Generalization by Solving Jigsaw Puzzles](https://mlsanity.com/paper/1903.06864/) (2019)
- [Improving robustness against common corruptions by covariate shift adaptation](https://mlsanity.com/paper/2006.16971/) (2020)
- [Self-Challenging Improves Cross-Domain Generalization](https://mlsanity.com/paper/2007.02454/) (2020)
- [Confidence Regularized Self-Training](https://mlsanity.com/paper/1908.09822/) (2019)

## Built on by (most cited first, 30 of 50)

- [Continual Test-Time Domain Adaptation](https://mlsanity.com/paper/2203.13591/) (2022)
- [A Comprehensive Survey on Test-Time Adaptation under Distribution Shifts](https://mlsanity.com/paper/2303.15361/) (2023)
- [EcoTTA: Memory-Efficient Continual Test-time Adaptation via Self-distilled Regularization](https://mlsanity.com/paper/2303.01904/) (2023)
- [TTN: A Domain-Shift Aware Batch Normalization in Test-Time Adaptation](https://mlsanity.com/paper/2302.05155/) (2023)
- [Batch Calibration: Rethinking Calibration for In-Context Learning and Prompt Engineering](https://mlsanity.com/paper/2309.17249/) (2023)
- [Source-Free Unsupervised Domain Adaptation: A Survey](https://mlsanity.com/paper/2301.00265/) (2022)
- [Improving Test-Time Adaptation via Shift-agnostic Weight Regularization and Nearest Source Prototypes](https://mlsanity.com/paper/2207.11707/) (2022)
- [SITA: Single Image Test-time Adaptation](https://mlsanity.com/paper/2112.02355/) (2021)
- [Beyond Model Adaptation at Test Time: A Survey](https://mlsanity.com/paper/2411.03687/) (2024)
- [Improved Test-Time Adaptation for Domain Generalization](https://mlsanity.com/paper/2304.04494/) (2023)
- [In Search of Lost Online Test-time Adaptation: A Survey](https://mlsanity.com/paper/2310.20199/) (2023)
- [Data-Free Knowledge Transfer: A Survey](https://mlsanity.com/paper/2112.15278/) (2021)
- [SATS: Self-Attention Transfer for Continual Semantic Segmentation](https://mlsanity.com/paper/2203.07667/) (2022)
- [CAFA: Class-Aware Feature Alignment for Test-Time Adaptation](https://mlsanity.com/paper/2206.00205/) (2022)
- [Listen, Adapt, Better WER: Source-free Single-utterance Test-time Adaptation for Automatic Speech Recognition](https://mlsanity.com/paper/2203.14222/) (2022)
- [Unified Entropy Optimization for Open-Set Test-Time Adaptation](https://mlsanity.com/paper/2404.06065/) (2024)
- [Optimization-Free Test-Time Adaptation for Cross-Person Activity Recognition](https://mlsanity.com/paper/2310.18562/) (2023)
- [Active Test-Time Adaptation: Theoretical Analyses and An Algorithm](https://mlsanity.com/paper/2404.05094/) (2024)
- [DARTH: Holistic Test-time Adaptation for Multiple Object Tracking](https://mlsanity.com/paper/2310.01926/) (2023)
- [ATTA: Anomaly-aware Test-Time Adaptation for Out-of-Distribution Detection in Segmentation](https://mlsanity.com/paper/2309.05994/) (2023)
- [SuperTickets: Drawing Task-Agnostic Lottery Tickets from Supernets via Jointly Architecture Searching and Parameter Pruning](https://mlsanity.com/paper/2207.03677/) (2022)
- [Uncovering Adversarial Risks of Test-Time Adaptation](https://mlsanity.com/paper/2301.12576/) (2023)
- [CloudFixer: Test-Time Adaptation for 3D Point Clouds via Diffusion-Guided Geometric Transformation](https://mlsanity.com/paper/2407.16193/) (2024)
- [Unraveling Batch Normalization for Realistic Test-Time Adaptation](https://mlsanity.com/paper/2312.09486/) (2023)
- [Test-time Batch Normalization](https://mlsanity.com/paper/2205.10210/) (2022)
- [Semantic Self-adaptation: Enhancing Generalization with a Single Sample](https://mlsanity.com/paper/2208.05788/) (2022)
- [Un-Mixing Test-Time Normalization Statistics: Combatting Label Temporal Correlation](https://mlsanity.com/paper/2401.08328/) (2024)
- [Decoupled Prototype Learning for Reliable Test-Time Adaptation](https://mlsanity.com/paper/2401.08703/) (2024)
- [Generalizing vision-language models to novel domains: A comprehensive survey](https://mlsanity.com/paper/2506.18504/) (2025)
- [Evaluating Continual Test-Time Adaptation for Contextual and Semantic Domain Shifts](https://mlsanity.com/paper/2208.08767/) (2022)

## Abstract (arXiv)

Deep neural networks have a clear degradation when applying to the unseen environment due to the covariate shift. Conventional approaches like domain adaptation requires the pre-collected target data for iterative training, which is impractical in real-world applications. In this paper, we propose to adapt the deep models to the novel environment during inference. An previous solution is test time normalization, which substitutes the source statistics in BN layers with the target batch statistics. However, we show that test time normalization may potentially deteriorate the discriminative structures due to the mismatch between target batch statistics and source parameters. To this end, we present a general formulation α-BN to calibrate the batch statistics by mixing up the source and target statistics for both alleviating the domain shift and preserving the discriminative structures. Based on α-BN, we further present a novel loss function to form a unified test time adaptation framework Core, which performs the pairwise class correlation online optimization. Extensive experiments show that our approaches achieve the state-of-the-art performance on total twelve datasets from three topics, including model robustness to corruptions, domain generalization on image classification and semantic segmentation. Particularly, our α-BN improves 28.4% to 43.9% on GTA5 rightarrow Cityscapes without any training, even outperforms the latest source-free domain adaptation method.