Title: SNAP: Low-Latency Test-Time Adaptation with Sparse Updates
Venue: NeurIPS 2025
Accepted: yes
Keywords: Test-Time Adaptation

Unsupervised Domain Adaptation
Abstract: Test-Time Adaptation (TTA) adjusts models using unlabeled test data to handle dynamic distribution shifts. However, existing methods rely on frequent adaptation and high computational cost, making them unsuitable for resource-constrained edge environments. To address this, we propose SNAP, a sparse TTA framework that reduces adaptation frequency and data usage while preserving accuracy. SNAP maintains competitive accuracy even when adapting based on only 1\% of the incoming data stream, demonstrating its robustness under infrequent updates. Our method introduces two key components: (i) Class and Domain Representative Memory (CnDRM), which identifies and stores a small set of samples that are representative of both class and domain characteristics to support efficient adaptation with limited data; and (ii) Inference-only Batch-aware Memory Normalization (IoBMN), which dynamically adjusts normalization statistics at inference time by leveraging these representative samples, enabling efficient alignment to shifting target domains. Integrated with five state-of-the-art TTA algorithms, SNAP reduces latency by up to 93.12\%, while keeping the accuracy drop below 3.3\%, even across adaptation rates ranging from 1\% to 50\%. This demonstrates its strong potential for practical use on edge devices serving latency-sensitive applications. The source code is available at https://github.com/chahh9808/SNAP.

SNAP: Low-Latency Test-Time Adaptation with Sparse Updates

Abstract

Test-Time Adaptation (TTA) adjusts models using unlabeled test data to handle dynamic distribution shifts. However, existing methods rely on frequent adaptation and high computational cost, making them unsuitable for resource-constrained edge environments. To address this, we propose SNAP, a sparse TTA framework that reduces adaptation frequency and data usage while preserving accuracy. SNAP maintains competitive accuracy even when adapting based on only 1% of the incoming data stream, demonstrating its robustness under infrequent updates. Our method introduces two key components: (i) Class and Domain Representative Memory (CnDRM), which identifies and stores a small set of samples that are representative of both class and domain characteristics to support efficient adaptation with limited data; and (ii) Inference-only Batch-aware Memory Normalization (IoBMN), which dynamically adjusts normalization statistics at inference time by leveraging these representative samples, enabling efficient alignment to shifting target domains. Integrated with five state-of-the-art TTA algorithms, SNAP reduces latency by up to 93.12%, while keeping the accuracy drop below 3.3%, even across adaptation rates ranging from 1% to 50%. This demonstrates its strong potential for practical use on edge devices serving latency-sensitive applications. The source code is available at https://github.com/chahh9808/SNAP .

1 Introduction

Deep learning models often suffer performance degradation under domain shifts caused by environmental changes or noise [37]. Test-Time Adaptation (TTA) offers a promising solution for domain shifts by utilizing only unlabeled test data without requiring source data. While TTA algorithms have advanced in complexity to improve accuracy in data streams [48, 30, 50, 53, 31, 43], they are typically designed for resource-rich servers, overlooking the computational limitations crucial for real-world deployment. Operations such as backpropagation, data augmentation, and model ensembling [50, 53, 55] result in substantial latency and memory consumption, making state-of-the-art (SOTA) TTA methods inefficient for practical use.

For edge devices with limited computational power, such as mobile devices or IoT sensors, the adaptation latency from TTA methods becomes a critical bottleneck, particularly in delay-sensitive applications such as autonomous driving and real-time health monitoring. Moreover, the model must keep up with the data stream in those applications, but high computational overhead could cause it to miss critical samples, resulting in inference lags and reduced accuracy. This issue is exacerbated with fast data streams, such as high-frame-rate videos or high-performance sensors. For example, even a

Model

TTA on

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Acc: 69%

Latency: 2.1s

*Adaptation Rate: 0.33

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: Adaptation latency

④

: Inference latency

Original TTA

TTA on

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Pre-trained

Model

Adapt

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Naive Sparse TTA

Latency: 6.7s

Acc: 81%

Adapt

batch

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Acc: 69%

: Adaptation

: Inference

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slight delay in processing sensor data can lead to dangerous situations in autonomous driving. A high adaptation latency accumulating with each batch not only undermines real-time performance but also limits the potential of TTA algorithms in latency-sensitive applications (Section 3). In response to this challenge, forward-only TTA methods [13, 29] propose adjusting lightweight components such as prototypes or prompts during inference. While these mechanisms improve efficiency, their reliance on fixed model parameters fails to adapt to dynamic distribution shifts [7, 53, 29]. Consequently, a robust performance of backpropagation-based approaches across diverse conditions (Appendix B.10) underscores the necessity of efficient model updates.

In online TTA scenarios where rapid response is required under strict resource constraints, Sparse TTA (STTA) offers a practical compromise by reducing the frequency of adaptation rather than eliminating it entirely. By adapting intermittently instead of at every batch, STTA significantly reduces computational overhead and latency. However, naïvely reducing update frequency degrades performance since only a limited data portion is utilized (Figure 1). Thus, the success of STTA hinges on strategically selecting representative stream samples to enable effective adaptation under sparse update schedules (detailed analysis in Section 5).

Existing sampling-based TTA methods are especially designed for handling dynamic data stream such as non-i.i.d. [6, 31, 53] or noisy data [7]. However, they are not optimized for data efficiency and continue to utilize a large proportion of samples. For example, EATA [30] reduces sample usage by filtering out unreliable samples but experiences performance degradation when reductions become too aggressive. Meanwhile, research in data-efficient deep learning has shown that selecting easy, class-representative samples is effective at low sampling rates (e.g., below 0.4) [51, 2]. However, these approaches depend on ground-truth labels, which are not available in TTA.

We propose SNAP : S parse N etwork A daptation for P ractical Test-Time Adaptation, a low-latency unsupervised domain adaptation framework for resource-constrained devices. SNAP balances adaptation accuracy with computational efficiency through two key components: Class and Domain Representative Memory (CnDRM) and Inference-only Batch-aware Memory Normalization (IoBMN). CnDRM stores a pool of class-representative samples (high pseudo-label confidence, balanced across predictions) and domain-representative samples (closest to the target domain centroid in feature space). This approach enables the model to adapt effectively to domain shifts with minimal data (Section 4.1). Meanwhile, IoBMN dynamically refines the normalization layers during inference by utilizing CnDRM's class-domain representative statistics to correct skewed feature distributions at each inference step. This keeps the model aligned with the evolving data distribution, enabling effective batch-wise adaptation without backpropagation (Section 4.2).

SNAP is a lightweight module that reduces latency while seamlessly integrating with existing TTA methods, preserving their adaptation behavior. To assess its effectiveness, we integrated SNAP with five SOTA TTA algorithms: Tent [48], EATA [30], SAR [31], CoTTA [50], and RoTTA [53]. We tested it on three widely-used TTA benchmarks (CIFAR10-C, CIFAR100-C, and ImageNetC [10]) across various adaptation rates (Section 5). We also validate SNAP on ImageNet-R [9] and ImageNet-Sketch [49] to assess generalization (Appendix B.11).

In addition, we measured SNAP's latency and memory usage on three popular edge devices-Raspberry Pi 4 [38], Raspberry Pi Zero 2 W [39], and NVIDIA Jetson Nano [32]-to assess its real-world applicability. SNAP significantly reduces latency while minimizing performance degradation from existing TTA methods. On a Raspberry Pi 4 testbed, it reduced CoTTA's latency by

Adapt batch

Timeline

⑦

up to 93.12% at an adaptation rate of 0.1 in CIFAR10-C, with no loss in performance. Moreover, SNAP maintained performance comparable to original TTA methods across adaptation rates from 0.01 to 0.5, achieving 77.12%-81.74% for Tent, close to the full adaptation accuracy of 80.43%. SNAP also operates efficiently under memory constraints, with low memory overhead and seamless integration with a memory-efficient TTA module [12], as detailed in Appendices B.7 and B.8.

2 Related work

Test-time adaptation. Test-time adaptation aims to improve model performance on out-ofdistribution data by using only the unlabeled test data stream to adapt the model. Test-time normalization [28, 40] adjusts the batch normalization (BN) statistics using test data to improve performance. Other works mainly involve updating the parameters of the model during test time. Tent [48] adapts the affine parameters of the BN layers to minimize the entropy of its predictions. EATA [30] builds upon Tent, sampling reliable and non-redundant samples and utilizing an anti-forgetting regularizer for efficiency. Other works introduce more complex schemes, primarily to improve robustness against more practical test-time scenarios. CoTTA [50] addresses a continually changing test-time environment by using weight-averaged and augmentation-averaged predictions with stochastic restoring. SAR [31] filters samples with large and noisy gradients to stabilize the model during wilder test-time scenarios. RoTTA [53] targets a practical test-time setting of changing distributions and correlative sampling by introducing a memory bank and a teacher-student model. We further analyze how prior TTA methods perform under sparse-update regimes and how our approach differs in Appendix B.3.

Test-time adaptation on edge devices. TTA on edge devices primarily inherit the challenges of on-device learning:, including limited memory and reduced computational efficiency [21]. Several memory-efficient TTA works have been proposed in this regard. MECTA [12] aims to reduce the memory consumption of gradient-based TTA, proposing an adaptive normalization layer to reduce the intermediate caches for backpropagation. EcoTTA [43] proposes memory-efficient continual TTA by adapting lightweight meta networks instead of the originals to reduce the size of intermediate activations. Despite works to promote memory-efficiency, the latency of TTA, especially on resource-constrained edge devices, has been generally overlooked. While many adaptation-based TTA [48, 30, 31, 53] update only the affine parameters for general time and memory concerns, they still involve computationally-heavy operations every batch, which can lead to high latency on edge devices. A recent work [1] introduces a more practical TTA evaluation protocol that penalizes slow TTA methods by providing them with fewer samples for adaptation.

Data-efficient deep learning. Data-efficient deep learning methods enable deep learning models to achieve competitive performance with less data. Among these methods, data selection, or data sampling, involves utilizing a small subset of the training data in an attempt to match that of fulldataset training. A branch of data-selection is score-based selection, which scores each sample based on some predefined metric, such as a sample's influence [16], difficulty [46, 34], prediction confidence [35], or consistency [14], and selects samples with scores in a certain range. Another set of data-selection methods involves optimization-based selection, which formulates an optimization problem to find an optimal subset that can best approximate full-dataset training [26, 52, 36]. While these approaches work well in their preconceived settings, they generally suffer performance drop as their settings change, such as a change in sampling rates. More recent studies such as Moderate Coreset [51] propose a more robust selection approach by using the distance of a sample to the class center as a score criterion, for an effective representation of the dataset.

3 Preliminaries

Our work addresses the challenge of test-time adaptation latency on edge devices, where efficient, low-latency inference must be achieved despite limited resources.

Test-time adaptation and its latency challenge on edge devices. In unsupervised domain adaptation, the source domain data D S = X S , Y is drawn from the distribution P S ( x , y ) , while the target domain data D T = X T , Y follows P T ( x , y ) , typically without known labels y j . Given a pre-trained model f ( · ; Θ) on the source domain D S , TTA adjusts the model to the target distribution P T using only target instances x j , updating the parameters Θ to reduce domain discrepancy [48].

On resource-constrained edge devices, frequent adaptation poses a significant bottleneck. Our experiments on a Raspberry Pi 4 [38] revealed that existing TTA methods incur a minimum latency of 3.83 seconds per batch (Figure 2), severely limiting real-time inference for fast data streams (e.g., autonomous driving [45, 22]). Additional latency tracking for other devices is reported in Appendix B.6. Even lightweight TTA algorithms suffer from considerable backpropagation overhead, creating bottlenecks on resource-constrained devices without GPU-level computation. More computationally intensive methods like CoTTA, which depend on data augmentation and ensembles, require over 70 seconds per adaptation step, rendering them impractical for edge devices (Figure 2).

55.76

Accuracy (%)

55.84

50.74

52.35

57.94

55.76

51.55

51.33

49.39

50.70

+SNAP

+SNAP

+SNAP

+SNAP

+SNAP

Tent

EATA

SAR

RoTTA

CoTTA

Average Latency per batch (s)

Components

forward

backprop

forward (student model)

teacher model update (EMA)

augmentations

stochasticrestore

augmentation&ensembleforloss calc

0.0

5.0

10.0

15.0//

65.0

70.0

A recent work [1] recognized latency as a crucial problem and proposed a TTA evaluation protocol that penalizes methods slower than the data stream rate. Instead of penalizing a model for being slow, we propose Sparse TTA , where the model adapts at sparse intervals to sustain real-time throughput. As real deployments involve devices with different computational capabilities and data streams of varying speeds, we believe a framework that effectively maintains various TTA methods' performance across different latency requirements is crucial.

Sparse test-time adaptation and adaptation rates. Sparse Test-Time Adaptation (STTA) lowers the frequency of model updates, a key factor in reducing adaptation latency on resource-constrained devices. Unlike conventional TTA methods that process full batches and incur significant overhead, STTA updates the model using only a subset of batches (Figure 1). The core parameter of STTA, the Adaptation Rate (AR) , determines the proportion of batches or samples used for adaptation compared to the Original TTA. By tuning the AR, STTA balances the performance and computational latency. Furthermore, STTA's periodic adaptation can be optimized by strategically distributing sparse model updates across selected intervals during inference. This approach helps distribute the adaptation overhead, smooths latency fluctuations across inference batches, and preserves overall performance.

4 Methodology

SNAP framework resolves the high latency and inefficiency issue of existing TTA methods. By introducing a Sparse TTA (STTA) strategy combined with a novel sampling method, SNAP minimizes adaptation delays while maintaining accuracy. The overall system, illustrated in Figure 3, consists of two primary components: (i) Class and Domain Representative Memory (CnDRM) for efficient sampling and (ii) Inference-only Batch-aware Memory Normalization (IoBMN) to correct feature distribution shifts during inference. Together, these components enable effective STTA with minimal computational overhead.

4.1 Class and Domain Representative Memory

CnDRM is a core component of SNAP that addresses the challenges of efficient data sampling for STTA. As the adaptation rate directly impacts the number of samples used for adaptation, this necessitates a careful sampling strategy to optimize performance with minimal data. Given this limited sampling rate, CnDRM selects both class and domain-representative samples to maintain model performance while minimizing adaptation overhead.

Motivation. Effective data sampling is essential for data-efficient deep learning, particularly when only a few samples are available. While score-based methods that prioritize difficult samples perform well at high sampling rates, selecting easy, class-representative samples is more effective at lower rates [2]. Moderate Coreset [51] also demonstrates that selecting samples near the class center improves performance in noisy-label settings, a principle that aligns with the STTA scenario where ground truth is unavailable.

Online data stream

t

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aware

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In addition, on real-world deployments, latency constraints often limit adaptation frequency, requiring models to function at low adaptation rates (e.g., 0.1). At such low rates, class-representative sampling alone is insufficient (Table 2), as it fails to capture distributional shifts between source and target domains. To overcome this limitation, we propose selecting both class- and domain-representative samples to enhance adaptation efficiency in low-data environments. Detailed theoretical analysis on the proposed efficient sampling strategy is in Appendix B.1.

Criteria 1: class representation. To ensure stable adaptation without ground truth labels, CnDRM selects high-confidence samples, avoiding low-confidence samples that often lie near decision boundaries and carry incorrect pseudo-labels. This ensures stable learning signals and reduces error propagation from incorrect pseudo-labels, supporting more effective and stable adaptation (Details in Appendix B.5). The confidence score C ( x ) for each sample x is calculated as: C ( x ) = max y ∈Y p ( y | x ; Θ) where p ( y | x ; Θ) is the softmax probability for class y . Only samples with confidence above a threshold τ conf are retained. For a balanced representation across diverse classes, CnDRM selects these high-confidence samples in a prediction-balanced manner. This helps maintain the model's overall classification capability by preventing bias towards certain classes when only a low sample rate is available for adaptation. By leveraging both high confidence and prediction balance, CnDRM effectively selects class-representative samples that are diverse and reliable, even without access to ground-truth labels.

Criteria 2: domain representation. In addition to class-representative sampling, CnDRM selects domain-representative samples to facilitate adaptation to new domain conditions. Building on the efficient class-representative sampling criteria, we argue that selecting samples close to the domain centroid would enhance performance in STTA. Our preliminary experiment results validate improved performance when selecting samples near the centroid (Figure 4). For ImageNet-C Gaussian noise, TTA with the closest 20% of samples achieved 26.65% accuracy, whereas the farthest 20% showed a lower accuracy of 18.52%.

As early layers in deep learning models tend to retain domain-specific features [54, 19, 42], we utilize the hidden features of early layers to identify domain-representative samples (Appendix B.4). Specifically, CnDRM uses the feature statistics (mean and variance) of the first normalization layer to assess domain representation, since domain discrepancies can be effectively mitigated through normaliza-

Close

Far

PCA Feature 1

PCA Feature 2

PCA Feature 1

PCA Feature 2

Domain centroid)

Sampled Instance

All test data (KDE)

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KDE

66.08

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tion adjustments using these statistics [28, 40]. Domain discrepancies in hidden features are substantially reduced after passing through a single normalization layer, significantly minimizing domain shift [20]. While deeper layers provide detailed information, using the first layer balances capturing domain-specific information and maintaining computational efficiency.

The domain centroid c d is computed using a momentum-based update of batch statistics from the normalization layer: µ domain ← (1 -β ) µ domain + βµ t and σ 2 domain ← (1 -β ) σ 2 domain + βσ 2 t , where µ t and σ 2 t are the mean and variance of the current batch t , and β is the momentum parameter. In our preliminary study, we found that using only the mean and standard deviation values before the first normalization was sufficient to calculate the domain centroid. The sampled instances effectively represented the domain and were correctly positioned in the embedding space for each criterion (Figure 4).

We formally define a domain-representative sample as one whose early-layer feature statistics are closest to the domain centroid, as measured by the Wasserstein distance [47]. The Wasserstein distance quantifies the similarity between two distributions by considering their mean and variance, evaluating how well a sample represents the domain. It is useful for capturing domain characteristics, thus widely used in domain generalization [42]. Following common practice in domain adaptation [20, 27], we approximate channel-wise feature distributions as independent univariate Gaussians (i.e., with diagonal covariance) to efficiently estimate mean/variance-level domain shifts, which yields the following closed-form expression:

For each sample x t , the feature statistics ( µ x t , σ x t ) are taken from the input to the normalization layer. Further clarification and assumption details are provided in Appendix B.2.

Algorithm 1 Class and Domain Representative Memory (CnDRM) Management

Memory management algorithm. CnDRM maintains a compact yet adaptive memory that jointly preserves class balance and domain representativeness while keeping computational overhead minimal. To achieve this, the memory size is fixed to match the batch size for efficiency. Within this limited capacity, samples are managed so that each class remains well-represented while the overall memory distribution stays close to the domain centroid. Specifically, when the memory reaches its capacity, the farthest samples from the domain centroid (those with the largest Wasserstein distance) are replaced by new, high-confidence samples that better align with both class balance and domain characteristics. This joint management ensures that the memory continually retains the most classand domain-representative samples under dynamic distribution shifts.

Algorithm 1 implements these procedures: lines 8 ∼ 16 handle both class balancing and the remove domain-centroid farthest sample operation, where the least representative sample (i.e., the one with the largest Wasserstein distance within an overrepresented class) is discarded. Lines 17 ∼ 20 perform the update domain-centroid operation using a momentum-based moving average (with β = 0 . 9 ) that enables the centroid to smoothly adapt to the evolving feature distribution. This linkage clarifies how CnDRM maintains a unified class-domain representative memory throughout continuous adaptation on edge devices.

4.2 Inference-only Batch-aware Memory Normalization

Motivation. Sparse Test-Time Adaptation (STTA) requires models to adapt to domain shifts with limited update opportunities. Consequently, stored adaptation batch statistics may become misaligned with subsequent inference data when updates are skipped. Traditional normalization methods, relying solely on test batch statistics, also struggle with such shifts. To address this, we propose Inference-only Batch-aware Memory Normalization (IoBMN), which stabilizes adaptation by leveraging representative memory statistics while selectively adjusting for distributional mismatches. This approach ensures both robustness and adaptability in STTA, significantly improving model stability, as demonstrated in our ablation study (Section 5).

Approach. Given a feature map f ∈ R B × C × L , where B is the batch size, C is the number of channels, and L is the number of spatial locations, the batch-wise statistics ¯ µ c and ¯ σ 2 c for the c -th channel are calculated as follows:

where ¯ µ m and ¯ σ 2 m are calculated from the most recent adapted CnDRM samples in the same way with Equation 2, using the memory capacity M with m representing the memory. We assume that µ m and σ 2 m follow the sampling distribution of the feature map size L and memory capacity M . The corresponding variances for the memory mean µ m and variance σ 2 m are calculated as:

For the normalization process to adapt efficiently to the current inference batch statistics, IoBMN corrects (¯ µ m , ¯ σ 2 m ) only when ¯ µ c (and ¯ σ 2 c ) significantly differ from ¯ µ m (and ¯ σ 2 m ) through soft shrinkage function:

where α ≥ 0 in IoBMN controls the reliance on the normalization layer statistics. A larger α gives more weight to the last adapted memory normalization statistics, whereas a smaller α emphasizes the current inference batch normalization statistics. The soft shrinkage function S λ ( x ; λ ) is defined as:

where λ is the threshold and x is the input. The function allows for proportional adjustments based on the magnitude of the values, where smaller values are adjusted less and larger values more, preserving the critical information inherent in the adapted memory normalization statistics.

Finally, the output of the IoBMN for each feature f b,c,l is computed as:

where γ and β are learnable affine parameters of normalization layer, and ϵ is a small constant added for numerical stability. In our experiments, we chose α as 4 to handle various out-of-distribution scenarios effectively. The parameter s is a hyperparameter that determines the degree of adjustment desired and can be tuned based on specific requirements.

IoBMN utilizes CnDRM's class-domain representative statistics and adjusts them based on the current inferencing batch statistics. This dual-statistic approach allows IoBMN to correct the outdated and skewed distribution of the memory, ensuring alignment with the data distribution at each inference point. By leveraging the statistics of the data used during model update points, IoBMN adapts effectively without significant computational overhead. Additionally, this method mitigates the performance degradation caused by the prolonged intervals between adaptations so that the model remains well-aligned with the evolving data distribution.

Methods

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CIFAR100-C

Tent

46.71

48.06

40.98

65.19

44.10

62.78

63.95

55.43

55.46

59.32

67.43

63.83

53.89

59.40

49.91

55.76

-

4

.

54

+ STTA

43.55

44.25

37.95

62.56

41.80

59.45

62.13

53.04

51.60

56.76

64.60

61.19

51.01

56.42

46.28

52.84

(

-

2

.

92)

3.34

+ SNAP

46.51

47.68

39.92

65.39

44.14

63.29

64.53

55.20

55.55

59.71

68.05

64.90

53.91

59.28

49.58

55.84

(

+

0

.

08)

3.67

CoTTA

42.14

42.92

37.92

55.40

41.01

55.18

55.39

49.46

50.61

50.86

61.35

47.44

48.69

54.38

48.11

49.39

-

74.77

+ STTA

28.53

29.53

26.45

42.19

30.34

44.69

41.88

34.44

33.93

39.03

45.49

31.17

37.25

36.17

36.84

35.86

(-13.53)

4.94

+ SNAP

41.72

42.62

37.46

58.43

41.24

57.33

57.96

50.34

51.17

52.29

63.59

51.32

49.68

54.78

47.89

50.52

(+1.13)

4.95

EATA

38.42

39.96

32.64

62.35

38.73

59.93

61.07

50.50

50.79

55.30

64.38

60.63

49.66

53.63

43.02

50.74

-

4.25

+ STTA

38.41

39.03

32.29

61.07

38.45

58.21

60.62

49.59

49.19

54.23

62.88

57.39

49.00

53.01

42.05

49.70

(-1.04)

3.13

+ SNAP

40.62

41.53

34.31

64.08

40.29

61.32

63.04

52.00

51.77

56.85

65.98

61.96

51.05

55.67

44.80

52.35

(+1.61)

3.51

SAR

50.75

52.00

43.87

65.44

46.30

63.60

64.68

58.41

58.26

61.34

68.03

67.68

54.53

61.52

52.72

57.94

-

6.68

+ STTA

43.92

45.28

38.64

63.36

42.58

60.36

62.78

53.39

52.23

57.54

65.41

60.88

52.07

56.80

47.16

53.49

(-4.45)

2.95

+ SNAP

46.29

47.60

39.95

65.26

44.00

63.09

64.97

55.08

55.17

59.73

68.13

64.72

53.84

58.98

49.54

55.76

(-2.18)

3.09

RoTTA

38.54

39.85

33.73

63.45

40.74

60.54

62.03

51.61

51.75

56.20

65.14

61.55

51.22

54.42

42.50

51.55

-

6.71

+ STTA

36.28

37.12

31.38

61.20

38.36

58.26

60.30

49.20

48.21

53.54

62.80

56.78

49.61

52.28

41.26

49.11

(-2.44)

2.96

+ SNAP

37.83

38.42

32.38

63.73

39.72

61.32

62.58

51.38

51.18

55.61

65.70

61.39

51.36

54.51

42.85

51.33

(-0.22)

2.99

ImageNet-C

Tent

27.03

28.98

28.64

24.66

23.63

38.70

45.77

44.82

38.06

54.59

64.61

16.84

51.64

55.54

49.38

39.53

-

38.33

+ STTA

22.00

23.51

23.07

19.38

18.86

32.15

42.29

39.70

34.33

51.62

63.70

15.79

47.74

52.35

45.54

35.47

(-4.06)

18.01

+ SNAP

26.21

27.85

27.50

23.62

22.73

36.01

44.11

42.19

38.15

52.95

64.57

30.23

48.56

53.71

47.09

39.03

(-0.50)

18.76

CoTTA

13.12

13.98

13.94

12.44

12.18

23.74

35.22

31.78

30.26

44.40

62.40

15.13

40.42

45.26

36.53

28.72

-

300.23

+ STTA

10.97

11.92

11.98

11.45

11.38

22.39

34.96

30.88

29.89

44.09

61.96

13.08

40.20

45.27

36.71

27.81

(-0.91)

161.98

+ SNAP

15.13

16.03

15.91

13.86

14.02

24.90

36.51

32.56

31.81

46.02

63.60

15.69

41.94

46.78

38.03

30.19

(+1.47)

163.24

EATA

29.62

31.79

31.17

26.89

26.30

40.65

47.44

46.29

40.78

55.57

64.97

38.02

52.66

56.03

50.26

42.56

-

31.98

+ STTA

22.43

23.78

23.26

19.38

19.42

32.18

43.22

40.65

36.64

52.38

63.87

24.59

48.13

52.89

46.33

36.61

(-5.95)

16.00

+ SNAP

26.10

27.29

27.13

22.38

22.15

33.45

43.92

40.96

36.68

52.71

63.77

27.93

48.47

53.23

47.46

38.24

(-4.32)

17.45

SAR

29.23

31.14

29.88

29.29

27.39

39.76

44.13

45.98

29.39

55.13

63.71

17.34

52.31

56.09

49.35

39.34

-

78.15

+ STTA

26.12

27.56

26.93

22.51

23.35

36.03

44.48

43.19

37.26

53.82

64.15

19.87

50.78

54.78

48.43

38.62

(

-

0

.

72)

21.39

+ SNAP

30.28

31.97

31.30

26.67

26.31

39.66

46.08

45.43

40.26

54.76

64.62

36.12

51.26

55.42

49.63

41.99

(+2.65)

23.99

RoTTA

20.60

22.83

19.81

10.46

10.10

21.31

31.83

39.66

32.09

46.08

62.22

20.27

42.54

47.47

40.67

31.20

-

87.00

+ STTA

14.77

15.59

15.33

13.17

13.19

23.85

35.38

32.73

30.77

45.22

63.08

15.62

41.05

46.15

37.19

29.54

(

-

1

.

66)

45.98

+ SNAP

15.35

16.20

16.01

13.67

13.66

24.27

35.62

33.04

31.02

45.38

62.95

15.96

41.06

46.17

37.44

29.85

(-1.36)

47.47

5 Experiments

This section outlines our experimental setup and presents the results obtained under various STTA settings. Refer to Appendix A for further details.

Scenario. We varied the Adaptation Rates (AR) to examine how different update frequencies affect both model accuracy and latency under latency-constrained scenarios. In our setup, AR controls how frequently the model is adapted and also corresponds to the memory sampling rate, as the memory size equals the batch size. The main evaluation was run with diverse AR values: 0.01, 0.03, 0.05, 0.1, 0.3, and 0.5. We report the mean accuracy and standard deviation over three random seeds. Latency was measured on three representative edge devices: Raspberry Pi 4 [38], Zero 2W [39], and Jetson Nano [32].

Dataset and model. We used three standard TTA benchmarks: CIFAR10-C , CIFAR100-C and ImageNet-C [10] for main evaluation. These datasets include 15 different types of corruption with five levels of severity, and we used the highest one. We employed ResNet18 [8] as the backbone network, utilizing models pre-trained on CIFAR10 and CIFAR100 [18]. We also use ResNet50 [8] and Vit-Base [4] pre-trained on ImageNet [3] from the TorchVision [25] library.

Baselines. SNAP is designed to integrate with existing TTA algorithms. Therefore, testing existing TTA algorithms under different ARs serves as our baseline (implementation details, including hyperparameters, are in Appendix A.1). We selected five SOTA TTA algorithms: (i) Tent [48] updates only BN affine parameters, (ii) CoTTA [50] updates the entire model parameters using a teacher-student framework, (iii) EATA [30], (iv) SAR [31], and (v) RoTTA [53].

Overall performance across various adaptation rates. Table 1 and Appendix C provide a performance comparison of baseline state-of-the-art (SOTA) TTA methods and SNAP integration across adaptation rates from 0.01 to 0.5 on CIFAR10/100-C and ImageNet-C. The results reveal that while STTA reduces adaptation latency by up to 93.38%, conventional SOTA algorithms suffer significant accuracy degradation in STTA settings. In contrast, SNAP effectively mitigates this performance drop. By utilizing minimal updates with only a fraction of the samples, SNAP consistently outperforms baseline methods and achieves accuracy comparable to fully adapted models. These findings highlight SNAP's ability to balance efficiency and performance, preserving or even improving classification accuracy in sparse adaptation scenarios.

Figure 5 further illustrates that SNAP maintains STTA performance even at adaptation rates as low as 0.01 while significantly reducing latency. In contrast, naïve STTA suffers substantial performance degradation as the adaptation rate decreases. Notably, computationally complex and latency-intensive method CoTTA benefits more from SNAP. This is because CoTTA updates all model parameters, making it highly dependent on an effective sampling strategy, underscoring the effectiveness of CnDRM. At higher adaptation rates (0.5

84

44

82

80

78

76

74

72

70

68

66

64

62

60

14

12

10

8

6

4

2

0

1

0.5

0.3

0.1

0.05

0.03

0.01

36

38

40

42

Latency per Batch (s)

Accuracy (%)

1

0.5

0.3

0.1

0.05

0.03

0.01

Adaptation Rate

Adaptation Rate

TENT+SNAP

TENT

EATA+SNAP

EATA

SAR+SNAP

SAR

RoTTA+SNAP

RoTTA

CoTTA+SNAP

CoTTA

Y

or 0.3), SNAP can even surpass fully adapted methods by selectively utilizing the most informative samples, similar to existing sampling-based TTA methods [30, 31, 6, 7]. With sufficient samples and update frequency, SNAP's class-domain representative sampling filters harmful data points, further improving performance. Overall, these results confirm that SNAP significantly reduces per-batch latency while preserving accuracy, demonstrating its effectiveness in resource-constrained environments. Extended results on various adaptation rates and datasets (CIFAR10/100-C and ImageNet-C) are reported in Appendix C.

Contribution of SNAP's individual components. We conducted an ablative evaluation to understand the effects of the individual components of SNAP (Table 2; more results on various adaptation rates and datasets are in Appendix C.4). CRM denotes prediction-balanced sampling with a confidence threshold, and CnDRM denotes both Class and Domain Representative sampling (the first component of SNAP). For inference, the default uses test batch normalization statistics, EMA uses the exponential moving average of the test batch, and IoBMN uses memory samples' statistics corrected to match that of the test batch (the second component of SNAP).

Contrary to the belief that low-entropy samples benefit TTA [30, 31], LowEntropy performed worse than Rand for STTA, due to limited updates causing poor or slow convergence. CRM, originally for data-efficient supervised learning [2, 51], outperformed Rand but remained inferior to CnDRM due to reliance on uncertain pseudo-labels instead of ground truth. The highest accuracy was achieved with IoBMN, which mainly leverages memory

statistics and adapts minimally to each test batch. These indicate that combining CnDRM and IoBMN in SNAP enhances performance in low-latency STTA.

Performance validation across diverse edge-devices. SNAP significantly reduces adaptation latency across a range of edge devices. At an adaptation rate of 0.05, latency was reduced by up to 91.3% on Raspberry Pi 4 [38], 86.2% on Jetson Nano [32], and 93.7% on Raspberry Pi Zero 2 W [39]. This consistent trend across varying hardware confirms SNAP's effectiveness in latency-sensitive edge deployments. Complete results across all adaptation rates and devices are provided in Appendix B.6.

Memory overhead and compatibility with memory-efficient TTA. SNAP's memory overhead primarily comes from the memory buffer in CnDRM and statistics stored for IoBMN. Empirical results confirm that this overhead is minimal, accounting for only 0.02% to 1.74% of the original memory usage across all algorithms. Additionally, SNAP improves average memory efficiency by reducing backpropagation frequency. Further theoretical and experimental analyses of memory usage are provided in Appendix B.7. SNAP is also compatible with memory-efficient TTA modules like MECTA [12]. Integrating MECTA with Tent + SNAP reduces peak memory usage by 32.08%, showcasing its effectiveness in meeting both latency and memory constraints (Appendix B.8).

Tent +SNAP EATA +SNAP SAR +SNAP RoTTA +SNAP CoTTA +SNAP 46.22% 52.23% 47.77% 40.75% SNAP on vision transformer. We validate SNAP on ViT-Base [4] by adapting CnDRM and IoBMN to instance-level layer normalization (LN), replacing batch statistics. This confirms that our core strategies, class-domain sample selection and normalization shift mitigation, generalize to LN. SNAP achieves up to 2.9× latency reduction while preserving or improving full adaptation accuracy across all five baselines (Figure 6). Details are in Appendix B.9.

13

20

Robustness under continuous and persistent distribution shifts. SNAP adapts efficiently to evolving domains by smoothly moving its domain centroid with minimal overhead. In a continuous stream of corruptions from ImageNet-C, it outperforms naïve STTA by over 2.5% on average. We further assess long-term

13

20

30

50

100

200

Tent

+SNAP

EATA

+SNAP

SAR

+SNAP

RoTTA

+SNAP

CoTTA

+SNAP

39.53%

46.22%

1.8×

48.43%

52.23%

1.7×

43.86%

47.77%

2.5×

42.93%

40.75%

2.6×

39.41%

Original (Full)

SNAP (Sparse)

Latency per batch (s, log scale)

30

400

600

50

100

200

39.53%

1.8

×

48.43%

1.7

×

43.86%

2.5

×

42.93%

2.6

×

41.25%

39.41%

2.9

×

Original (Full)

SNAP (Sparse)

Latency per batch (s, log scale)

robustness under temporally correlated and recurring shifts [11]. Combined with SNAP, accuracy remains consistently above 50% over 10 adaptation rounds, whereas naive STTA alone degrades sharply, dropping to 16.97%. These results highlight SNAP's ability to maintain stable performance across both continuous and persistent distribution changes. Details are in Appendices B.13 and B.14.

Robustness in single-sample (BS=1) adaptation scenario. In highly constrained environments where the batch size is limited to one, SNAP maintains strong performance. It achieves 51.80% accuracy with an adaptation rate of 0.1, closely matching the full SAR [31] baseline at 52.21% and performing over 5× better than naïve STTA. CnDRM continues to effectively select informative samples, while IoBMN leverages memory-based statistics to adaptively normalize each input under this extreme regime. Further details are provided in Appendix B.15.

Impact of memory size and learning rate. SNAP demonstrates robustness to both memory sizes and learning rates. It adapts effectively with a memory size equal to the batch size, as larger sizes offer only 1 ∼ 2% marginal gains before saturation. Likewise, it outperforms all baselines across learning rates, showing up to 5 ∼ 10% absolute gains under sparse adaptation. These results underscore SNAP's efficiency and stability under constrained adaptation. Full analyses are in Appendices B.16 and B.17.

6 Discussion and conclusion

Limitations and societal impacts. SNAP uses a fixed adaptation rate, but dynamically adjusting it based on distribution shifts or system load could improve responsiveness. The confidence threshold in CnDRM is also fixed as a simple safeguard, which may limit adaptability. Dynamically tuning this threshold based on data characteristics could further enhance sampling efficiency. In addition, our implementation reduces average latency by adapting sparsely across batches, rather than explicitly optimizing backpropagation delay, due to PyTorch [33] constraints that require backpropagation to run as a single block. Future work could explore distributing the backpropagation step allocation across batches to further enhance applicability. Furthermore, deploying deep learning on edge devices at scale can raise societal concerns, such as carbon emissions [41]. By lowering computational overhead, SNAP helps mitigate these environmental impacts. It also reduces the need to transmit user data to the server, supporting stronger privacy in real-world applications.

Conclusion. We highlight the often-overlooked issue of TTA latency, a critical factor for resourceconstrained edge devices. To address this, we propose SNAP, a lightweight STTA framework that significantly reduces latency while preserving accuracy. SNAP leverages class-domain representative memory for adaptation and optimizes inference by adapting normalization layers using memory to account for domain shifts. Extensive experiments and ablation studies validate its effectiveness.

400

41.25%

2.9×

600

Acknowledgments and Disclosure of Funding

This work was partly supported by the Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No.2024-00444862, Non-invasive near-infrared based AI technology for the diagnosis and treatment of brain diseases), the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (RS-2024-00337007), and the Institute of Information & Communications Technology Planning &Evaluation (IITP) grant funded by the Korea government (MSIT) (RS-2025-25442824, AI Star Fellowship Program (Ulsan National Institute of Science and Technology)). ※ MSIT: Ministry of Science and ICT

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A Experiment details

All experiments presented in this paper were conducted using three random seeds (0, 1, 2), and we report the average accuracies along with their corresponding standard deviations. To ensure efficiency in experimentation, accuracy measurements were obtained using NVIDIA GeForce RTX 3090 GPUs, as the performance differences attributable to the random seed are negligible. Latency measurements were mainly conducted on a Raspberry Pi 4 [38], equipped with a Quad-core Cortex-A72 (ARM v8) 64-bit SoC @ 1.8GHz CPU and 4GB RAM. In addition, two more edge-devices: NVIDIA Jetson Nano [32] and Raspberry Zero 2 W [39] are also utilized for latency measurements.

A.1 Baseline implementation details

In this study, we utilized the official implementations of the baseline methods. To ensure consistency, we adopted the reported best hyperparameters documented in the respective papers or source code repositories as much as possible. Also, we present information about the implementation specifics of the baseline methods and provide a comprehensive overview of our experimental setup, including detailed descriptions of the employed hyperparameters.

We adopt hyperparameters from the original papers or the official code of the baselines for consistency. To assess the generality of SNAP, the test batch sizes were set to 16 for all baseline methods to ensure a fair comparison. To minimize overhead and maintain consistency with inference batches, we set the size of CnDRM equal to the batch size. TTA is conducted in an online manner, with adaptation or inference performed per batch. When there was a conflict between the implementation of SNAP and certain components of the existing baseline methods, we prioritized SNAP's features for fair evaluation at the STTA setting.

Tent [48] We update the BN affine parameters using the SGD optimizer [24] with a learning rate of l = 1 e -3 for CIFAR10/100C and l = 1 e -4 for ImageNet-C. For separate experimentation on the ViT, we used a learning rate of l = 2 e -4 .

CoTTA [50] We update all model parameters using the Adam optimizer [15] with a learning rate of l = 1 e -4 . Furthermore, we set CoTTA's teacher model EMA factor to α = 0 . 99 , the restoration factor to p = 0 . 1 , and the anchor probability to p th = 0 . 9 .

EATA [30] We use the SGD optimizer with a learning rate of l = 1 e -4 . We set the entropy threshold as E 0 = 0 . 4 × ln | N | , where N is the total number of classes.

SAR [31] We use SAM [5] with the base optimizer as SGD with a learning rate of l = 1 e -3 . For fair evaluation, we replaced the sample filtering scheme with SNAP's CnDRM.

RoTTA [53] We use the SGD optimizer with a learning rate of l = 1 e -3 . For fair evaluation, we replaced RoTTA's RBN and CSTU with SNAP's CnDRM and IoBMN. For the teacher-student structure, we set the teacher model's exponential moving average update rate as v = 1 e -3 .

Finally, we list the hyperparameters specific to the components of SNAP. The confidence threshold for CnDRM τ conf is set to 0.4 for CIFAR10-C, 0.45 for CIFAR100-C, and 0.5 for ImageNet-C. The entropy threshold for our ablation study τ entr is set to log(10) × 0 . 40 for CIFAR10-C and log(100) × 0 . 40 for CIFAR100-C, as referenced in a previous work using entropy-based filtering [30]. Additionally, the parameters for the soft shrinkage function in IoBMN are fixed with α = 4 for Tent, CoTTA, SAR, RoTTA, and α = 2 for EATA.

B Additional discussions

B.1 Theoretical analysis on class and domain representative sampling criteria

The sampling strategy in SNAP's CnDRM module is grounded in theoretical insights from dataefficient learning and generalization under constrained adaptation settings. Under latency-constrained scenarios, models can only adapt intermittently. This raises the following question:

Which subset of streaming samples yields the greatest adaptation gain when only a fraction ρ = n/N of them can be used for weight updates?

Selection ratio and phase transition. Let ρ = n/N ∈ (0 , 1] denote the adaptation ratio, where n is the number of selected samples for model update out of N total seen test samples. Theoretical and empirical studies [2, 44, 17] show that the optimal selection strategy varies significantly depending on the value of ρ :

When ρ > 0 . 6 (high adaptation rate), selecting low-confidence samples near decision boundaries provides maximal information gain.

When ρ ≤ 0 . 5 (sparse adaptation), selecting high-confidence, representative samples near class or domain centroids leads to better generalization.

This dichotomy is supported analytically in [2], which shows that in underparameterized regimes, boundary samples may inject noisy gradients and destabilize learning.

Illustrative example. Consider a binary classification task where inputs x i ∼ N (0 , 1 √ d I d ) , and labels are assigned by y i = sign( x i 1 ) . The Bayes-optimal classifier aligns with e 1 , the first basis vector. Suppose we select a subset ( X S , y S ) ∈ R d × n ×{-1 , 1 } n and compute the ridge regression solution:

As shown in prior work [2], in the sample-deficient regime ( n ≪ d ), the solution w S aligns best with the true decision direction when trained on high-confidence samples. In contrast, in the samplesufficient regime ( n ≫ d ), boundary samples become more beneficial for refining decision boundaries.

Sampling criterion under sparse adaptation. Based on this, the optimal update subset S ∗ ⊂ D test under ρ ≪ 1 can be defined as:

where µ c i is the estimated feature-space class centroid. This motivates our use of class- and domainrepresentative memory (CnDRM), which prioritizes confident, centroid-aligned samples for parameter updates under low-frequency adaptation.

Under sparse adaptation ( ρ ≪ 1 ), selecting the most informative subset of test samples becomes critical. Our method prioritizes samples that are both semantically reliable (class-representative) and statistically aligned (domain-representative).

For the class-representative criterion, we follow insights from [2], which show that in the sampledeficient regime, high-confidence samples, those far from the decision boundary, yield better generalization than boundary samples. Rather than explicitly computing class centroids, we approximate class-representative samples by selecting those with the highest prediction confidence:

where Conf ( x i ) = max j f j ( x i ) is the softmax confidence score and τ is a confidence threshold.

To additionally enforce domain-level representativeness, we compute the Wasserstein-2 distance between each candidate sample and the estimated domain distribution. Specifically, each domain d is modeled as a Gaussian N ( ν d , Σ d ) , where:

Each sample x i is treated as an empirical distribution N ( µ i , Σ i ) using a local batch of neighboring features. The closed-form squared 2-Wasserstein distance between two Gaussians is given by:

Combining both criteria, our final selection strategy becomes:

i.e., we select a subset of high-confidence samples that are also distributionally aligned with the estimated domain centroid. This ensures that parameter updates occur on samples that are both semantically stable and statistically representative under test-time domain shift.

Practical implementation. In our system, we operate with ρ < 0 . 5 (e.g., update every two test batches). While this reduces update opportunities, the degradation in performance is mitigated via CnDRM's informed sample selection. In addition, SNAP integrates IoBMN (Inference-only Batch-aware Memory Normalization), which updates batch norm statistics from all incoming samples, even if they are not used for weight updates. This reduces covariate shift and maintains normalization stability across domains.

B.2 Assumptions and derivation of the Wasserstein formulation

The closed-form expression in Equation 1 assumes that feature distributions are Gaussian with diagonal covariance. This section clarifies the underlying assumptions and derivation.

Distribution definition. The distribution in Equation 1 refers to the empirical distribution of scalar feature activations per channel , rather than the input data distribution. We consider each channel's activation statistics (mean and variance) in a deep layer's feature map.

Wasserstein approximation and assumptions. To compute the Wasserstein distance efficiently, the feature distributions are approximated as univariate Gaussian distributions for each channel. These distributions are assumed to be independent, corresponding to a diagonal covariance assumption. The detailed assumptions are as follows:

Gaussian assumption: Each channel's activations are assumed to follow a Gaussian distribution N ( µ, σ 2 ) , which simplifies the formulation since Gaussian distributions are fully determined by their mean µ and variance σ 2 . This approximation is commonly adopted in deep learning, where normalized feature activations tend to exhibit near-Gaussian behavior in high-dimensional feature spaces.

Diagonal covariance: The covariance matrix for each Gaussian is assumed to be diagonal, implying independence across channels. This assumption is widely used in domain adaptation and transport-based methods, as it reduces the computational complexity of full covariance estimation while focusing on per-channel variance shifts.

2-Wasserstein distance for Gaussian distributions: Under these assumptions (independent Gaussian distributions), the squared 2-Wasserstein distance between two univariate Gaussian distributions N ( µ 1 , σ 2 1 ) and N ( µ 2 , σ 2 2 ) is given by:

This closed-form expression enables efficient computation of the Wasserstein distance without estimating full covariance matrices, which is computationally expensive.

Such approximations are widely adopted in the domain adaptation literature [20, 27], as they balance computational efficiency and empirical performance while providing a meaningful measure of domain-level similarity.

B.3 Comparison with prior TTAs under sparse update constraints

While prior TTA studies have partially explored using memory banks and the correction of Batch Normalization (BN) statistics at inference time, our key contribution lies in systematically redesigning these components for sparse-update regimes in resource-constrained environments, which impose fundamentally different computational and statistical constraints.

CnDRM vs. Prior memory-based sampling (RoTTA [53], NOTE [6], SAR [31], and EATA [30]) Previous methods assume frequent adaptation, updating every batch and using more than 50% of test samples. They typically select temporally balanced or low-entropy samples for updates. In contrast, our goal is Sparse TTA (e.g., 10% adaptation rate), where such filtering leaves too few useful samples for effective adaptation. To address this, CnDRM avoids low-entropy filtering and instead selects representative samples based on domain centroids and class confidence. This approach enables efficient adaptation with minimal latency. Theoretical analysis (Appendix B.1) and ablation results (Table 2, Appendix C.4) show that prior entropy-based filtering performs worse than even random selection under sparse-update settings.

IoBMN vs. Instance-wise BN correction (NOTE [6]) NOTE corrects BN statistics per instance, which introduces latency proportional to the number of test samples. In contrast, IoBMN leverages domain-class statistics from CnDRM's memory to correct batch BN statistics efficiently while remaining compatible with batch inference. The memory statistics are adaptively shifted toward batch statistics to mitigate skew from sparse updates. This design enhances computational efficiency and normalizes using adaptation-involved samples, yielding consistent performance gains (Table 2, Appendix C.4).

B.4 Domain influence in early layer representations

In deep learning models, early layers capture low-level features such as textures, edges, and frequency components [54]. These features are inherently domain-specific, making these layers more sensitive to shifts in input data distribution-a critical challenge for tasks requiring domain adaptation and generalization [19, 42]. This sensitivity arises because early layers encapsulate domain-specific patterns that may not generalize to new distributions. Under the covariate shift assumption [37], while input distributions differ between source and target domains, the conditional distribution of labels remains the same. This discrepancy between input distributions makes early layers particularly vulnerable to domain shifts.

Visualizing early layer feature embeddings using 2D PCA on CIFAR10C domains reveals distinct domain-specific patterns, highlighting

PCA Feature 1

PCA Feature 2

Noise (Gau.)

Blur (Mot.)

Weather (Snow.)

Digital (Cont.)

the significant influence of domain information in these representations (Figure 7). Our preliminary experiments further confirm that sparse TTA, using the Wasserstein distance between moving batch normalization statistics and instance-specific statistics derived from early layer hidden features, can significantly improve performance. Selecting instances closer to the target domain distribution center using this distance metric yields better adaptation results, as demonstrated by performance comparisons between the top 20% and bottom 20% of samples (Figure 4). These findings emphasize the crucial role of domain-sensitive early layers in achieving effective adaptation.

B.5 Analysis on confidence threshold on pseudo-label accuracy

We analyzed the impact of using a confidence threshold for pseudo-label selection by comparing random sampling with high-confidence sampling across three benchmarks: CIFAR10-C, CIFAR100-C, and ImageNet-C. Table 3 shows that high-confidence sampling consistently outperformed random sampling, achieving significantly higher pseudo-label accuracy in all datasets. This result demonstrates the effectiveness of selecting high-confidence samples to improve the quality of pseudo-labels, thereby enhancing model adaptation under domain shift conditions.

B.6 Latency tracking of SNAP on diverse edge-devices

Tent

Original TTA

SNAP-TTA

To evaluate the latency efficiency of SNAP on resource-constrained edge devices, we measured the adaptation latency across three devices: NVIDIA Jetson Nano [32], Raspberry Pi 4 [38], and Raspberry Pi Zero 2 W [39]. These experiments compared the latency of SNAP with the Original TTA framework, specifically focusing on five state-of-the-art TTA algorithms: Tent [48], EATA [30], SAR [31], RoTTA [53], and CoTTA [50]. The experiments were conducted at an adaptation rate of 0.1, demonstrating the effectiveness of SNAP in reducing adaptation latency while maintaining competitive accuracy. Figure 8 illustrates the latency performance for each device. It is evident 0 10 20 30 40 50 CoTTA RoTTA SAR EATA Average Latency per Batch (s)

0

5

10

15

CoTTA

RoTTA

SAR

EATA

Tent

Average Latency per Batch (s)

Original TTA

SNAP-TTA

0

10

20

30

40

50

CoTTA

RoTTA

SAR

EATA

Tent

Average Latency per Batch (s)

Original TTA

SNAP-TTA

0

200

400

600

800

CoTTA

RoTTA

SAR

EATA

Tent

Average Latency per Batch (s)

Original TTA

SNAP-TTA

RoTTA SAR EATA Tent Original TTA SNAP-TTA Figure 8: Latency comparison between SNAP-TTA and Original TTA across five state-of-the-art TTA algorithms (Tent, EATA, SAR, RoTTA, CoTTA) on three edge devices: (a) NVIDIA Jetson Nano, (b) Raspberry Pi 4, and (c) Raspberry Pi Zero 2 W. SNAP-TTA demonstrates significant latency reductions while maintaining competitive adaptation performance. The experiments were conducted at an adaptation rate of 0.1.

CoTTA

0 200 400 600 800 Average Latency per Batch (s) that SNAP achieves a significant reduction in adaptation latency compared to the Original TTA framework. Notably, the latency reduction was proportional to the adaptation rate, validating the efficiency of SNAP in sparse adaptation scenarios. For instance, the latency for CoTTA was reduced by up to 87.5% on the Raspberry Pi 4, emphasizing the practical benefits of SNAP in latency-sensitive environments. Additionally, similar trends were observed across other devices, including the resourcelimited Raspberry Pi Zero 2 W. Since SNAP is hardware-agnostic, accuracy was not measured separately for each device, and no accuracy differences are expected. The results confirm that SNAP not only ensures substantial latency reductions but also adapts effectively to real-world conditions on diverse edge devices, proving its suitability for deployment in latency-sensitive applications.

B.7 Memory overhead of SNAP

The SNAP framework achieves substantial latency reduction and accuracy improvements with minimal memory overhead, even under resource-constrained scenarios like edge devices. In this section, we present both a theoretical analysis of the memory requirements and empirical results obtained from evaluations on a Raspberry Pi 4[38] (CPU-only edge device).

The memory overhead of SNAP arises from two main components: (1) the memory buffer in Class and Domain Representative Memory (CnDRM) for storing representative samples, including both feature statistics (mean and variance) and the raw image samples, and (2) the statistics required for Inference-only Batch-aware Memory Normalization (IoBMN). For a batch size B , the total theoretical memory overhead can be expressed as: Memory Overhead = B × ( Image Size +2 × Feature Dimension × Bytes per Value )+ Feature Dimension × Bytes per Value × 2 . The last term accounts for the storage of IoBMN statistics (mean and variance for each feature channel). The image size is calculated based on the dataset resolution and data type.

For ResNet18 on CIFAR10-C, CIFAR10 images have a resolution of 32 × 32 × 3 with each value stored as 1 byte. For a feature dimension of 512 and batch size B = 16 , the total overhead is: Image Overhead = 16 × (32 × 32 × 3 × 1) = 49 , 152 bytes (48 KB) , Feature Overhead (CnDRM) = 16 × (512 × 2 × 4) = 65 , 536 bytes (64 KB) , Feature Overhead (IoBMN) = 512 × 2 × 4 = 4 , 096 bytes (4 KB) . Thus, the total memory overhead is: Total Overhead = 48 KB + 64 KB + 4 KB = 116 KB .

For ResNet50 on ImageNet-C, ImageNet images have a resolution of 224 × 224 × 3 , stored as 1 byte per value. For a feature dimension of 2048 and batch size B = 16 , the total overhead is: Image Overhead = 16 × (224 × 224 × 3 × 1) = 12 , 044 , 928 bytes (11.5 MB) , Feature Overhead (CnDRM) = 16 × (2048 × 2 × 4) = 262 , 144 bytes (256 KB) , Feature Overhead (IoBMN) = 2048 × 2 × 4 = 16 , 384 bytes (16 KB) . Thus, the total memory overhead is: Total Overhead = 11 . 5 MB +256 KB +16 KB ≈ 11 . 77 MB .

Table 7 shows the empirical memory usage of SNAP compared to Original TTA methods (Tent, EATA, CoTTA, SAR, and RoTTA). The results were averaged across three seeds of experiments and represent the memory footprint observed in a CPU-only edge device, Raspberry Pi 4. While minor variations in measurements are expected due to the nature of CPU memory footprint tracking, the results robustly indicate that the actual memory overhead of SNAP on edge devices is extremely low across all algorithms, ranging from 0.02% to 1.74%. Furthermore, while peak memory usage is either slightly increased or remains comparable to Original TTA methods, the average memory usage of SNAP is consistently lower. This is because SNAP performs backpropagation infrequently, which is the most memory-intensive operation in TTA.

These findings demonstrate that SNAP's memory overhead is negligible compared to its benefits in latency reduction and accuracy improvements . By leveraging a small memory buffer for representative samples and minimizing backpropagation operations, SNAP not only achieves a lightweight memory profile but also becomes more efficient in terms of average memory usage compared to Original TTA. This lightweight design, combined with its advantages in latency and accuracy, underscores the practicality of SNAP for deployment in latency-sensitive applications on edge devices.

B.8 Integration of SNAP with memory-efficient TTA algorithm

This section evaluates the integration of SNAP with MECTA [12], a memory-efficient TTA algorithm, to demonstrate its applicability for resource-constrained edge devices. The experimental setup follows the evaluation settings presented in the MECTA paper to ensure a fair and consistent comparison. Specifically, we analyze the performance of Tent and EATA, enhanced with MECTA and further integrated with SNAP, using the ResNet50 model with a batch size of 64 on the ImageNet-C dataset.

Table 8 presents the classification accuracy and peak memory usage for Tent+MECTA and EATA+MECTA configurations with and without SNAP. Integrating SNAP with Tent+MECTA improves accuracy from 35.21% to 39.52%, while reducing peak memory usage by approximately 30% compared to the Tent baseline. Similarly, SNAP boosts the accuracy of EATA+MECTA from 35.55% to 42.86% while maintaining an efficient memory footprint.

Further details are provided in Table 9, which evaluates the combination of SNAP with MECTA across various corruption types and adaptation rates (AR = 0.3, 0.1, and 0.05). These results show that SNAP consistently outperforms baseline configurations across all adaptation rates and corruption types. This demonstrates the robustness of SNAP when integrated with MECTA and its suitability for real-world applications.

By adhering to the evaluation settings of the MECTA paper, this study ensures high reliability and comparability of results. The findings confirm that SNAP is highly compatible with MECTA, significantly improving both accuracy and memory efficiency. This synergy highlights the potential of combining SNAP and MECTA for deployment in resource-constrained environments such as edge devices.

B.9 Modification for layer normalization of Vision Transformer

The main text describes the use of Batch Normalization (BN) statistics for calculating domain centroids and centroid-instance distances, with subsequent adjustment of memory statistics to match the target test batch using the Inference-only Batch-aware Memory Normalization (IoBMN) method. Specifically, these calculations leverage the mean and variance across batches as follows:

where B represents the batch size, L the number of spatial locations, and c the channel index.

However, modern models like Vision Transformer (ViT) utilize Layer Normalization (LN) instead of BN. Unlike BN, which calculates statistics across the entire batch, LN normalizes each instance independently by using the statistics calculated over individual feature dimensions. Specifically, for a feature vector f b belonging to the b -th instance, LN computes:

where C is the number of channels. This difference implies that LN operates without batch-level interactions, focusing solely on within-instance normalization, which makes the method inherently more suitable for handling variable batch sizes, particularly in latency-sensitive applications like those considered in our Test-Time Adaptation (TTA) setting.

Despite the differences between BN and LN, the fundamental mechanism of using feature statistics to capture domain information remains valid. The key domain characteristics in early layer features are preserved in both normalization types, enabling the construction of a domain centroid that reflects the distributional characteristics of the test data. For LN, this centroid can be computed by aggregating across instances instead of across batches:

where M is memory capacity. This modified approach allows the domain centroid to still represent the overall domain-specific characteristics effectively, despite the lack of direct batch-level statistics.

Furthermore, this methodology extends seamlessly to other normalization layers, such as Group Normalization (GN). In GN, the statistics are computed across smaller groups of channels within

each instance, but the procedure for aggregating these statistics to form a domain centroid remains the same-by averaging the group-level statistics across instances.

To maintain the core concept of selecting domain-representative samples with minimal modifications, we continue to use the memory of high-confidence domain-representative samples in the Inferenceonly Batch-aware Memory Normalization (IoBMN) strategy. The adjustment for LN requires: 1. Calculating LN-specific centroids as described in Equation 15. 2. Replacing BN statistics with LN statistics in the IoBMN module, thereby aligning the feature normalization during inference with the domain-representative information derived from memory.

The effectiveness of this modification was validated experimentally, as shown in Table 10, 11, where ViT models using LN showed improved performance even under sparse TTA conditions. This indicates that, with minimal adjustments, SNAP remains effective for ViT with LN. The core principle of utilizing domain-representative statistics for aligning test-time feature distributions continues to provide significant benefits, ensuring robust adaptation in shifting domains with limited latency and computational overhead.

B.10 Comparison with forward-only TTA methods

Forward-only TTA methods, such as T3A [13] and FOA [29], aim to reduce computational burden by removing gradient-based updates. Instead, they update lightweight components: class prototypes in T3A and learned prompts in FOA. While these methods improve runtime efficiency, they exhibit structural limitations that hinder their robustness under dynamic distribution shifts.

Dataset

Method

Gau.

Shot

Imp.

Def.

Gla.

Mot.

Zoom

Snow

Fro.

Fog

Brit.

Cont.

Elas.

Pix.

JPEG

Lat.(s)

ResNet50

ImageNet-C

(i.i.d)

14.03

14.21

14.56

12.97

13.07

23.02

34.67

30.79

27.84

43.95

61.51

12.57

39.79

44.50

36.11

28.24

18.35

T3A

±0.09

±0.43

±0.07

±0.18

±0.06

±0.21

±1.17

±0.15

±0.29

±0.06

±0.22

±0.91

±0.19

±1.46

±0.51

±0.39

±0.59

26.21

27.85

27.50

23.62

22.73

36.01

44.11

42.19

38.15

52.95

64.57

30.23

48.56

53.71

47.09

39.03

18.76

Tent+SNAP

±0.14

±0.19

±0.16

±0.15

±0.23

±0.17

±0.12

±0.21

±0.18

±0.11

±0.27

±0.15

±0.13

±0.26

±0.19

±0.30

ViT-Base

41.34

40.96

42.68

36.27

29.94

40.34

40.89

47.20

59.07

63.71

72.95

46.98

44.75

45.40

55.87

47.22

694.8

FOA (K=28)

±0.21

±0.39

±0.20

±0.06

±0.27

±2.03

±1.56

±0.14

±0.07

±0.12

±0.14

±0.51

±8.41

37.53

35.84

39.36

34.25

27.45

37.85

34.43

43.65

56.10

62.84

71.79

39.38

44.29

41.33

53.06

43.94

81.43

FOA (K=2)

±0.30

±0.12

±0.03

±0.27

±0.16

±0.12

±0.06

±0.11

±0.19

±0.04

±0.68

±0.18

±0.09

±0.05

±0.37

±4.12

41.98

42.72

43.18

38.16

33.30

43.89

39.44

47.19

53.50

54.11

73.25

40.25

47.77

52.53

56.99

47.23

83.51

Tent+SNAP

±0.12

±0.22

±0.13

±0.11

±0.13

±0.21

±0.18

±0.09

±0.18

±0.20

±0.08

±0.25

±0.17

±0.12

±0.24

±0.16

±0.32

ResNet50

ImageNet-C

(non-i.i.d)

11.75

11.94

11.44

11.30

10.98

19.98

31.30

27.16

24.51

38.35

56.31

10.89

37.41

42.95

32.52

25.25

18.82

T3A

±0.06

±0.22

±0.05

±0.17

±1.34

±0.12

±0.27

±0.07

±0.18

±1.02

±0.23

±1.39

±0.49

±0.42

±0.57

24.00

24.69

24.78

21.37

21.15

32.20

42.83

39.26

35.41

51.17

62.89

21.25

46.95

52.31

45.60

36.39

18.98

Tent+SNAP

±0.11

±0.25

±0.14

±0.13

±0.12

±0.19

±0.22

±0.16

±0.24

±0.09

±0.28

±0.18

±0.15

±0.23

±0.14

±0.29

ViT-Base

38.36

36.23

39.47

33.07

25.35

36.44

35.80

42.86

55.45

61.67

70.60

39.87

41.81

43.05

52.42

43.50

710.2

FOA (K=28)

±0.11

±0.41

±0.05

±0.20

±0.04

±0.19

±1.26

±0.14

±0.24

±0.08

±0.19

±0.20

±1.43

±0.54

±0.40

±7.33

35.84

33.74

36.03

30.48

23.24

34.34

32.03

40.98

53.98

59.78

68.24

29.79

39.50

39.50

50.80

40.62

85.19

FOA (K=2)

±0.17

±0.00

±0.81

±0.09

±0.04

±0.04

±0.06

±0.06

±0.07

±0.09

±0.04

±0.22

±0.03

±0.07

±0.13

±5.84

38.02

38.31

40.22

35.37

30.20

40.17

37.20

44.57

54.78

52.01

73.19

24.68

45.64

47.08

55.66

43.81

87.54

Tent+SNAP

±0.73

±0.50

±0.83

±0.11

±0.60

±0.48

±0.54

±0.27

±0.77

±0.22

±0.32

±0.47

±0.81

±0.83

±0.52

±0.51

Prototype-based. T3A maintains a fixed feature extractor and updates per-class prototypes using pseudo-labels from incoming samples. Although it avoids backpropagation, T3A accumulates a growing support set of query features per pseudo-label to refine class-wise prototypes. This not only increases memory usage, but also incurs non-negligible latency during inference, especially when the number of classes is large (e.g., 1000-way classification in ImageNet) or when operating on edge devices. Matching a test sample against all stored support features becomes increasingly costly in such settings. As shown in Table 12, T3A achieves latency comparable to Tent+SNAP but consistently performs worse in accuracy, especially under non-i.i.d. ImageNet-C streams. This illustrates the limitation of relying solely on forward-only label-space correction without feature-level adaptation.

Prompt-based. FOA [29] introduces learnable prompts to adapt ViT encoders without backpropagation. However, it suffers from a trade-off between latency and accuracy, which is determined by the number of forward passes (K) required per test sample. While FOA theoretically avoids gradients, it performs K repeated forward steps to refine prompts, still incurring notable cost on edge devices. As shown in Table 12, FOA with its default configuration (K = 28) incurs significantly higher latency than Tent+SNAP, while achieving similar accuracy. Reducing K to 2 reduces latency to a comparable level, but results in substantial performance degradation, showing strong sensitivity to prompt update

depth. Moreover, FOA fails to generalize to CNNs, where the original paper [29] reports lower performance than Tent due to structural misalignment with the ViT-specific prompt.

Conclusion. In contrast, SNAP with Tent performs sparse backpropagation on confidently selected samples, striking a balance between low latency and high robustness. Despite using gradients, our latency profiling shows that Tent+SNAP remains within the latency range of forward-only methods, while outperforming them in accuracy across both i.i.d. and non-i.i.d. domains. This demonstrates the efficacy of targeted feature-level adaptation over purely forward-only correction.

B.11 Robustness in challenging out-of-distribution domains

To validate SNAP under more visually challenging and abstract domain shifts, we additionally apply SNAP to two nontrivial out-of-distribution datasets: ImageNet-R and ImageNet-Sketch . These datasets feature semantic deformation (R), sketch-style abstraction (Sketch), and both differ significantly from typical texture- and structure-rich natural images seen in ImageNet.

We test SNAP with an adaptation rate (AR) of AR=0.1 on five representative TTA backbones (Tent, CoTTA, EATA, SAR, and RoTTA) and compare results with full adaptation (AR=1.0). As summarized in Table 13, SNAP consistently maintains competitive performance with considerably reduced latency, demonstrating its suitability for low-overhead deployment under difficult real-world shifts.

B.12 Efficient strategy for re-calculation of sample's distance

The domain centroid in our framework is updated using a momentum-based approach to effectively capture recent shifts in the target domain. This ensures that the centroid remains adaptive to evolving distributions without being overly influenced by temporary fluctuations. However, during sparse adaptation (SA), where model updates occur at extended intervals, the data distribution can shift substantially between updates. Consequently, distances calculated for older samples may become outdated, leading to inconsistencies when comparing them to more recently added samples that are evaluated based on the updated centroid.

To address this issue efficiently, our Class and Domain Representative Memory (CnDRM) recalculates the distance of samples only when the shift in the domain centroid exceeds a predefined significance threshold. Specifically, if the change in the domain centroid ∆ c domain surpasses a threshold τ ∆ , the distances of all samples in memory are updated to reflect the new domain conditions. This threshold-based approach ensures that recalculations occur only when necessary, thereby minimizing computational costs while maintaining the representativeness of the memory.

In practice, we observed that the performance was not significantly affected as long as the threshold τ ∆ was not set too high, indicating robustness to the choice of threshold. Based on these observations, we set τ ∆ = 0 . 1 and used this value consistently for all evaluations. By focusing recalculations on significant shifts, this strategy preserves consistency in sample selection, ensuring that both older and newer samples are compared fairly in the context of the current domain characteristics without excessive computational overhead.

B.13 Strategy for continuous domain shift setting

In our proposed framework, the centroid used for selecting domain-representative samples naturally adapts to changes in the domain as new data is encountered. This mechanism inherently ensures that the centroid evolves to reflect the characteristics of the current domain, allowing for effective performance even under continual Test-Time Adaptation (TTA) scenarios, where the domain may gradually or abruptly shift during adaptation.

Instead of employing additional mechanisms like z-score evaluation to detect domain shifts, we rely on the natural adaptability of the centroid to adjust to the incoming data. This simplifies the design and avoids unnecessary overhead while maintaining robustness. As the domain characteristics evolve, the centroid continuously aligns with the new domain without requiring explicit detection of changes or manual intervention.

To validate the effectiveness of SNAP under continual domain shift scenarios, we conducted experiments across various benchmark datasets with incremental and abrupt domain shifts. Table 14 summarizes the results, demonstrating that SNAP maintains strong performance across evolving domains without requiring additional computational overhead for explicit domain shift detection.

These results indicate that SNAP effectively handles both incremental and abrupt domain shifts, consistently outperforming baseline methods. By leveraging the natural adaptability of the centroid, SNAP provides a robust solution for continual domain adaptation in real-world scenarios. Notably, SNAP mitigates catastrophic forgetting not only through its sparse adaptation strategy but also by leveraging domain centroid-based sampling, allowing performance to be sustained longer in continual shift scenarios. Unlike Tent, CoTTA is specifically designed for continual domain shift environments, which highlights its superior performance under such conditions.

Future work could explore augmenting this adaptive mechanism by incorporating techniques like zscore evaluation to enable even more responsive adjustments. For instance, a z-score-based approach could further refine the centroid's responsiveness to subtle, gradual domain shifts by monitoring discrepancies between incoming data statistics and the current centroid. Such enhancements could make the system even more effective at handling continual domain evolution, particularly in scenarios with complex or noisy data streams.

AR

Method

Gau.

Shot

Imp.

Def.

Gla.

Mot.

Zoom

Snow

Fro.

Fog

Brit.

Cont.

Elas.

Pix.

JPEG

24.68

19.65

5.12

0.63

0.43

0.40

0.44

0.41

0.30

0.33

0.42

0.24

0.32

0.31

0.31

3.60

Tent

±0.45

±1.22

±0.05

±0.02

±0.04

±0.06

±0.03

±0.03

±0.04

±0.05

±0.04

±0.02

±0.05

±0.04

±0.23

28.71

30.60

22.91

6.13

1.62

0.87

0.88

0.64

0.64

0.66

0.75

0.44

0.60

0.63

0.61

6.45

+ SNAP

±0.66

±1.82

±2.25

±0.90

±0.20

±0.13

±0.07

±0.08

±0.06

±0.05

±0.01

±0.05

±0.08

±0.07

±0.07

±0.43

10.99

12.21

11.54

11.28

11.13

22.08

34.80

30.69

29.45

43.87

61.92

12.76

40.03

44.99

36.43

27.61

CoTTA

±0.40

±0.04

±0.30

±0.13

±0.15

±0.07

±0.18

±0.04

±0.19

±0.09

±0.16

±0.13

±0.14

±0.16

±0.15

15.19

15.97

15.91

13.94

14.18

24.76

36.50

32.61

31.76

46.14

63.60

15.60

42.17

46.77

38.08

30.21

0.1

+ SNAP

±0.17

±0.11

±0.02

±0.04

±0.03

±0.07

±0.23

±0.04

±0.06

±0.14

±0.04

±0.02

±0.06

±0.12

±0.08

23.31

27.08

22.71

9.72

4.14

2.03

1.16

0.66

0.45

0.47

0.61

0.33

0.47

0.47

0.46

6.27

Tent

±0.37

±1.13

±2.50

±3.35

±3.00

±1.53

±0.75

±0.22

±0.12

±0.09

±0.16

±0.09

±0.08

±0.08

±0.07

±0.90

27.10

33.41

31.78

19.85

16.94

14.75

12.46

5.53

2.69

1.47

1.52

0.67

0.88

0.89

0.84

11.39

+ SNAP

±0.23

±0.62

±1.50

±2.53

±4.27

±2.30

±1.18

±0.49

±0.40

±0.09

±0.07

±0.98

11.04

12.25

11.73

11.62

11.25

22.05

34.89

30.73

29.50

44.09

61.87

12.87

40.15

45.06

36.53

27.71

CoTTA

±0.39

±0.42

±0.59

±0.13

±0.13

±0.20

±0.17

±0.18

±0.09

±0.18

±0.17

±0.19

±0.14

±0.23

15.20

15.89

15.93

13.81

14.15

24.74

36.68

32.51

31.71

46.11

63.48

15.73

42.20

46.69

38.05

30.19

0.05

+ SNAP

±0.15

±0.02

±0.04

±0.03

±0.16

±0.27

±0.04

±0.20

±0.05

±0.09

±0.19

±0.12

±0.04

B.14 Robustness under persistent distribution shifts

To evaluate the long-term stability of SNAP under temporally correlated and recurring domain shifts, we adopt the evaluation setup (persist-TTA) of work [11], which repeatedly cycles through non-i.i.d. CIFAR10-C corruptions across 10 rounds. This scenario emulates continual adaptation in environments where domain drift is both persistent and revisited.

We apply SNAP on top of CoTTA [50], a method specifically designed for continual test-time adaptation. While CoTTA alone initially performs well, we observe a steady degradation across rounds as it accumulates shift-induced bias and overfits to recent domains. In contrast, combining

CoTTA with SNAP enables the model to preserve robust performance even after multiple adaptation cycles.

The key to this stability lies in SNAP's architecture: (1) class-balanced memory to prevent label bias, (2) sparse but confident updates to mitigate overfitting, (3) IoBMN for adapting normalization statistics to each incoming sample, and (4) exponential moving average (EMA) domain centroids to smooth domain shift tracking. These collectively stabilize long-term adaptation dynamics without the need for explicit shift detection.

Experimental results. Table 15 and Figure 9 shows adaptation accuracy over 10 rounds. While CoTTA gradually collapses after the 5th round, integration with SNAP maintains accuracy above 50%, showing clear stability under persistent shifts.

These results confirm that SNAP enhances long-term TTA robustness by stabilizing both parameter and feature statistics over time. This makes it a reliable plug-in module for continual test-time adaptation pipelines.

B.15 Robustness in single-sample (BS=1) adaptation scenario

To investigate the robustness of SNAP when adaptation is performed on a per-sample basis, we evaluate its performance in a single-sample adaptation setting, where the adaptation batch size is limited to 1. This scenario reflects highly constrained edge environments with limited memory or streaming inputs, where adaptation must occur with minimal latency and granularity.

To support this setup, we adopt the SAR [31] architecture, which natively supports a batch size of 1 and sparse update routines. SAR allows us to test SNAP with an adaptation rate of 0.1, meaning only one in every ten test samples is used for weight updates, using a single memory sample.

Table 16: Evaluation of SNAP (AR=0.1) with SAR on a single-sample (BS=1) adaptation scenario on ImageNet-C. Results are averaged over 3 random seeds (0, 1, 2).

SNAP achieves strong gains even when adapting from just one memory sample. When only one sample is used for adaptation, our method still selects the representative sample with high prediction confidence and low Wasserstein distance to the domain centroid, enabling stable model updates.

1

2

3

4

5

6

7

8

9

10

Adaptation Round

10

20

30

40

50

60

Accuracy (%)

CoTTA (Full adapt)

SNAP (AR=0.1)

Meanwhile, IoBMN continues to apply adaptive normalization to every incoming test sample, mitigating covariate shift even when parameter updates are sparse. Although small batches can slow the class distribution balancing process and moving domain centroid updates under skewed domains, we found that this effect has limited influence on overall adaptation performance and stability.

Evaluation protocol. We average performance over three random seeds (0, 1, 2) to ensure stability across different data orderings. Table 16 reports both the mean and standard deviation of accuracy.

These results demonstrate that SNAP preserves its robustness and sample-wise adaptability even under minimal adaptation frequency and granularity. CnDRM identifies meaningful memory samples, while IoBMN provides per-sample normalization, together enabling consistent performance in BS=1 settings.

B.16 Impact of memory size on SNAP performance

The memory size of the Class and Domain Representative Memory (CnDRM) in SNAP has implications for both performance and privacy. Increasing memory size allows storing more samples, which intuitively could improve adaptation. However, such an approach raises privacy concerns and needs additional memory and latency when storing sensitive samples. To evaluate the trade-off, we conducted experiments on ImageNet-C under Gaussian noise corruption, using Tent + SNAP(adaptation rate 0.3) with a batch size of 16 and varying the memory size.

As shown in Table 17, increasing the memory size beyond the base configuration of 16 does not lead to significant performance gains. This observation highlights the efficiency of SNAP's representative sampling strategy, which prioritizes storing samples based on proximity to class and domain centroids. The saturation in accuracy suggests that a carefully aligned memory size to the batch size is sufficient to balance computational efficiency, performance, and privacy considerations.

Table 17: Performance comparison with varying memory sizes on ImageNet-C.

In conclusion, to minimize computational overhead while ensuring robust test-time adaptation, the memory size in SNAP is designed to align with the batch size. This configuration addresses privacy and memory overhead risks by limiting the number of stored samples without compromising adaptation effectiveness.

B.17 Effect of learning rate on sparse and full adaptation

To investigate the impact of learning rates on the performance of SNAP and baseline methods, we conducted experiments under sparse adaptation settings. Initially, the same learning rate was applied for each SOTA TTA algorithms across all adaptation rates to ensure fair comparisons (Table 26, 27, 22, 23, 24,and 25). However, as sparse adaptation inherently limits the number of updates, the updates might be insufficient at lower adaptation rates and explored the effect of increasing the learning rate.

The results, summarized in Table 18, 19, and 20, reveal that higher learning rates improve the accuracy of both the naive baseline and SNAP under sparse settings. Notably, while the naive TTA baseline benefits from a higher learning rate, its performance still falls short of that achieved with full adaptation. In contrast, SNAP surpasses the performance of full adaptation at optimal learning rates, demonstrating its ability to leverage sparse adaptation effectively. At the same time, applying these higher learning rates to full adaptation results in model instability and collapse, underscoring the need to carefully tune learning rates based on adaptation frequency. Therefore, we selected a stable learning rate of 1 × 10 -4 for the evaluations in our work that balances model convergence and performance across all adaptation rates. These findings suggest that SNAP not only adapts effectively under sparse settings but also maintains robustness under optimized learning rates.

In conclusion, selecting an appropriately high learning rate for sparse adaptation significantly enhances performance while ensuring model stability. This strategy is particularly useful for real-world deployment of SNAP, where computational efficiency and robust performance are paramount.

B.18 Evaluation on real-world sensor data

To validate SNAP's generalizability to other real-world domains, we further test SNAP on HARTH [23], a human activity recognition dataset that collects data from two three-axial accelerometers attached to participants' thigh and lower back. Unlike our main evaluations, which focus on 2D vision and corruption-based domain shifts, HARTH introduces a distinct domain shift caused by sensor positioning and user variation .

We evaluate SNAP with an adaptation rate (AR) of 0.1 on Tent [48] and SAR [31]. The base model is composed of four one-dimensional convolutional layers followed by a fully-connected layer, and is trained on the source domain, composing of data collected from the back of 15 participants. The target domain is the data collected from the thigh of the remaining 7 participants. As shown in Table 21, SNAP improves accuracy even with sparse updates, demonstrating its effectiveness under realistic shifts

C Detailed experiment results

In this section, we provide detailed experimental results for the performance comparison of SNAP across a wide range of adaptation rates. We evaluated the performance on CIFAR10-C, CIFAR100-C, and ImageNet-C datasets with adaptation rates of 0.01, 0.03, 0.05, 0.1, 0.3, and 0.5, and across five state-of-the-art (SOTA) TTA algorithms: Tent [48], EATA [30], SAR [31], CoTTA [50], and RoTTA [53]. This comprehensive evaluation resulted in a total of 150 combinations (3 datasets, 6 adaptation rates, 5 algorithms).

The results demonstrate that, regardless of the adaptation rate, dataset, or the TTA algorithm, integrating SNAP consistently outperforms the baseline methods. Specifically, SNAP achieved the highest accuracy across nearly all of these 150 combinations, effectively demonstrating its robustness in both high and low adaptation settings. For CIFAR10-C and CIFAR100-C, SNAP showed substantial performance improvements compared to the baseline, even at very low adaptation rates (e.g., 0.01 and 0.05). Similarly, for ImageNet-C, SNAP maintained superior accuracy across diverse corruption types.

These results highlight that SNAP effectively balances adaptation and latency, ensuring optimal performance even when the adaptation rate is sparse and regardless of the underlying TTA algorithm. This consistent superiority across all 150 combinations underscores SNAP's suitability for practical, real-world applications on resource-constrained devices.

C.1 CIFAR10-C

AR

Methods

Gau.

Shot

Imp.

Def.

Gla.

Mot.

Zoom

Snow

Fro.

Fog

Brit.

Cont.

Elas.

Pix.

JPEG

64.65

67.08

58.48

85.00

62.61

82.76

84.63

79.01

77.66

83.32

88.00

82.34

74.16

77.11

69.40

75.75

Tent

±0.55

±0.58

±0.42

±0.60

±0.44

±0.70

±0.55

±0.74

±0.91

±0.48

±0.56

±0.93

±0.60

±0.48

±0.57

67.71

69.84

59.53

87.10

64.66

85.73

86.35

80.68

78.92

85.60

90.19

86.72

76.16

78.86

70.95

77.93

+ SNAP

±0.82

±1.10

±0.15

±0.25

±0.20

±0.20

±0.23

±0.14

±0.08

±0.31

±0.20

±0.17

±0.42

±0.30

±0.33

59.27

61.18

56.33

72.22

57.37

74.27

72.61

70.03

68.68

74.82

79.72

65.57

66.92

64.13

65.25

67.22

CoTTA

±0.66

±1.12

±0.06

±1.43

±1.10

±1.46

±1.11

±1.02

±0.92

±1.09

±1.07

±1.14

±0.98

±1.05

71.42

73.31

65.91

85.23

67.01

84.19

84.91

80.80

80.56

84.19

90.00

82.09

76.31

79.79

75.18

78.73

+ SNAP

±0.29

±0.12

±0.13

±0.11

±0.21

±0.20

±0.14

±0.19

±0.14

±0.23

±0.05

±0.29

±0.21

±0.20

64.68

67.01

58.07

84.90

62.56

82.64

84.57

78.77

77.16

83.09

87.80

81.62

74.05

76.99

69.31

75.55

EATA

±0.31

±0.37

±0.24

±0.54

±0.33

±0.67

±0.61

±0.71

±0.92

±0.44

±0.47

±0.59

±0.28

±0.41

±0.71

±0.51

67.36

68.73

59.35

87.05

64.36

85.62

86.48

81.31

78.73

85.33

90.03

86.31

76.04

78.79

70.90

77.76

+ SNAP

±0.33

±0.26

±0.37

±0.22

±0.18

±0.18

±0.25

±0.24

±0.22

±0.15

±0.24

±0.07

±0.12

±0.27

±0.23

64.79

66.32

57.58

84.66

62.46

81.42

84.13

78.87

77.20

82.62

88.10

82.12

74.04

75.38

69.13

75.25

SAR

±0.13

±0.86

±0.69

±0.72

±0.26

±1.52

±0.26

±0.81

±1.24

±0.41

±0.74

±0.05

±0.52

±0.62

66.00

68.85

58.47

86.54

63.06

85.26

86.13

80.38

78.17

85.17

90.93

85.96

75.27

77.37

70.61

77.21

+ SNAP

±0.17

±0.75

±0.42

±0.25

±0.28

±0.09

±0.09

±0.27

±0.13

±0.36

±0.20

±0.31

±0.28

±0.30

±0.29

63.21

64.87

56.60

84.64

62.16

82.31

84.13

78.16

76.39

82.90

87.44

81.47

73.59

76.02

68.09

74.80

RoTTA

±0.37

±0.62

±0.28

±0.52

±0.31

±0.63

±0.56

±0.71

±0.95

±0.62

±0.65

±0.42

±0.40

±0.33

±0.52

65.28

66.91

57.88

86.75

63.51

85.48

86.17

80.46

78.38

85.24

89.99

85.82

75.66

77.98

70.15

77.05

0.05

+ SNAP

±0.32

±0.22

±0.06

±0.25

±0.13

±0.13

±0.23

±0.26

±0.13

±0.23

±0.03

±0.16

±0.19

±0.29

±0.18

64.36

66.21

57.65

84.73

62.95

83.07

84.50

78.46

76.99

83.00

88.07

82.62

73.93

76.50

68.82

75.46

Tent

±0.43

±0.16

±1.01

±0.48

±0.52

±0.50

±0.32

±0.82

±0.32

±0.36

±0.43

±0.23

±0.48

66.32

68.38

59.00

86.93

64.04

85.58

86.35

80.78

78.68

85.34

90.08

86.19

75.77

78.37

70.49

77.49

+ SNAP

±0.61

±0.71

±0.52

±0.19

±0.24

±0.05

±0.02

±0.05

±0.31

±0.05

±0.06

±0.08

±0.23

60.38

61.26

56.71

72.44

57.58

74.64

72.73

69.68

68.34

74.64

79.52

67.28

67.42

64.89

66.19

67.58

CoTTA

±1.71

±1.94

±2.47

±2.23

±1.85

±1.74

±2.61

±2.03

±2.02

±2.52

±2.37

±1.89

±1.77

±1.73

±1.98

71.12

73.68

66.34

85.30

66.64

84.25

84.55

80.88

80.11

84.06

89.89

81.98

76.27

79.77

75.35

78.68

+ SNAP

±0.47

±0.29

±0.24

±0.01

±0.12

±0.13

±0.15

±0.15

±0.14

±0.14

±0.37

±0.19

±0.26

±0.08

±0.21

63.99

65.95

57.39

84.71

62.66

83.11

84.44

78.42

76.63

82.97

88.00

82.55

73.85

76.46

68.91

75.34

EATA

±0.87

±0.44

±1.05

±0.48

±0.62

±0.52

±0.33

±0.75

±0.26

±0.26

±0.47

±0.33

±0.29

±0.56

±0.50

66.16

67.60

58.81

86.95

64.06

85.49

86.34

80.79

78.65

85.24

90.09

86.23

75.88

78.48

70.56

77.42

+ SNAP

±0.03

±0.41

±0.36

±0.13

±0.17

±0.36

±0.08

±0.01

±0.25

±0.13

±0.12

±0.08

±0.18

±0.47

±0.19

63.72

65.75

57.89

84.37

62.45

81.47

82.46

78.32

76.79

81.93

88.60

82.72

73.89

74.55

68.79

74.91

SAR

±0.29

±0.65

±0.81

±0.69

±1.61

±2.95

±0.81

±0.24

±1.33

±0.68

±0.29

±0.43

±0.98

±0.61

±0.85

65.40

67.68

58.37

86.72

63.11

85.10

86.18

79.93

78.05

84.92

90.93

85.58

75.30

77.22

69.97

76.96

+ SNAP

±0.33

±0.60

±0.45

±0.18

±0.16

±0.16

±0.29

±0.17

±0.31

±0.22

±0.14

±0.14

±0.30

±0.30

±0.27

63.36

65.10

56.64

84.62

62.41

82.96

84.35

78.10

76.42

82.69

87.90

82.34

73.56

76.09

68.39

75.00

RoTTA

±0.55

±0.56

±0.49

±0.67

±0.43

±0.23

±0.25

±0.53

±0.32

±0.25

±0.44

±0.31

±0.50

65.27

67.05

58.05

86.79

63.48

85.46

86.25

80.39

78.34

85.19

90.10

85.94

75.67

78.04

69.75

77.05

0.03

+ SNAP

±0.32

±0.19

±0.22

±0.21

±0.18

±0.33

±0.09

±0.08

±0.15

±0.16

±0.08

±0.12

±0.09

±0.27

±0.17

62.43

64.13

55.85

84.03

62.21

82.47

83.87

77.71

76.55

82.75

87.35

81.83

73.24

75.34

67.73

74.50

Tent

±1.70

±1.51

±1.35

±1.07

±1.20

±0.88

±0.93

±0.66

±0.18

±0.14

±1.11

±1.81

±1.33

±1.18

±1.50

±1.10

65.51

67.26

58.05

86.89

63.53

85.44

85.97

80.58

78.35

85.12

90.09

85.86

75.66

78.38

70.12

77.12

+ SNAP

±0.24

±0.31

±0.28

±0.07

±0.33

±0.20

±0.12

±0.12

±0.16

±0.21

±0.11

±0.08

±0.21

±0.33

±0.21

59.75

59.44

54.47

71.12

57.11

72.47

72.83

66.05

65.14

69.75

75.12

64.31

66.22

62.65

64.76

65.41

CoTTA

±4.69

±6.21

±5.57

±5.10

±4.35

±4.52

±4.80

±7.60

±7.65

±9.79

±6.79

±6.46

±4.50

±5.36

±5.91

71.79

73.61

65.98

85.34

66.76

84.26

84.93

80.64

80.38

83.94

89.98

82.47

76.48

79.61

75.60

78.79

+ SNAP

±0.22

±0.29

±0.58

±0.36

±0.26

±0.12

±0.21

±0.45

±0.30

±0.42

±0.08

±0.64

±0.26

±0.24

±0.29

±0.31

62.36

63.92

55.73

84.05

62.24

82.38

83.90

77.66

76.48

82.67

87.34

81.82

73.30

75.31

67.76

74.46

EATA

±1.73

±1.66

±1.39

±1.10

±1.18

±0.85

±0.93

±0.72

±0.15

±0.17

±1.12

±1.81

±1.24

±1.20

±1.52

±1.12

65.49

67.19

57.93

86.92

63.65

85.42

85.97

80.46

78.13

85.07

90.03

85.87

75.69

78.20

70.03

77.07

+ SNAP

±0.29

±0.04

±0.40

±0.41

±0.18

±0.28

±0.24

±0.18

±0.27

±0.13

±0.20

±0.11

±0.13

±0.23

62.50

64.13

55.65

82.30

62.22

77.21

80.11

77.66

76.75

79.12

89.45

81.97

73.39

69.39

67.83

73.31

SAR

±1.83

±3.37

±1.21

±6.27

±6.19

±3.28

±1.79

±1.97

±1.21

±1.65

±2.57

65.06

66.93

57.66

86.76

62.78

85.05

85.94

79.95

77.62

84.65

90.72

85.48

75.34

75.72

69.61

76.62

+ SNAP

±0.17

±0.11

±0.51

±0.29

±0.24

±0.21

±0.48

±0.18

±0.37

±0.21

±0.62

±0.13

±1.35

±0.25

±0.36

62.25

63.71

55.59

84.05

62.17

82.32

83.86

77.56

76.39

82.64

87.27

81.75

73.21

75.15

67.75

74.38

RoTTA

±1.65

±1.68

±1.46

±1.12

±1.37

±0.83

±0.90

±0.75

±0.24

±1.12

±1.82

±1.21

±1.48

±1.13

65.32

66.94

57.85

86.91

63.44

85.32

85.98

80.49

78.22

85.04

90.01

85.77

75.75

78.15

70.06

77.02

0.01

+ SNAP

±0.25

±0.12

±0.29

±0.31

±0.24

±0.22

±0.14

±0.24

±0.20

±0.15

±0.06

±0.24

±0.11

±0.07

±0.47

±0.21

C.2 CIFAR100-C

AR

Methods

Gau.

Shot

Imp.

Def.

Gla.

Mot.

Zoom

Snow

Fro.

Fog

Brit.

Cont.

Elas.

Pix.

JPEG

40.69

41.55

35.14

62.26

40.26

58.92

61.06

51.21

50.00

55.52

64.05

58.45

50.50

54.68

44.36

51.24

Tent

±0.62

±0.52

±0.23

±0.60

±0.43

±0.88

±0.31

±0.33

±0.62

±1.06

±0.26

±0.69

±0.54

42.87

44.87

37.60

65.01

42.22

62.22

63.72

54.03

53.68

58.03

67.05

63.08

52.97

57.67

46.94

54.13

+ SNAP

±0.37

±0.70

±0.08

±0.01

±0.31

±0.45

±0.39

±0.47

±0.50

±0.15

±0.12

±0.13

±0.31

26.15

26.89

25.26

39.48

28.34

41.41

38.77

32.06

30.84

35.56

41.60

28.52

34.99

33.60

34.54

33.20

CoTTA

±0.60

±0.32

±0.44

±0.71

±0.74

±1.14

±0.85

±0.65

±1.12

±1.36

±0.45

±0.82

±0.54

±0.75

42.02

42.70

37.67

58.30

41.57

57.47

58.02

50.55

51.31

52.34

63.63

51.25

49.76

54.94

47.98

50.63

+ SNAP

±0.21

±0.13

±0.31

±0.26

±0.37

±0.14

±0.18

±0.27

±0.32

±0.17

±0.16

±0.49

±0.18

±0.05

±0.12

±0.22

38.46

39.05

33.47

61.07

38.52

58.16

60.59

49.60

49.18

54.41

63.15

57.06

49.09

52.87

42.49

49.81

EATA

±0.14

±0.58

±0.23

±0.63

±0.29

±0.48

±0.55

±0.47

±0.24

±0.43

±1.37

±0.88

±0.42

±0.50

40.49

41.64

34.37

64.28

40.38

61.52

63.17

51.66

52.12

56.50

66.03

62.01

51.76

55.66

44.83

52.43

+ SNAP

±0.21

±0.43

±0.15

±0.20

±0.51

±0.30

±0.18

±0.53

±0.52

±0.21

±0.36

±0.12

±0.12

±0.23

±0.32

±0.29

40.28

41.62

35.35

62.84

40.37

59.51

61.68

51.29

50.66

55.60

64.43

58.49

50.90

54.82

44.64

51.50

SAR

±0.07

±0.62

±0.04

±0.26

±0.41

±0.28

±0.81

±0.40

±0.62

±0.82

±0.64

±0.27

±0.43

±0.43

41.76

44.24

36.89

64.34

41.54

62.13

63.39

53.24

52.91

57.54

66.89

62.41

52.70

57.23

46.63

53.59

+ SNAP

±0.29

±0.44

±0.21

±0.37

±0.15

±0.24

±0.33

±0.02

±0.22

±0.60

±0.50

±0.15

±0.47

±0.57

±0.33

36.38

37.38

31.78

61.44

38.26

58.18

60.19

48.98

48.30

53.50

62.73

56.52

49.37

52.19

41.60

49.12

RoTTA

±0.12

±0.42

±0.45

±0.06

±0.20

±0.42

±0.53

±0.18

±0.28

±0.17

±0.42

±0.90

±0.49

±0.19

±0.28

37.67

38.66

32.47

63.95

40.18

61.33

62.52

51.47

51.32

55.67

65.89

61.24

51.47

54.52

42.84

51.41

0.05

+ SNAP

±0.12

±0.21

±0.12

±0.16

±0.20

±0.47

±0.14

±0.36

±0.21

±0.24

±0.15

±0.14

±0.15

±0.23

38.55

39.28

33.77

61.64

39.66

58.83

60.89

49.45

49.51

54.64

63.48

57.29

50.34

53.44

43.28

50.27

Tent

±0.17

±0.15

±0.16

±0.25

±0.39

±0.48

±0.29

±0.51

±0.42

±0.58

±0.33

±0.26

±0.37

41.22

42.20

35.31

64.48

40.82

61.96

63.50

52.84

52.36

57.18

66.50

62.17

52.12

56.48

45.72

52.99

+ SNAP

±0.33

±0.27

±0.36

±0.06

±0.60

±0.02

±0.30

±0.40

±0.40

±0.33

±0.02

±0.41

±0.17

±0.18

±0.40

±0.28

27.11

27.73

25.87

40.25

29.52

42.16

39.60

32.74

32.23

36.60

43.33

29.13

36.45

34.51

35.96

34.21

CoTTA

±1.11

±2.05

±1.41

±2.62

±1.49

±2.21

±2.51

±2.42

±1.71

±2.75

±2.80

±2.42

±1.82

±1.66

±1.75

±2.05

41.77

42.85

37.50

58.61

41.15

57.65

58.05

50.45

51.34

52.72

63.49

51.63

49.87

55.24

48.14

50.70

+ SNAP

±0.24

±0.19

±0.08

±0.22

±0.16

±0.22

±0.32

±0.65

±0.20

±0.07

±0.61

±0.17

±0.13

±0.36

±0.26

37.94

38.63

32.00

61.02

39.08

58.52

60.28

48.73

49.15

53.89

63.03

56.64

49.45

52.93

42.11

49.56

EATA

±0.32

±0.21

±0.91

±0.33

±0.30

±0.66

±0.42

±0.32

±0.97

±0.53

±0.49

±0.47

±0.44

±0.47

39.87

41.12

34.48

64.14

40.27

61.91

63.09

52.37

51.93

56.36

66.02

61.88

51.83

55.60

44.59

52.36

+ SNAP

±0.89

±0.20

±0.08

±0.23

±0.09

±0.00

±0.43

±0.42

±0.44

±0.26

±0.05

±0.15

±0.04

±0.11

±0.45

±0.26

38.33

39.19

33.15

61.77

39.78

59.09

61.02

49.67

49.86

54.71

63.59

57.45

50.37

53.67

42.88

50.30

SAR

±0.25

±0.26

±0.43

±0.21

±0.06

±0.33

±0.25

±0.54

±0.65

±0.31

±0.49

±0.18

±0.39

±0.32

±0.51

39.84

41.83

34.94

63.70

40.49

61.45

63.17

52.27

51.91

56.69

65.91

61.31

51.68

56.06

44.95

52.41

+ SNAP

±0.07

±0.28

±0.26

±0.16

±0.28

±0.07

±0.51

±0.17

±0.25

±0.27

±0.52

±0.22

±0.18

±0.16

±0.28

36.24

36.94

31.15

60.87

38.28

58.25

59.88

48.43

48.17

53.32

62.73

56.18

49.23

52.12

41.28

48.87

RoTTA

±0.03

±0.21

±0.09

±0.17

±0.14

±0.53

±0.36

±0.52

±0.61

±0.47

±0.39

±0.31

±0.61

37.85

38.68

32.78

63.97

39.75

61.41

62.57

51.53

51.38

55.68

65.56

61.25

51.53

54.84

42.96

51.45

0.03

+ SNAP

±0.20

±0.20

±0.31

±0.24

±0.17

±0.16

±0.52

±0.27

±0.28

±0.37

±0.20

±0.13

±0.19

±0.26

±0.33

±0.25

36.08

36.95

31.31

61.03

38.09

57.63

58.76

48.24

48.65

53.45

62.14

55.07

48.59

51.82

40.68

48.57

Tent

±0.42

±0.21

±0.47

±0.51

±0.56

±0.53

±0.31

±0.47

±0.87

±0.19

±0.49

±2.13

±0.25

±0.58

±0.04

±0.54

38.40

39.40

33.26

63.85

40.36

61.23

62.79

51.92

51.73

56.20

65.83

60.95

51.82

54.75

43.53

51.73

+ SNAP

±0.06

±0.16

±0.11

±0.36

±0.24

±0.06

±0.00

±0.17

±0.29

±0.00

±0.30

±0.16

±0.18

26.59

27.92

24.86

41.34

28.91

43.09

40.11

34.33

33.32

37.99

44.78

28.80

36.26

34.70

35.67

34.58

CoTTA

±1.64

±1.79

±1.51

±2.21

±2.85

±2.87

±1.61

±2.67

±2.03

±3.61

±2.18

±1.90

±1.66

±1.47

±2.13

42.05

42.91

37.50

58.70

41.22

57.38

58.14

50.39

51.13

52.23

63.42

51.74

49.87

54.84

47.72

50.62

+ SNAP

±0.05

±0.17

±0.08

±0.12

±0.36

±0.17

±0.33

±0.68

±0.43

±0.12

±0.17

±0.50

±0.09

±0.25

±0.26

36.10

37.05

31.03

60.86

37.83

57.64

58.77

48.02

48.75

53.37

62.18

54.95

48.55

51.89

40.75

48.51

EATA

±0.27

±0.59

±0.50

±0.37

±0.57

±0.32

±0.50

±1.26

±0.09

±0.43

±0.15

±0.65

±0.02

±0.55

38.54

39.78

33.11

63.82

39.98

61.33

62.53

51.76

51.50

56.03

65.94

61.16

51.47

54.52

43.67

51.68

+ SNAP

±0.14

±0.15

±0.22

±0.53

±0.20

±0.24

±0.12

±0.32

±0.44

±0.19

±0.11

±0.04

±0.27

±0.04

±0.21

36.04

37.02

31.38

61.13

38.07

58.00

59.08

48.44

48.84

53.52

62.57

55.19

48.87

52.01

40.71

48.72

SAR

±0.00

±0.26

±0.30

±0.44

±0.59

±0.36

±0.47

±0.92

±0.16

±0.50

±2.20

±0.15

±0.57

±0.19

±0.50

37.91

38.85

32.92

63.17

39.35

60.51

62.01

51.11

50.48

55.47

65.07

59.69

51.24

54.10

42.80

50.98

+ SNAP

±0.39

±0.25

±0.23

±0.45

±0.51

±0.26

±0.11

±0.28

±0.41

±0.16

±0.15

±0.15

±0.47

±0.06

±0.28

35.55

36.34

30.55

60.76

37.42

57.50

58.57

47.87

48.31

53.11

61.90

54.70

48.25

51.37

40.29

48.16

RoTTA

±0.33

±0.31

±0.45

±0.50

±0.50

±0.56

±0.30

±0.28

±0.97

±0.23

±0.62

±1.98

±0.08

±0.62

±0.11

±0.52

37.82

38.72

32.60

63.53

39.80

61.00

62.27

51.42

51.33

55.71

65.64

60.89

51.50

54.27

42.92

51.30

0.01

+ SNAP

±0.16

±0.05

±0.01

±0.49

±0.37

±0.23

±0.06

±0.12

±0.42

±0.14

±0.18

±0.18

±0.19

±0.47

±0.21

C.3 ImageNet-C

C.4 Additional results on ablation study

In this section, we provide additional details on the ablation study to evaluate the contributions of the CnDRM and IoBMN components in SNAP. Specifically, we measured the average accuracy across 15 corruption types on CIFAR10-C and CIFAR100-C datasets under varying adaptation rates (0.3, 0.1, 0.05) to thoroughly assess the effectiveness of each component.

Tables 28 and 29 summarize the results for different combinations of CnDRM and IoBMN across these adaptation rates. The results indicate that the combination of CnDRM (Class and Domain Representative sampling) and IoBMN (inference using memory statistics corrected to match the test batch) consistently yields the highest accuracy. This trend is observed across all evaluated adaptation rates, suggesting that both components contribute significantly to enhancing adaptation performance.

Moreover, individual evaluations show that each component has a distinct positive effect, as evidenced by consistently higher accuracy compared to using no adaptation or only a single component. This emphasizes the complementary nature of CnDRM and IoBMN, which together provide robust adaptation capabilities for domain-shifted scenarios. These tables provide further insight into the benefits of each configuration and how the synergy of CnDRM and IoBMN results in improved robustness against various corruptions.

D License of assets

Datasets CIFAR10/CIFAR100 (MIT License), CIFAR10-C/CIFAR100-C (Creative Commons Attribution 4.0 International), ImageNet-C (Apache 2.0), and ImageNet-R/Scketch (MIT License).

Codes Torchvision for ResNet18, ResNet50, and VitBase-LN (Apache 2.0), the official repository of CoTTA (MIT License), the official repository of Tent (MIT License), the official repository of EATA (MIT License), the official repository of SAR (BSD 3-Clause License), the official repository of RoTTA (MIT License), the official repository of T3A (MIT License), the official repository of FOA (NTUITIVE License) and the official repository of MECTA (Sony AI).

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Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes SNAP a test-time adaptation algorithm with low latency. It has two components: (1) CnDRM for selecting representative samples to update the model with partial data, and (2) IoBMN for leveraging these representative samples in adaptation. The algorithm saves lots of computation, while preserve most of the effectiveness of TTA algorithms.\n\nSTRENGTHS AND WEAKNESSES:\n# Sterngths\n- Achieving better efficiency-effectiveness trade-off in TTA algorithms is an important topic in TTA, especially when recent works are more and more complicated with only marginal improvements. It is important to evaluate whether TTA algorithms can be useful in practice. \n- The proposed algorithm in clear and intuitive in high-level, easy to understand. \n- The experiment in comprehensive on benchmarking datasets.\n- I appreciate the experiments on popular edge devices, which are rarely seen in previous works. \n\n# Major Weaknesses\n- I am confused about the role of IoBMN. It is proposed as an replacement of standard BN adaptor, and use only the chosen samples in CnDRM. (1) However, it requires a forward pass to get the prediction and calculated scores used in CnDR. Does it mean the algorithm requires two forward passes for adaptation? (2) All the feature map for all samples are always available, why not just use the standard BN, with additional moving average? \n\n# Minor Weaknesses\n- Equation (1): I think this equation might only be true if you assume the feature distribution is Gaussian, with diagonal covariance matrix, (and requires a few lines of derivation). The author should (1) clearly define the distribution considered here (which is NOT data distribution, but the distribution of each scalar in the network) and (2) clearly state the assumptions to compute Wasserstein distance. \n- Notation around Equation (2) is quite confusing. I believe m is a sample index, instead of a channel index. Should it be averaged over channel C and locaion L, instead of B and L? Also, if it is already normalized, why divided by C*M in Equation 3? I suggestion the author check these notation and give clear definition.\n\nQUESTIONS:\n- In CnDRM, the author argue in criteria 2 that \"selecting samples close to the domain centroid would enhance performance in STTA\". In the previous EATA paper (one of the baselines the author consider), they instead drop the testing samples whose prediction is too close to the testing sample mean, which is a clear contradiction with this paper. Although the similarities are calculated in slightly different levels (early layer feature v.s. final prediction), could you explain what is the key differences, and are there any contradiction when combining these two methods?\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-06-29"}

comments: SUMMARY:
This paper proposes SNAP, a sparse and efficient Test-Time Adaptation (TTA) framework designed for resource-constrained edge environments. Unlike existing TTA methods that require frequent updates and high computation, SNAP maintains high accuracy while adapting with as little as 1% of the test data. It introduces two key components: (1) Class and Domain Representative Memory (CnDRM), which stores a compact set of representative samples for efficient adaptation, and (2) Inference-only Batch-aware Memory Normalization (IoBMN), which updates normalization statistics during inference using these samples.

STRENGTHS AND WEAKNESSES:
1. Strengths

- This paper addresses an important yet often overlooked challenge in current TTA research: the trade-off between latency and accuracy. By focusing on resource-constrained edge environments and identifying frequent adaptation as a key bottleneck, the authors highlight a novel and practical direction for the field.
- A particularly noteworthy contribution is that, after adaptation, the model often outperforms its initial performance (e.g., in Tent, EATA, and CoTTA). This is significant, as most prior TTA methods only aim to maintain the original accuracy rather than improve upon it.
- The proposed method is plug-and-play, making it easy to integrate into existing pipelines. Additionally, the extensive results in the Appendix across different adaptation rates are helpful and provide a comprehensive understanding of the method’s robustness and generalizability.

2. Weakness
- This work adopts a fixed adaptation rate/CnDRM safeguard. Can the authors provide dynamic tuning (i.e., learning this rate) and efficiency metrics?

QUESTIONS:
Please refer to the above.

LIMITATIONS:
yes
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-07-01

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces SNAP, a sparse Test-Time Adaptation (TTA) framework designed to address the high latency and computational cost of existing TTA methods on resource-constrained edge devices. SNAP employs two key components: Class and Domain Representative Memory (CnDRM) for efficient sample selection and Inference-only Batch-aware Memory Normalization (IoBMN) for dynamic feature alignment. Extensive experiments on CIFAR-C, ImageNet-C, and real edge devices (e.g., Raspberry Pi, Jetson Nano) demonstrate significant latency reductions while maintaining accuracy. The framework integrates seamlessly with five SOTA TTA algorithms, showcasing broad applicability.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n1. The paper effectively identifies the critical challenge of TTA latency on edge devices, a gap overlooked in prior work, and provides a targeted solution with sparse adaptation.\n\n2. CnDRM and IoBMN are innovative and combines class-domain representativeness and lightweight normalization adjustments to balance accuracy and efficiency.\n\n3. Experiments cover diverse datasets, adaptation rates, and edge devices, with thorough ablation studies validating component contributions. Latency and memory overhead are rigorously measured, enhancing reproducibility.\n\n4. The framework’s compatibility with existing TTA methods and minimal memory overhead (0.02–1.74%) make it highly applicable to real-world edge deployments.\n\nWeaknesses:\n\n1. In lines 191-196, the authors aim to determine domain-representative samples. However, after introducing the calculation of the Wasserstein distance, the text abruptly stops. It fails to elaborate on what domain-representative samples are and how to obtain them. Specifically, the definition of domain-representative samples (e.g., whether they refer to samples whose feature distributions are close to the target domain centroid) and the operational steps for selection (e.g., threshold criteria or sampling strategies based on Wasserstein distance rankings) remain unclear. This leaves readers without a complete understanding of the sample selection mechanism, potentially affecting the reproducibility and interpretability of the method.\n\n2. Besides, in Algorithm 1 (Table), the operations of \"Remove domain-centroid farthest sample\" and \"Update domain-centroid\" are not described anywhere in the paper. Specifically, there is no explanation of the criteria for determining the \"farthest sample\" (e.g., whether it is based on the Wasserstein distance defined in Equation 1) or the specific mechanism for \"updating the domain centroid\" (e.g., momentum update parameters or frequency). These omissions make it difficult for readers to fully understand the dynamic management process of the memory pool, potentially affecting the reproducibility of the method and the interpretation of experimental results.\n\n3. In the paper, the two key concepts of Adaptation Rate (mentioned in Line 132) and sampling ratio (mentioned in Line 134) proposed in relation to Sparse TTA are not clearly explained. \n\n4. In the experimental section, the paper states that two networks were used for ImageNet. However, neither the caption of Table 1 nor the main text specifies which network was employed for the ImageNet data presented in Table 1.\n\nQUESTIONS:\nPlease refer to the weaknesses.\n\nLIMITATIONS:\nYes. The authors have addressed the limitations in Section 5.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 5, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a sparse and training-free TTA framework designed for resource-constrained edge environments. It introduces two key components: (i) CnDRM, which selects representative samples for efficient adaptation, and (ii) IoBMN, an inference-only normalization strategy. SNAP achieves up to 93.12% latency reduction with less than 3.3% accuracy drop, showing potential for real-world deployment.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n1. The approach is well-motivated, clearly addressing the challenges of deploying TTA models at the edge by proposing a training-free solution that leverages class/domain representatives samples.\n\n2. The structure of the method/work is articulated in a way that facilitates understanding for the reader.\n\nWeaknesses\n\n1. The paper lacks empirical evaluation over realistic datasets aligned with the motivating applications mentioned by the authors, such as autonomous driving, real-time health monitoring, or high-frame-rate video analysis. This limits the demonstration of the practical utility and scalability of the method under real-world conditions.\n2. Another important concern relates to the dynamics of the model during early inference steps. Since the proposed class and domain representative memory requires accumulation over time, it is unclear how the model performs in the initial stages when batch size is small (e.g., bs=1). The paper does not provide sufficient analysis or discussion on convergence behavior or how long it takes for the memory to stabilize and yield reliable performance.\n3. The core methodological components are not particularly novel. The use of memory banks for test-time adaptation has been explored in prior work, such as RoTTA[51], and the strategy of correcting Batch Normalization statistics at inference time has also been studied (e.g., in Note[6]). The authors should position their contributions more clearly by providing module-level comparisons to these related methods to highlight what is new and effective.\n4. One of the key contributions of this work lies in its inference-only normalization strategy. However, training-free TTA paradigms are not new and have been widely explored in existing literature. The authors have not sufficiently discussed related works in this area, such as [1,2,3,4]. Authors are suggested to provide a more in-depth analysis to better highlight the unique contributions of their method in this aspect.\n5. Several key claims are not sufficiently substantiated by empirical evidence. For instance, the statements in lines 62–64 and 157–159 make strong assertions about the effectiveness of the method in correcting skewed feature distributions and selecting diverse and reliable samples without ground-truth supervision. However, the paper does not include specific ablations or diagnostic experiments to validate these points.\n\n\n[1] AdaNPC: Exploring Non-Parametric Classifier for Test-Time Adaptation\n\n[2] Parameter-free Online Test-time Adaptation\n\n[3] Unraveling Batch Normalization for Realistic Test-Time Adaptation\n\n[4] Dynamically Instance-Guided Adaptation: A Backward-free Approach for Test-Time Domain Adaptive Semantic Segmentation\n\nQUESTIONS:\nSee weaknesses and try to address all of my concerns.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-08"}