# A Probabilistic Framework for Lifelong Test-Time Adaptation

arXiv: https://arxiv.org/abs/2212.09713 · HTML: https://mlsanity.com/paper/2212.09713/

## Key facts

- Cited by 46 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 52 references that are in the map.
- First posted on arXiv 19 Dec 2022.

## Builds on (most cited first, 30 of 34)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [Unsupervised Domain Adaptation by Backpropagation](https://mlsanity.com/paper/1409.7495/) (2014)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [Learning Transferable Features with Deep Adaptation Networks](https://mlsanity.com/paper/1502.02791/) (2015)
- [Self-training with Noisy Student improves ImageNet classification](https://mlsanity.com/paper/1911.04252/) (2019)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [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)
- [RobustBench: a standardized adversarial robustness benchmark](https://mlsanity.com/paper/2010.09670/) (2020)
- [Deep Visual Domain Adaptation: A Survey](https://mlsanity.com/paper/1802.03601/) (2018)
- [Learning to Adapt Structured Output Space for Semantic Segmentation](https://mlsanity.com/paper/1802.10349/) (2018)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [FDA: Fourier Domain Adaptation for Semantic Segmentation](https://mlsanity.com/paper/2004.05498/) (2020)
- [Continual Test-Time Domain Adaptation](https://mlsanity.com/paper/2203.13591/) (2022)
- [Efficient Test-Time Model Adaptation without Forgetting](https://mlsanity.com/paper/2204.02610/) (2022)
- [Measuring Robustness to Natural Distribution Shifts in Image Classification](https://mlsanity.com/paper/2007.00644/) (2020)
- [Improving robustness against common corruptions by covariate shift adaptation](https://mlsanity.com/paper/2006.16971/) (2020)
- [Revisiting Batch Normalization For Practical Domain Adaptation](https://mlsanity.com/paper/1603.04779/) (2016)
- [Universal Source-Free Domain Adaptation](https://mlsanity.com/paper/2004.04393/) (2020)
- [Progressive Feature Alignment for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1811.08585/) (2018)
- [NOTE: Robust Continual Test-time Adaptation Against Temporal Correlation](https://mlsanity.com/paper/2208.05117/) (2022)
- [3D Common Corruptions and Data Augmentation](https://mlsanity.com/paper/2203.01441/) (2022)
- [SENTRY: Selective Entropy Optimization via Committee Consistency for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2012.11460/) (2020)

## Built on by (most cited first, 30 of 46)

- [A Comprehensive Survey on Test-Time Adaptation under Distribution Shifts](https://mlsanity.com/paper/2303.15361/) (2023)
- [A Comprehensive Survey of Forgetting in Deep Learning Beyond Continual Learning](https://mlsanity.com/paper/2307.09218/) (2023)
- [SoTTA: Robust Test-Time Adaptation on Noisy Data Streams](https://mlsanity.com/paper/2310.10074/) (2023)
- [In Search of Lost Online Test-time Adaptation: A Survey](https://mlsanity.com/paper/2310.20199/) (2023)
- [Towards Real-World Test-Time Adaptation: Tri-Net Self-Training with Balanced Normalization](https://mlsanity.com/paper/2309.14949/) (2023)
- [Ranked Entropy Minimization for Continual Test-Time Adaptation](https://mlsanity.com/paper/2505.16441/) (2025)
- [What, How, and When Should Object Detectors Update in Continually Changing Test Domains?](https://mlsanity.com/paper/2312.08875/) (2023)
- [PCoTTA: Continual Test-Time Adaptation for Multi-Task Point Cloud Understanding](https://mlsanity.com/paper/2411.00632/) (2024)
- [Decomposing the Neurons: Activation Sparsity via Mixture of Experts for Continual Test Time Adaptation](https://mlsanity.com/paper/2405.16486/) (2024)
- [AETTA: Label-Free Accuracy Estimation for Test-Time Adaptation](https://mlsanity.com/paper/2404.01351/) (2024)
- [Reshaping the Online Data Buffering and Organizing Mechanism for Continual Test-Time Adaptation](https://mlsanity.com/paper/2407.09367/) (2024)
- [Variational Continual Test-Time Adaptation](https://mlsanity.com/paper/2402.08182/) (2024)
- [Temporal Test-Time Adaptation with State-Space Models](https://mlsanity.com/paper/2407.12492/) (2024)
- [Controllable Continual Test-Time Adaptation](https://mlsanity.com/paper/2405.14602/) (2024)
- [Parameter-Selective Continual Test-Time Adaptation](https://mlsanity.com/paper/2407.02253/) (2024)
- [UniTTA: Unified Benchmark and Versatile Framework Towards Realistic Test-Time Adaptation](https://mlsanity.com/paper/2407.20080/) (2024)
- [Continual Test-Time Adaptation for Object Detection with Adaptive Monitoring and Randomized Restoration](https://mlsanity.com/paper/2406.16439/) (2024)
- [Hybrid-TTA: Continual Test-time Adaptation via Dynamic Domain Shift Detection](https://mlsanity.com/paper/2409.08566/) (2024)
- [On the Adversarial Risk of Test Time Adaptation: An Investigation into Realistic Test-Time Data Poisoning](https://mlsanity.com/paper/2410.04682/) (2024)
- [When and Where to Reset Matters for Long-Term Test-Time Adaptation](https://mlsanity.com/paper/2603.03796/) (2026)
- [Probabilistic Test-Time Generalization by Variational Neighbor-Labeling](https://mlsanity.com/paper/2307.04033/) (2023)
- [Test-Time Training for Semantic Segmentation with Output Contrastive Loss](https://mlsanity.com/paper/2311.07877/) (2023)
- [Few Clicks Suffice: Active Test-Time Adaptation for Semantic Segmentation](https://mlsanity.com/paper/2312.01835/) (2023)
- [Class-aware Domain Knowledge Fusion and Fission for Continual Test-Time Adaptation](https://mlsanity.com/paper/2510.12150/) (2025)
- [Test-time Adaptation Meets Image Enhancement: Improving Accuracy via Uncertainty-aware Logit Switching](https://mlsanity.com/paper/2403.17423/) (2024)
- [FIESTA: Fisher Information-based Efficient Selective Test-time Adaptation](https://mlsanity.com/paper/2503.23257/) (2025)
- [Dance Across Shifts: Forward-Facilitation Continual Test-Time Adaptation through Dynamic Style Bridging](https://mlsanity.com/paper/2605.18608/) (2026)
- [Beyond Entropy: Style Transfer Guided Single Image Continual Test-Time Adaptation](https://mlsanity.com/paper/2311.18270/) (2023)
- [When Test-Time Adaptation Meets Self-Supervised Models](https://mlsanity.com/paper/2506.23529/) (2025)
- [Stabilizing Open-Set Test-Time Adaptation via Primary-Auxiliary Filtering and Knowledge-Integrated Prediction](https://mlsanity.com/paper/2508.18751/) (2025)

## Abstract (arXiv)

Test-time adaptation (TTA) is the problem of updating a pre-trained source model at inference time given test input(s) from a different target domain. Most existing TTA approaches assume the setting in which the target domain is stationary, i.e., all the test inputs come from a single target domain. However, in many practical settings, the test input distribution might exhibit a lifelong/continual shift over time. Moreover, existing TTA approaches also lack the ability to provide reliable uncertainty estimates, which is crucial when distribution shifts occur between the source and target domain. To address these issues, we present PETAL (Probabilistic lifElong Test-time Adaptation with seLf-training prior), which solves lifelong TTA using a probabilistic approach, and naturally results in (1) a student-teacher framework, where the teacher model is an exponential moving average of the student model, and (2) regularizing the model updates at inference time using the source model as a regularizer. To prevent model drift in the lifelong/continual TTA setting, we also propose a data-driven parameter restoration technique which contributes to reducing the error accumulation and maintaining the knowledge of recent domains by restoring only the irrelevant parameters. In terms of predictive error rate as well as uncertainty based metrics such as Brier score and negative log-likelihood, our method achieves better results than the current state-of-the-art for online lifelong test-time adaptation across various benchmarks, such as CIFAR-10C, CIFAR-100C, ImageNetC, and ImageNet3DCC datasets. The source code for our approach is accessible at https://github.com/dhanajitb/petal.