Continual Test-Time Domain Adaptation

Qin WangOlga FinkLuc Van GoolDengxin Dai

article2022CVPR647 citations

Introduces CoTTA, a continual test-time adaptation framework that prevents error accumulation and catastrophic forgetting in dynamically shifting target domains through averaged predictions and stochastic weight restoration.

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Real-world machine perception systems, such as autonomous vehicles, operate in non-stationary and continually changing environments where conditions like weather and lighting shift unpredictably. Adapting pre-trained neural networks to these shifts in real time is critical, but privacy constraints, bandwidth limits, or legal barriers frequently prevent access to the original source training data. Existing test-time adaptation methods assume stationary target domains and typically rely on self-training techniques that rapidly suffer from catastrophic forgetting and error accumulation when exposed to changing data streams.

The article develops and evaluates a continual test-time domain adaptation framework (CoTTA) designed to adapt off-the-shelf pre-trained models on unlabeled, streaming target data without requiring source data or model retraining.

The researchers assessed the approach across five continuous adaptation benchmarks, including image classification datasets with 15 corruption types and varying severities (CIFAR-10, CIFAR-100, and ImageNet) as well as an adverse-weather driving semantic segmentation task (Cityscapes to ACDC). The method addresses error propagation by generating refined self-training targets through an exponential moving average teacher network, applying confidence-triggered test-time data augmentations only during significant domain shifts. To counter catastrophic forgetting, the method stochastically restores approximately 1% of the model weights back to their original pre-trained values after each gradient update, allowing updates across all neural network layers rather than being restricted to batch normalization parameters.

The evaluation demonstrated that the proposed method consistently outperformed standard baselines across all tasks without destabilizing over long sequences. On the standard CIFAR-10 corruption benchmark, the method achieved an average classification error rate of 16.2%, significantly improving upon existing continuous entropy-minimization baselines (20.7%) and static models (43.5%). Under gradually shifting corruptions, the approach maintained an error rate of 10.4% compared to 30.7% for continuous entropy minimization. On the more challenging CIFAR-100 benchmark, it reduced the average error rate to 32.5% compared to 60.9% for continuous entropy baselines, which suffered severe performance degradation over time. On the adverse-condition driving segmentation task across repeated multi-round cycles, the approach achieved a 58.6% mean intersection-over-union score, preventing the long-term degradation observed in baseline models and maintaining stable performance across diverse neural network architectures, including vision transformers.

These findings indicate that effective continual adaptation does not require source data access or restricted parameter updates, provided that pseudo-label noise is controlled and source knowledge is periodically injected. In mission-critical deployments like autonomous transport and edge perception, this framework reduces operational safety risks and avoids the heavy infrastructure costs associated with continuously retraining models or transmitting centralized data.

Organizations deploying automated perception in dynamic operating environments should consider adopting weight-averaged pseudo-labeling alongside source weight restoration when deploying off-the-shelf models into the field. Prior to broader operational rollout, engineering teams should validate optimal confidence thresholds and evaluate computational overhead, as executing multiple test-time augmentations per frame introduces latency trade-offs that must be tuned to meet real-time processing requirements.

École Polytechnique Fédérale de Lausanne ETH Zurich KU Leuven Max Planck Institute for Informatics classification classification methods machine perception continual test-time domain adaptation test-time training continual learning

arXiv: 2203.13591

Paper: Tent: Fully Test-Time Adaptation by Entropy Minimization, Dequan Wang et al. (2021). It introduces Tent, the foundational test-time adaptation framework via entropy minimization that serves as the baseline and core problem setup addressed by CoTTA.
Paper: Do We Really Need to Access the Source Data? Source Hypothesis Transfer for Unsupervised Domain Adaptation, Jian Liang et al. (2020). It develops source-free domain adaptation via pseudo-labeling and information maximization without source data access, establishing principles extended by continual test-time methods.
Paper: Test-Time Training with Self-Supervision for Generalization under Distribution Shifts, Yu Sun et al. (2019). It establishes the paradigm of online test-time training on streaming unlabeled inputs to mitigate distribution shifts during inference.
Paper: Learning without Forgetting, Zhizhong Li et al. (2016). It provides the foundational framework for learning new tasks while preventing catastrophic forgetting in neural networks without accessing historical data.
Paper: Averaging Weights Leads to Wider Optima and Better Generalization, Pavel Izmailov et al. (2018). It explores weight-averaging mechanisms in parameter space that inspire teacher-model EMA updates used to stabilize pseudo-labeling under domain shifts.

Paper: Feature Alignment and Uniformity for Test Time Adaptation, Shuai Wang et al. (2023). It advances test-time adaptation for streaming out-of-distribution inputs by introducing feature alignment, uniformity, and self-distillation constraints across adaptation batches.
Paper: Contrastive Test-Time Adaptation, Dian Chen et al. (2022). It presents an alternative test-time adaptation paradigm that refines streaming pseudo-labels using online contrastive learning and memory queues.
Paper: A Comprehensive Survey of Continual Learning: Theory, Method and Application, Liyuan Wang et al. (2023). It provides an expansive survey synthesizing continual learning theory, stability-plasticity tradeoffs, and modern adaptation mechanisms across sequential non-stationary streams.

Cover for Continual Test-Time Domain Adaptation

Abstract

Test-time domain adaptation aims to adapt a source pre-trained model to a target domain without using any source data. Existing works mainly consider the case where the target domain is static. However, real-world machine perception systems are running in non-stationary and continually changing environments where the target domain distribution can change over time. Existing methods, which are mostly based on self-training and entropy regularization, can suffer from these non-stationary environments. Due to the distribution shift over time in the target domain, pseudo-labels become unreliable. The noisy pseudo-labels can further lead to error accumulation and catastrophic forgetting. To tackle these issues, we propose a continual test-time adaptation approach~(CoTTA) which comprises two parts. Firstly, we propose to reduce the error accumulation by using weight-averaged and augmentation-averaged predictions which are often more accurate. On the other hand, to avoid catastrophic forgetting, we propose to stochastically restore a small part of the neurons to the source pre-trained weights during each iteration to help preserve source knowledge in the long-term. The proposed method enables the long-term adaptation for all parameters in the network. CoTTA is easy to implement and can be readily incorporated in off-the-shelf pre-trained models. We demonstrate the effectiveness of our approach on four classification tasks and a segmentation task for continual test-time adaptation, on which we outperform existing methods. Our code is available at \url{this https URL}.

Topics

classification classification methods machine perception regularization non-stationary environment frequency domains parameter adaptation time frequency domain test-data volume

Keywords

continual test-time domain adaptation test-time training continual learning catastrophic forgetting domain shifts stochastic restore domain randomization target domain distribution augmentation-averaged predictions

1 Introduction
2 Related Work
2.1 Domain Adaptation
2.2 Test-time Adaptation
2.3 Continuous Domain Adaptation
2.4 Continual Learning
2.5 Domain Generalization
3 Continual Test-Time Domain Adaptation
3.1 Problem Definition
3.2 Methodology
4 Experiments
4.1 Datasets and tasks
4.2 Experiments on CIFAR10-to-CIFAR10C
4.3 Experiments on CIFAR100-to-CIFAR100C
4.4 Experiments on ImageNet-to-ImageNet-C
4.5 Experiments on Cityscapes-to-ACDC
5 Conclusion
References

Knowls

Knowl 1 — Continual Test-Time Domain Adaptation Problem Formulation
definition
Online Continual Test-Time Domain Adaptation (CTTA) is the problem setting where an off-the-shelf neural network $f_{\theta_0}$ , pre-trained on labeled source domain data $(\mathcal{X}^S, \mathcal{Y}^S)$ with parameters $\theta_0$ , is adapted online to an unlabeled target data stream $\mathcal{X}^T$ without access to source data or future target data.

At each discrete time step $t$ , the model receives a target input $x_t^T \in \mathcal{X}^T$ sampled from a non-stationary, continually shifting target distribution. The model must produce an online prediction $\hat{y}_t^T = f_{\theta_t}(x_t^T)$ immediately upon receiving $x_t^T$ , and subsequently update its parameters $\theta_t \to \theta_{t+1}$ before encountering $x_{t+1}^T$ . Unlike standard unsupervised domain adaptation (which accesses labeled source data) or standard test-time adaptation (which assumes a single static target domain or allows offline batches/domain resets), CTTA operates under long-term non-stationary distribution shifts where the model must continually adapt without suffering from error accumulation or catastrophic forgetting.
Knowl 2 — Teacher-Student Consistency via Exponential Moving Average Weights
model/method
To reduce error accumulation from noisy pseudo-labels during online continual adaptation, the Continual Test-Time Adaptation (CoTTA) framework uses a dual-network student-teacher architecture. The student network $f_{\theta_t}$ has trainable parameters $\theta_t$ , and the teacher network $f_{\theta'_t}$ maintains weight-averaged parameters $\theta'_t$ , both initialized to the source pre-trained model parameters $\theta_0$ .

At time step $t$ , given target input $x_t^T$ , the student model generates class probability predictions $\hat{y}_t^T = f_{\theta_t}(x_t^T) \in [0, 1]^C$ across $C$ classes. The student is updated by minimizing the cross-entropy consistency loss with respect to teacher-derived soft pseudo-label targets $y'^T_t$ :

$\mathcal{L}_{\theta_t}(x_t^T) = - \sum_{c=1}^C y'^T_{tc} \log \hat{y}^T_{tc}$

where $y'^T_{tc}$ is the target probability assigned to class $c$ . After updating the student weights $\theta_t \to \theta_{t+1}$ via gradient descent, the teacher network weights are updated via an exponential moving average (EMA):

$\theta'_{t+1} = \alpha \theta'_t + (1 - \alpha) \theta_{t+1}$

where $\alpha \in [0, 1)$ is a smoothing momentum factor. The final online prediction output for $x_t^T$ is the class with the highest probability under the teacher's prediction.
Knowl 3 — Confidence-Gated Augmentation-Averaged Pseudo-Labels
model/method
To boost pseudo-label quality under severe domain distribution shifts while avoiding performance drops on familiar inputs, CoTTA estimates domain shift using the source model's confidence and applies test-time augmentation conditionally.

Let $\text{conf}(f_{\theta_0}(x_t^T)) = \max_c (f_{\theta_0}(x_t^T))_c$ denote the prediction confidence of the original source pre-trained model $f_{\theta_0}$ on the input $x_t^T$ , and let $p_{th}$ be a predefined confidence threshold. The augmentation-averaged prediction from the teacher model across $N$ stochastic augmentations $\{\text{aug}_i\}_{i=0}^{N-1}$ is computed as:

$\tilde{y}'^T_t = \frac{1}{N} \sum_{i=0}^{N-1} f_{\theta'_t}(\text{aug}_i(x_t^T))$

The refined teacher pseudo-label $y'^T_t$ supplied to the consistency loss is determined by:

$y'^T_t = \begin{cases} \hat{y}'^T_t = f_{\theta'_t}(x_t^T) & \text{if } \text{conf}(f_{\theta_0}(x_t^T)) \ge p_{th} \\ \tilde{y}'^T_t & \text{otherwise} \end{cases}$

When source confidence is high (indicating minimal domain shift), the unaugmented teacher prediction $\hat{y}'^T_t$ is used directly. When confidence falls below $p_{th}$ (indicating a large domain gap), averaging predictions over $N$ augmented variants reduces pseudo-label noise and error propagation.
Knowl 4 — Stochastic Parameter Restoration to Source Weights
model/method
To prevent catastrophic forgetting and avoid model collapse when updating all trainable layers over prolonged sequences of domain shifts, CoTTA applies stochastic restoration to the student network parameters after each gradient update.

For any trainable weight tensor $W_{t+1}$ at step $t+1$ (such as convolution or linear weight matrices) with corresponding source pre-trained tensor $W_0$ , a binary mask tensor $M$ of identical shape is sampled element-wise from a Bernoulli distribution:

$M \sim \text{Bernoulli}(p)$

where $p \in (0, 1)$ is a small restoration probability (e.g., $p = 0.01$ ). The updated weight tensor is then computed by stochastic blending:

$W_{t+1} = M \odot W_0 + (1 - M) \odot W_{t+1}$

where $\odot$ denotes the element-wise (Hadamard) product. By stochastically reverting a small fraction $p$ of weights back to their original source values $W_0$ , the model prevents parameter drift away from the source distribution, acting as a structural regularizer that enables full-network continual adaptation rather than restricting updates solely to batch normalization parameters.
Knowl 5 — CoTTA Online Continual Test-Time Adaptation Algorithm
algorithm
The Continual Test-Time Adaptation (CoTTA) algorithm adapts a pre-trained model online over a streaming sequence of unlabeled test samples from changing environments.
Input: Source pre-trained model $f_{\theta_0}(x)$ , data stream $\{x_t\}_{t=1}^T$ , restore probability $p$ , smoothing factor $\alpha$ , confidence threshold $p_{th}$ , number of augmentations $N$
Output: Online predictions $\{y^*_t\}_{t=1}^T$ , adapted student $f_{\theta_{T+1}}$ , adapted teacher $f_{\theta'_{T+1}}$
Initialize teacher network weights $\theta'_0 \leftarrow \theta_0$
for each time step $t = 1, 2, \dots, T$ do
    Receive target sample $x_t$
    Compute source confidence $c_t \leftarrow \max_c (f_{\theta_0}(x_t))_c$
    if $c_t \ge p_{th}$ then
         $y'^T_t \leftarrow f_{\theta'_t}(x_t)$
    else
         $y'^T_t \leftarrow \frac{1}{N} \sum_{i=0}^{N-1} f_{\theta'_t}(\text{aug}_i(x_t))$
    end if
    Compute online output prediction $y^*_t \leftarrow \arg\max_c y'^T_{tc}$
    Compute student prediction $\hat{y}_t \leftarrow f_{\theta_t}(x_t)$
    Compute cross-entropy consistency loss $\mathcal{L} \leftarrow - \sum_c y'^T_{tc} \log \hat{y}_{tc}$
    Update student parameters $\theta_{t+1} \leftarrow \theta_t - \eta \nabla_{\theta_t} \mathcal{L}$
    Update teacher parameters $\theta'_{t+1} \leftarrow \alpha \theta'_t + (1 - \alpha) \theta_{t+1}$
    for each trainable tensor $W_{t+1} \in \theta_{t+1}$ with initial value $W_0$ do
        Sample mask $M \sim \text{Bernoulli}(p)$
         $W_{t+1} \leftarrow M \odot W_0 + (1 - M) \odot W_{t+1}$
    end for
end for

Knowl 6 — CIFAR-10 to CIFAR-10C Continual Adaptation and Component Ablation

data/table

Evaluation of online continual test-time domain adaptation on CIFAR-10 to CIFAR-10C at severity level 5 using WideResNet-28, with 10,000 images per corruption evaluated in continuous sequence across 15 corruption types. Hyperparameters: Adam optimizer (learning rate $10^{-3}$ ), $N = 32$ augmentations, $p = 0.01$ .

Method	W-avg	A-avg	S-Rest	Gaus	shot	imp	defoc	glass	motn	zoom	snow	frost	fog	brit	cntrst	elast	pixel	jpeg	Mean
Source				72.3	65.7	72.9	46.9	54.3	34.8	42.0	25.1	41.3	26.0	9.3	46.7	26.6	58.5	30.3	43.5
BN Stats Adapt				28.1	26.1	36.3	12.8	35.3	14.2	12.1	17.3	17.4	15.3	8.4	12.6	23.8	19.7	27.3	20.4
Pseudo-label				26.7	22.1	32.0	13.8	32.2	15.3	12.7	17.3	17.3	16.5	10.1	13.4	22.4	18.9	25.9	19.8
TENT-online*				24.8	23.5	33.0	12.0	31.8	13.7	10.8	15.9	16.2	13.7	7.9	12.1	22.0	17.3	24.2	18.6
TENT-continual				24.8	20.6	28.6	14.4	31.1	16.5	14.1	19.1	18.6	18.6	12.2	20.3	25.7	20.8	24.9	20.7
CoTTA (Ours)	✓			27.2	22.8	30.8	12.1	30.1	13.9	11.9	17.2	16.0	14.3	9.4	13.1	19.9	15.4	19.9	18.3
CoTTA (Ours)	✓	✓		24.5	21.0	26.0	12.3	27.9	13.9	12.0	16.6	15.9	14.7	9.4	13.6	19.8	14.7	18.7	17.4
CoTTA (Ours)	✓	✓	✓	24.3	21.3	26.6	11.6	27.6	12.2	10.3	14.8	14.1	12.4	7.5	10.6	18.3	13.4	17.3	16.2

Note: TENT-online requires oracle domain boundary information to reset model weights at each new domain, which is unavailable in standard CTTA. TENT-continual exhibits severe error accumulation, degrading to 24.9% on the final domain (mean 20.7%). Each component of CoTTA incrementally reduces mean error: weight averaging (18.3%), augmentation averaging (17.4%), and stochastic restoration (16.2% with standard deviation 0.1% over 5 seeds).

Knowl 7 — Gradually Changing Corruption Evaluation on CIFAR-10C

data/table

In realistic environments, distribution shifts occur gradually rather than in abrupt severity jumps. In the gradually changing setup, severity transitions smoothly through $1 \to 2 \to 3 \to 4 \to 5 \to 4 \to 3 \to 2 \to 1$ within each corruption type, with domain transitions occurring at severity level 1. Results are averaged over 10 randomly shuffled corruption sequences.

Under gradual shift, TENT-continual suffers catastrophic error accumulation and parameter drift, reaching 30.7% average error (worse than the non-adapted source baseline of 24.8%). CoTTA reduces the error rate to 10.4%, demonstrating robust stability under continuous transitions.

Knowl 8 — Continual Test-Time Adaptation on CIFAR-100C

data/table

Classification error rate (%) on the 100-class CIFAR-100 to CIFAR-100C benchmark under continual online adaptation across 15 corruption types at severity level 5 using a pre-trained ResNeXt-29 architecture.

Method	Gaus	shot	imp	defoc	glass	motn	zoom	snow	frost	fog	brit	cntrst	elast	pixel	jpeg	Mean
Source	73.0	68.0	39.4	29.3	54.1	30.8	28.8	39.5	45.8	50.3	29.5	55.1	37.2	74.7	41.2	46.4
BN Stats Adapt	42.1	40.7	42.7	27.6	41.9	29.7	27.9	34.9	35.0	41.5	26.5	30.3	35.7	32.9	41.2	35.4
Pseudo-label	38.1	36.1	40.7	33.2	45.9	38.3	36.4	44.0	45.6	52.8	45.2	53.5	60.1	58.1	64.5	46.2
TENT-continual	37.2	35.8	41.7	37.9	51.2	48.3	48.5	58.4	63.7	71.1	70.4	82.3	88.0	88.5	90.4	60.9
CoTTA (Ours)	40.1	37.7	39.7	26.9	38.0	27.9	26.4	32.8	31.8	40.3	24.7	26.9	32.5	28.3	33.5	32.5

TENT-continual collapses as corruptions progress (error rises from 37.2% on Gaussian to 90.4% on JPEG, with a mean of 60.9%). In contrast, CoTTA maintains stable adaptation throughout the sequence, achieving a mean error of 32.5% (an improvement of 2.9% over BN Stats Adapt and 13.9% over the unadapted source model).

Knowl 9 — Continual Semantic Segmentation on Cityscapes-to-ACDC Benchmark

data/table

Long-term continual test-time semantic segmentation evaluated using a pre-trained Segformer-B5 model on Cityscapes adapted continually to four adverse conditions from ACDC (Fog $\to$ Night $\to$ Rain $\to$ Snow) repeated for 10 consecutive cycles (40 condition shifts total, 400 unlabeled images per condition). Predictions evaluated at original resolution ( $1920 \times 1080$ ) using mean Intersection-over-Union (mIoU, %).

	Round 1				Round 4				Round 7				Round 10				All
Method	Fog	Night	Rain	Snow	Fog	Night	Rain	Snow	Fog	Night	Rain	Snow	Fog	Night	Rain	Snow	Mean
Source	69.1	40.3	59.7	57.8	69.1	40.3	59.7	57.8	69.1	40.3	59.7	57.8	69.1	40.3	59.7	57.8	56.7
BN Stats Adapt	62.3	38.0	54.6	53.0	62.3	38.0	54.6	53.0	62.3	38.0	54.6	53.0	62.3	38.0	54.6	53.0	52.0
TENT-continual	69.0	40.2	60.1	57.3	66.5	36.3	58.7	54.0	64.2	32.8	55.3	50.9	61.8	29.8	51.9	47.8	52.3
CoTTA (Ours)	70.9	41.2	62.4	59.7	70.9	41.0	62.7	59.7	70.9	41.0	62.8	59.7	70.8	41.0	62.8	59.7	58.6

TENT-continual and BN Stats Adapt perform poorly on Segformer-B5 because Vision Transformers rely primarily on LayerNorm rather than BatchNorm; TENT's performance degrades steadily from 69.0% (Round 1 Fog) down to 29.8% (Round 10 Night) and 47.8% (Round 10 Snow). CoTTA adapts all trainable parameters without layer-type restrictions, maintaining consistent high performance (58.6% overall mIoU vs 56.7% source) across all 10 recurring cycles.

Knowl 10 — Continual Test-Time Adaptation on ImageNet-to-ImageNet-C

data/table

Average classification error (%) on ImageNet-to-ImageNet-C evaluated on a pre-trained ResNet-50 across 10 diverse corruption sequences at corruption severity level 5.

Across 10 diverse sequence orderings of corruption types, CoTTA achieves an average error rate of $63.0 \pm 1.8\%$ , consistently outperforming the source baseline (82.4%), test-time batch statistics adaptation (72.1%), test-time augmentation baseline (71.4%), and TENT-continual (66.5%).

Coverage note — None was omitted; all key contributions including problem setup, algorithmic formulation, mathematical modeling, and empirical benchmarks on CIFAR-10C, CIFAR-100C, ImageNet-C, and Cityscapes-to-ACDC were included.

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Citation

MLA

Wang, Q., et al. “Continual Test-Time Domain Adaptation”. arXiv, 2022, http://arxiv.org/abs/2203.13591v1.

APA

Wang, Q., Fink, O., Gool, L. V., & Dai, D. (2022). Continual Test-Time Domain Adaptation. arXiv. http://arxiv.org/abs/2203.13591v1

Chicago

Wang, Q., O. Fink, L. V. Gool, and D. Dai. 2022. “Continual Test-Time Domain Adaptation”. arXiv. http://arxiv.org/abs/2203.13591v1.

Harvard

Wang, Q. et al. (2022) “Continual Test-Time Domain Adaptation”, arXiv [Preprint]. Available at: http://arxiv.org/abs/2203.13591v1.

Vancouver

1. Wang Q, Fink O, Gool LV, Dai D (2022) Continual Test-Time Domain Adaptation. arXiv

BibTeX

@article{wang2022continual,
  title = {Continual Test-Time Domain Adaptation},
  author = {Wang, Qin and Fink, Olga and Gool, Luc Van and Dai, Dengxin},
  year = {2022},
  journal = {arXiv},
  url = {http://arxiv.org/abs/2203.13591v1},
  eprint = {2203.13591}
}

Metadata:arXiv

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Metric	Source Baseline	BN Stats Adapt	TENT-continual	CoTTA (Ours)
Avg. Error Rate (%)	24.8	13.7	30.7	10.4 $\pm$ 0.2

Continual Test-Time Domain Adaptation

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Knowls

Knowl 1 — Continual Test-Time Domain Adaptation Problem Formulation

Knowl 2 — Teacher-Student Consistency via Exponential Moving Average Weights

Knowl 3 — Confidence-Gated Augmentation-Averaged Pseudo-Labels

Knowl 4 — Stochastic Parameter Restoration to Source Weights

Knowl 5 — CoTTA Online Continual Test-Time Adaptation Algorithm

Knowl 6 — CIFAR-10 to CIFAR-10C Continual Adaptation and Component Ablation

Knowl 7 — Gradually Changing Corruption Evaluation on CIFAR-10C

Knowl 8 — Continual Test-Time Adaptation on CIFAR-100C

Knowl 9 — Continual Semantic Segmentation on Cityscapes-to-ACDC Benchmark

Knowl 10 — Continual Test-Time Adaptation on ImageNet-to-ImageNet-C

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