SNAP: Low-Latency Test-Time Adaptation with Sparse Updates
Authors: Hyeongheon Cha
Dong Min Kim
Hye Won Chung
Taesik Gong
Sung-Ju Lee
Venue: NeurIPS 2025 poster ()
Keywords: Test-Time Adaptation
Unsupervised Domain Adaptation
Primary area: general_machine_learning
TL;DR: We propose SNAP, a novel low-latency Test-Time Adaptation framework that enables efficient model adaptation on edge devices by using sparse updates, significantly reducing computation while maintaining accuracy.

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
Hyeongheon Cha'
Dong Min Kim! Hye Won Chung' Taesik Gong²
Sung-Ju Leel
School of Electrical Engineering, KAIST, Daejeon, Republic of Korea
Department of Computer Science and Engineering, UNIST, Ulsan, Republic of Korea
bbyeongheon,donge dongmin hwchung, wwwchhungprofssii. / ac. taesik. wowillk.gnngunis...c..
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, sparse TTA framework that reduces adaptation frequency and data usage while preserving accuracy. SNAP maintains competitive accuracy even when adapting based on only I % of the in- coming 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 adapta- tion 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 ttate-of-the-ane 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: //ggttuttb//t//////////// com/ cww.hhh08hSMAA
Introduction
Deep learning models often suffer performance degradation under domain shifts caused by environ- mental changes noise [37]. Test-Time Adaptation (TTA) offers promising solution for domain shifts by utilizing only unlabeled test data without requiring source data. While TTA algorithms have advanced in complexity improve accuracy in data streams [48, 30, 50, 53, 31, 43), they typically designed for resource-rich servers, overlooking the computational limitations crucial for real-world deployment. Operations such backpropagation, data augmentation, and model ensem- bling [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 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 high-frame-rate videos or high-performance sensors. For example, even
Corresponding authors.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

---

Online data stream
4
Original TTA
Delay
Adapt
Latency: 6.7s
batch
Timeline
Adaptation
Adaptation
Adaptation
Acc: 81%
Naive Sparse TTA
Pro trained Model
Adapt batch
1
Inferencee Infelence-Onlly
4
Införence-Onily
Latency: 2.15
TTA on Edge devices
Timeline
Adaptation 1
12
8
Adaptation 4
14
15
Adapt
Acc: 69%
Adaptation
Inference
*Adaptation Rate: 0.33
Figure I: Comparison of average latency per batch and accuracy between the Original and Naïve Sparse TTA upproaches on edge devices processing an online data stream. With an adaptation rate of 0.33, adaptation occurs once every three batches, reducing latency proportional to the rate but leading to significant accuracy drop compared with fully adapting Original TTA.
slight delay in processing sensor data 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-sensitivy 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-baeee approaches across diverse conditions (Appendix B. B0) 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 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-base -bsed TTA methods are especially designed for handling dynamic data stream such non-ii.d [6, 31, 53] or noisy data [7]. However, they 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 reasseeprreeentttive samples is effective at low sampling rates (e.g.. below 0.4) [51, 2]. However, these approaches depend on ground- -ruth labels, which are not available in TTA.
We propose SNAP: Sparse Network Adaptation for Practical Test-Time Adaptation, a low-latency unsupervised domain adaptation framework for resource-comstrained 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 pool of class- representative samples (high pscudo-label confidence, balanced across predictions) and space). This approach enables the model to adapt effectively to domain shifts with minimal data (Section 4.1). Meanwhile, loBMN 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).
samples (closest to the target domain centroid in feature
SNAP a lightweight module that reduces latency while scamlessly integrating with existing TTA methods, preserving their adaptation behavior. To assess its effecctivnness, 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 (CIFARIO-C, CIFARI00-C, and ImageNet- C [10]] across various adaptation rates (Section 5). We also validate SNAP on ImageNet-R [9] and ImageNet-Skkech [49] to assess generalization (Appendix B.1
In addition, we measured SNAP's latency and memory usage on three popular edge de- vices- Raspberry Pi 4 [38]. Raspberry Pi Zero 2 W [39], and NVIDIA Jetson Nano [32]-to assess real-world applicability. SNAP significantly reduces latency while minimizing performance degradation from existing TTA methods. On Raspberry Pi 4 testbed, it reduced CoTTA's latency by

---

up to 93.12% at an adaptation rate of 0.1 in CIFARIO-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. 77.12%-81.74 -8.74% 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 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 out-of- distribution data by using only the unlabeled test data stream to adapt the model. Test-time normaliza- tion [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 minimize the entropy of its predictions. EATA [30] builds upon Tent, sampling reliable and non ron-renundant samples and utilizing an anti-forgetting regularizer for efficiency. Other works introduce more complex schemes, primarily improve robustness against more practical test-time scenarios. CoTTA [50] addresses continually changing test-time environ- ment by using weight-averaged and augmentaation-averaeed 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 memory bank and 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-basee TTA, proposing an adaptive normalization layer to reduce the intermediate caches for backpropagation. EcoTTA [43] proposes memory-efficien 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 computationalll-heary operations every batch, which can lead 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 full- dataset 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]. consistency [14], and selects samples with scores in certain range. Another set of data-selection methods involves optimization based selection, which formulates an optimization problem to find 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 change in sampling rates. More recent studies such Moderate
as their settings change, such Coreset [51] propose a more robust selection approach by using the distance of a sample to the class center 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 adapta- tion, the source domain data Ds = X y is drawn from the distribution Ps y), while the target domain data D X", y follows Pr y), typically without known labels yj. Given a pre-trained model f(: θ) on the source domain Ds. TTA adjusts the model to the target distribution Pr using only target instances x,. updating the parameters @ to reduce domain discrepancy [48].
3

---

On resource- cooource-oonstaaneed edge devices, frequent adaptation poses a significant bottleneck. Our experiments on a Raspberry Pi 4 [38] revealed that existing TTA methods incur 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 back- propagation overhead, creating bottlenecks 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 im- practical for edge devices (Figure 2).
Components
howed
backprop
EATA
teacher model update (EMA)
forard istudent model)
50.74
+SNAP
augmenttttions
52.35
stochedic
SAR
sugmentation encemble for loss oil
57.94
+SNAP
55.76
RoTTA
51.55
+SNAP
51.33
CoTTA
49.39
+SNAP
50.70
65.0
20.0
Average Latency per batch (s)
Figure Component latency and overall accuracy comparison between full SOTA TTA and SNAP (sparse update with frequency 0.1) on CIFAR100-C, measured on Raspberry Pi 4. SNAP matches accuracy with significantly lower cost.
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 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 cooouucc-constrained
the frequency of model updates, key factor in reducing adaptation latency devices. Unlike conventional TTA methods that process full batches and incur significant overhead, STTA updates the model using only 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 Sparse TTA (STTA) strategy combined with 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 domainn-representatiee samples to maintain model performance while minimizing adaptation overhead.
Motivation. Effective data sampling essential for data-efficient deep learning, particularly when only few samples are available. While score-based methods that prioritize difficult samples perform well at high sampling rates, selecting easy, class-representattive samples is more effective at lower rates [2]. Moderate Coreset [51] also demonstrates that selecting samples near the class center improves performance noisy-label settings, a principle that aligns with the STTA scenario where ground truth is unavailable.

---

Adact Samples
Update Memory
Update Memory
Latency
Timeline
Adaptation
12
3
Adaptation
15
16
Adapt
Acc
Adapt via CnDRM
Inference via loBMN
(a) Sparse adaptation via Domaann Representative Memory
Inference-onll only Batch aware
Betch-
CocRu
Memory Normalization
High Cartdeece
Butcch
MI
IoBMN S,0MN--OBM)
soft
CNORy
Battc
Centrold
LOBNAL
Low Contdeece
Utilize Memory Normalization (MN) stats
Domain
Bascs
CnDRM
Domain Cent. Far
Correct via Inference-only BN (loEN) stats
Figure 3: Design overview of SNAP. The framework consists of two primary components: (a) Class and Domain Representative Memory (CnDRM), which efficiently selects representative samples to minimize adaptation overhead, and (b) Inference-only Batch-aware Memory Normalization (IoBMN), which corrects feature distribution shifts during inference. Together, these components implement the Sparse TTA (STTA) strategy, reducing latency while maintaining model accuracy.
In addition, on real-world deployments, latency constraints often limit adaptation frequency, requiring models function at low adaptation rates (e.g.. 0.1). 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 elass- and domain-repressntatiiv samples to enhance adaptation efficiency in low-data environments. Detailed theoretical analysis on the proposed efficient sampling strategy in Appendix B.
Criteria 1: class representation. To ensure stable adaptation without ground truth labels, CnDRM selects high- 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 calculated as: C(x) max ply/x; +) where p(y|x; Q) is the softmax probability for class y. Only samples with confidence above a threshold T are retained. For balanced representation across diverse classes, 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.
CnDRM selects these high-coofidence samples in a prediction-balanee
domain representation. In addition to class-ropresentattve sampling, Cn- DRM selects domain-representative samples facilitate adaptation new domain condi- tions. Building on the efficient class-representative sampling criteria, we argue that select- ing samples close the domain centroid would enhance performance in STTA. Our prelim- inary experiment results validate improved performance when selecting samples near the cen- troid (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%.
Criteria 2:
As early layers in deep learning mod- els tend retain domain-specifer fea- tures [54, 19, 42], we utilize the hid- den features of early layers identify semain-repressnntaan
Close
Wasserstein distance (instance Domain centroid)
Far
PCA Feature
PCA
Sampled Inttones teit daso A000
2
PCA 2
samples (Ap- pendix 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 ef- fectively mitigated through normaliza-
Accuracy: 26.65 %
Accuracy: 18.52
Figure 4: Sampling visualization and accuracy comparison between the closest 20% and farthest 20% samples from the domain centroid on ImageNet-C Gaussian noise.
5

---

tion adjustments using these statistics [28, 40]. Domain discrepancies in hidden features are substan- tially reduced after passing through 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 Ca is computed using a momentum- normalization layer: Pdomoin f (1 Hddominn + 8μg and o domain f (1 200 3o where be and of are the mean and variance of the current batch t, and [ 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 calculate the domain centroid. The sampled instances effectively represented the domain and were correctly positioned in the embedding space for each criterion (Figure 4).
update of batch statistics from the
We formally define a domain-representaaie sample as one whose early-layer feature statistics are closest to the domain centroid, measured by the Wasserstein distance [47]. The Wasserstein distance quantifies the similarity between two distributions by considering their mean and variance, evaluating how well 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], 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 cosed-form expression:
W (Xt: Cdomain) (Hxx, - Mdommin )2
(Txx domasn )
(1)
For each sample Xt, the feature statistics (μx,, Tx,) are taken from the input to the normalization layer. Further clarification and assumption details are provided in Appendix B.2.
Algorithm Class and Domain Representative Memory (CnDRM) Management
Require: test data stream Zt, memory M with capacity N, confidence threshold Teonf, adaptation
rate 1/k
for batch b E (1,..., B) do
2: Yo + f(b: +)
3:
for each sample x, in batch b do
4: Ú. < Y((]
5:
confidence + C(zz; θ)
6:
(xxx 0x2 + mean & variance of early feature Wa. < W WJz, Cdomain) /eon/ then Add s, (z,, Dt. Ct. Wv,) to M
7:
8:
if confidence
9:
b Add class-representattvee samples
[M| N then
11:
I, +- class with most samples in M
if De & I then
Remove domain-centroic farthest sample
13:
$ farthest <
arg Max,,a,,,MME Wzz
else
15:
Sfarthest + arg MAX.,EMMAK =MAM- Wx.
Remove Sfarthest from M
17: Cdomain + (1 Cdomaain + 8c,
Update domain-centron
Recalculate ws, for all s; in M
19:
if b mod k = 0 then
Adaptation occurs every l batches
20:
Update model θ using samples in M
Memory management algorithm. CnDRM maintains a compact yet adaptive memory that jointly preserves class balance and domain representativeness while keeping computational overhead min- imal. 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 class- and domain remmainnrprrsentatiie samples under dynamic distribution shifts.

---

Algorithm implements these procedures: lines 8~~16 handle both class balancing and the remove centai--entroid 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~~00 perform the update domain--entroid operation using a momentum-basee moving average (with / 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 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 E BxCxLL where B is the batch size, C' is the number of channels, and the number of spatial locations, the batch-wise statisties jie and of for the c-th channel are calculated as follows:
B
Po B ΣE
1 B b= 1=1
EX
(Sr.c. mbbo),
BXL b=1
where Jm and 8² 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 Jm and o2 follow the sampling distribution of the feature map size I, and memory capacity M. The corresponding variances for the memory mean pmm and variance of are calculated as:
27
$2 L M
(3)
M
For the normalization process to adapt efficiently to the current inference batch statistics, IoBMN corrects (im, ) only when Te (and o²)) significantly differ from pm (and ) through soft
shrinkage function:
fmm JoBMN j.m + Sx Pm:: CUS p..)).., (o JBBMMN)2 o. + Sx of as,z) )
where a 2 in IoBMN controls the reliance on the normalization layer statisties. larger a gives more weight to the last adapted memory normalization statistics, whereas a smaller emphasizes the current inference batch normalization statistics. The soft shrinkage function Sx(r; A) is defined as:
Sx(x; X) = sign(r) max([=] - X, 0),
(5)
where À is the threshold and 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 statisties.
Finally, the output of the loBMN for each feature Sb,c,t is computed as:
(oJoBMNy3) : fb.a.1 1
JoBMN
IoBMN(fu.c.i Pm,. o Mm
JoBMN
3,
(6)
JoBBMNN +
where 7 and 3 are learnable affine parameters of normalization layer, and is a small constant added for numerical stability. In our experiments, we chose a as 4 to handle various out-of-distribution scenarios effectively. The parameter is hyperparameter that determines the degree of adjustment desired and can be tuned based on specific requirements.
loBMN utilizes CnDRM's class- representative statistics and adjusts them based on the current inferencing batch statistics. This dual-statistic approach allows loBMN 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, loBMN 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.
7

---

Table 1: Classification accuracy (%) and latency per batch (s) measured on Raspberry Pi 4, compar- ing with and without SNAP (AR=0.I) on CIFARI00-C (ResNet18) and ImageNet-C (ResNet50). Bold numbers indicate the highest accuracy on the sparse setting. Extended results for CIFARIO-C and other ARs (0.01, 0.03, 0.05, 0.3, and 0.5) are in Appendix C.
Methods
Can
Shot
Imp
Def.
Gia
Moe.
Zoom
Snow
Fro.
Pog
Brit.
Cont.
Elax.
Fix.
JPBG
Arg.
A/Aet)
Lat.
CIFARIOOC
Text
40.98
62.78
63.95
46
59.40
49:91
STTA
48.25
37.95
59.45
62.13
$1.60
64.60
51.01
56.42
(-2.02)
3.54
SNAP
47.68
39.92
41.14
63.29
64.53
55.55
59.71
68.05
53.91
59.25
[40.05]
3.67
42.92
37.92
55.40
55.18
55.29
50.61
50.95
01:35
54.38
STTA
26.08
39:01
57.25
16.17
(13.53)
42.3
52.29
54.78
47.89
52.64
38.75
53,63
92:39
+NNAP
34.31
65:08
44.89
SAR
52.00
45.87
65.44
64.68
54.53
60.52
STTA
58.64
62-08
65
52.00
(-445))
2.95
64.97
ReTTA
63.45
56.30
54.43
STTA
50.
41.
(-2.44)
+SNAP
62.5%
66.70
54.51
ImaggeNet
Tea
27.05
28.56
28.64
24.66
23.63
38.70
45.77
04.82
38.06
54.59
64.61
16.84
51.64
55.54
19.38
39.53
38.33
STTA
22.00
23.07
19:38
18.86
52.15
42.29
39.70
54.33
51.62
63.70
47.74
52.35
(-.00))
18.01
SNAP
26,31
27.85
27.50
2362
22.73
36.01
44.11
41.19
38.15
$2.98
64.57
50.23
48.56
53.71
67.09
59.03
(-0.50)
18.76
OCTTA
13:12
13:96
13.94
12.46
12.18
23.74
35.20
31.78
30
44. 40
62.40
15.13
45.26
36.53
28.73
500.23
SITTA
10.97
11:92
11 9K
11.45
11:36
22.90
34.56
90.85
70.80
44.00 09
61.
13.08
40.3 30.30
45 27
56.71
27.81
(-0.9))
161 98
SNNP
15.13
16,03
15.91
13386
14.02
24.90
36.51
31.56
31.81
46.02
63.60
15.09
41.94
46.78
38,03
36.19
(+1.47)
163.34
FATA
29.62
31.79
31.17
26.89
26.30
J0.65
47.44
46.29
40.76
55.57
64.97
58.02
$2.66
56.01
50.26
42.56
$1.96
SITA
22.45
23.78
25.26
19:38
19:42
32.18
43.22
40.65
36.64
$2.38
63.87
24.50
15.13
52.
46.33
56.61
(-5.05)
16.00
SNAP
26.30
27.29
27.13
22.38
22.15
33.45
43.92
48.96
36.65
52.71
63,77
27.93
85.47
53.23
47.46
35.24
(-4.32)
17.45
SAR
29.25
31.14
29.85
29.29
27.39
39.76
44.13
45.95
20.39
55.13
63.71
17.34
52.31
56,09
09.35
39.34
75.15
STTA
26.12
27.56
26.95
22.51
23.25
35,03
44.48
43.19
37.26
53.82
64.15
19.87
50.76
54.78
63.43
38,02
[.072)
21.39
SNAP
30.28
31.97
31.30
26.67
26.31
39.66
46.08
45.45
46.36
$4.76
64.62
56,12
$1.36
55.42
29.63
41.99
(+2.05)
23.99
ROTTA
20.60
2285
1981
10.46
10.10
21.31
31.83
39.66
32.09
46.08
02. 22
20.21
42.54
47.47
40.67
$1.20
57.00
SITA
14.77
15.59
15:33
13.17
13.19
23,85
35.18
32.75
30.77
45.2 22
80 05
15.82
41.05
46.11 15
57. 19.19
29.54
[-1.00)
45.98
SNAP
15.35
16.20
16.01
1367
13,66
24.27
38.62
33.04
31.02
45.38
62.95
15.96
41.06
46.17
37.44
29.85
1-1 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 conetcy-contrrained scenarios. In 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: CIFAR1O-C, CIFAR100-C and IetgeNet-CC [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] the backbone network, utilizing models pre-trained on CIFARIO and CIFAR 100 [18]. We also use ResNet50 [8] and Vit-Base [4] pre-trained on ImageNet [3] from the Vorcon [25] library.
Baselines. SNAP is designed to integrate with existing TTA algorithms. Therefore, testing existing
TTA algorithms under different ARs serves 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 teacher-student framework, (ii) EATA [30], (iv) SAR [31], and (v) RoTTA[53].
Overall performance across various adaptation rates. Table 1 and Appendix C provide perfor- mance comparison of baseline state-of sfate-of-the-eee the-art (SOTA) TTA methods and SNAP integration across adaptation rates from 0.01 to 0.5 on CIFAR 1A/1100000-C and Imtge 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.
8

---

Figure 5 further illustrates that SNAP maintains STTA performance even at adaptation rates as low as 0.01
Latency Batch
Accurnry 196
while significantly reducing latency.
In contrast, naïve STTA suffers sub-
stantial performance degradation as
the adaptation rate decreases. No-
tably, computationally complex and cetency-intensiie method CoTTA ben- efits more from SNAP. This is be- cause CoTTA updates all model pa- rameters, making it highly dependent on an effective sampling strategy, derscoring the effectiveness of Cn- DRM. At higher adaptation rates (0.5 or 0.3), SNAP can even surpass fully adapted methods by selectively utilizing the most informative samples, similar to existing sampling-baser TTA methods [30, 31, 6, 7J. 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-constraingg environ- ments. Extended results on various adaptation rates and datasets (CIFARI0/100-C and ImageNet-C) are reported in Appendix C.
Adaptation Rate
Adaptation Rate
0.5 0.3
0.05
0.01
0.5
01 0.03
TENT-SNAP
- EATA-SNAP
SAR+SNAP
RoT RoTTRASMAP - COTTANNNAP
EATA
RoTTA
Figure 5: Latency on Raspberry Pi 4 and CIFAR ac-
curacy across adaptation rates. Due SNAP's negligible overhead, solid and dotted lines overlap in the latency plot. Marker size indicates standard deviation.
Contribution of SNAP's individual components. We conducted an ablative evaluation under- stand 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 confi- dence 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 loBMN uses memory samples' statistics corrected match that of the test batch (the second component of SNAP).
Contrary to the belief that low-entropy sam- ples benefit TTA [30, 31], LowEntropy per- formed worse than Rand for STTA, due to lim- ited updates causing poor slow convergence. CRM, originally for data-efficient supervised learning [2, 51], outperformed Rand but re- mained 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 low-latency STTA.
Table 2: Classification accuracy (%) comparison of ablative settings on the STTA (AR=0.1). Perfor- mance averaged over all 15 CIFARIO-C corruptioss.
Mathol
Tess
CoTTA
EATA
SAR
RoTTA
Nave
76.81 111e
66.42 2012
76.29 11:1
76.01 12mn
74.75 2015
Random
77.08 2314
65.61
2018
76.59
23:33
76.33
2310
75.01 2011
LowEncoopy
75.66
63.19
2014
74.59
4612
74.41
4118
72.60 2013
CRM
77.37
65.71
201
77.38
1025
74.36
1311
75,27
2017
CoDRM
77.46 23m
77.89
2111
17.17
20:5
76.85
75.64 201
CaDRM-EMA
78.02 4112
72.19 4015
37.05 am:1
76.84
1113
76.15 2a1d
CaDRM-laBMIN
78.95 1306
78.83
78.61
10:35
78.06
13m
77.07
2013
Performance validation across diverse edge-devices. SNAP significantly reduces adaptation latency across 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- 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 statisties 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- 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).

---

SNAP on vision transformer. We validate SNAP on ViT-Base [4] by adapting CnDRM and IoBMN to instance-level layer normalization (LN), replacing batch statisties. This confirms that our core strategies, class-domain sample selection and normalization shift mitigation, generalize to LN. SNAP achieves up to 2.9x latency reduction while preserving or improving full adaptation accuracy across all five baselines (Figure 6). Details are in Appendix B.9.
Tent
Original (Pul)
+SMP
SNAP (Sparse)
EATA SNAP
40.43%
59.21%
1.7x
43.86%
SNAP
ROTTA
42.9395
2.6x
CoTTA
41.25%
+SNAP
29.43%
2.9x
c0o
Robustness under continuous and persistent distri- bution shifts. SNAP adapts efficiently to evolving domains by smoothly moving its domain centroid with minimal overhead. In continuous stream of corrup- tions from ImageNet-C, it outperforms naive STTA by over 2.5% average. We further assess long-term 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.
Latency per batch (s, log scale)
Figure 6: Latency comparison of full (orig- inal) and sparse (SNAP) TTA on ViT- Base [4], ImageNet-C. Accuracy values annotated to the right of each bar.
Robustness in single-sample (BS=1) adaptation scenario. In highly constrained environments where the batch size is limited one, SNAP maintains strong performance. achieves 51.80% accuracy with an adaptation rate of 0.1, closely matching the full SAR [31] baseline at 52.21% % and performing over 5x better than naive STTA. CnDRM continues 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. adapts effectively with a memory size equal to the batch size, larger sizes offer only 1~22% 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 based on distribution shifts system load could improve responsiveness. The confidence threshold in CnDRM also fixed as a simple safeguard, which may limit adaptability. Dynamically tuning this threshold based 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 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. 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 resource- constrained edge devices. To address this, we propose SNAP, 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.
10

---

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. NN.22024-0444462.
Non-invasive mear-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 & Evaluation (IITP) grant funded by the Korea government (MSIT) R0S-2025-254428222 Al Star Fellowship Program (Ulsan National Institute of Science and Technology)). * MSIT: Ministry of Science and ICT
Communications Technology Planning
References
[1] Motasem Alfarra, Hani Itani, Alejandro Pardo, Shyma Yaser Alhuwaider, Merey Ramazanova, Juan Camilo Perez, Zhipeng Cai, Matthias Müller, and Bernard Ghanem. Evaluation of test- time adaptation under computational time constraints. In Proceedings of the 4 International Conference on Machine Learning, volume 235 Proceedings of Machine Learning Research, pages 976-991. PMLR, 21-27 Jul 2024.
[2] Hoyong Choi, Nohyun Ki, and Hye Won Chung. Bws: best window selection based on sample scores for data pruning across broad ranges. In Proceedings of the 41 International Conference on Machine Learning. JMLR.org. 2024.
[3] Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large- scale hicrarchical image database. In 2009 IEEE Conference on Computer Vision and Pattern Recognition, pages 248-255, 2009.
[4] Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai Thomas Unterthiner, Mostafa Dehghami. Matthias Minderer, G Heigold. S Gelly, et al. An image is worth 16x16 words: Transformers for image recognition at scale. In International Conference Learning Representations, 2020.
[5] Pierre Foret, Ariel Kleiner, Hossein Mobahi, and Behnam Neyshabur. Sharpness-aware min- imization for efficiently improving generalization. In International Conference on Learning Representations, 2021.
[6] Taesik Gong, Jongheon Jeong, Taewon Kim, Yewon Kim, Jinwoo Shin, and Sung-Ju Lee. NOTE: Robust continual test-time adaptation against temporal correlation. In Advances in Neural Information Processing Systems, 2022.
[7] Taesik Gong, Yewon Kim, Taeckyung Lee, Sorn Chottananurak, and Sung-Ju Lee. SoTTA: Robust test-time adaptation noisy data streams. In Thirty-seventh Conference Neural Information Processing Systems, 2023.
[8] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for im- age recognition. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, June 2016.
[9] Dan Hendrycks, Steven Basart, Norman Mu, Saurav Kadavath, Frank Wang, Evan Dorundo, Rahul Desai, Tyler Zhu, Samyak Parajuli, Mike Guo, Dawn Song, Jacob Steinhardt, and Justin Gilmer. The many faces of robustness: A critical analysis of out-of-distribution generalization. ICCV, 2021.
[10] Dan Hendrycks and Thomas Dietterich. Benchmarking neural network robustness to common corrpttion and perturbations. In International Conference Learning Representations, 2019.
[11] Trung-Hieu Hoang, Duc Minh Vo, and Minh N. Do. Persistent test-time adaptation in recurring testing scenarios. In Thirty-eighth Conference on Neural Information Processing Systems, 2024,
[12] Junyuan Hong, Lingjuan Lyu, Jiayu Zhou, and Michael Spranger. Mecta: Memory-econonic continual test-time model adaptation. In International Conference on Learning Representations, 2023.

---

[13] Yusuke Iwasawa and Yutaka Matsuo. Test-time classifier adjustment module for model -aggos-g domain generalization. Advances Neural Information Processing Systems, volume 34, pages 2427-2440. Curran Associates, Inc., 2021.
[14] Ziheng Jiang, Chiyuan Zhang, Kunal Talwar, and Michael C Mozer. Characterizing structural regularities of labeled data in overparameterized models. In Proceedings of the 38th Interna- tional Conference on Machine Learning, volume 139 of Proceedings of Machine Learning Research, pages 5034-5044. PMLR, 18-24 Jul 2021.
[15] Diederick P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. In Interna- tional Conference on Learning Representations, 2015.
[16] Pang Wei Koh and Percy Liang. Understanding black box predictions via influence functions. In Proceedings of the 34th International Conference on Machine Learning, volume 70 of Proceedings of Machine Learning Research, pages 1885-1894. PMLR, 06-11 Aug 2017.
[17] Germain Kolossov, Andrea Montanari, and Pulkit Tandon. Towards statistical theory of data selection under weak supervision. In The Twelfth International Conference on Learning Representations, 2024.
[18] A. Krizhevsky and G. Hinton. Learning multiple layers features from tiny images. Master's thesis, Depariment of Computer Science, University of Toronto, 2009.
[19] Kimin Lee, Kibok Lee, Honglak Lee, and Jinwoo Shin. A simple unified framework for detecting dittr---istiittionn samples and adversarial attacks. Advances in neural information processing systems, 31, 2018.
[20] Yanghao Li, Naiyan Wang, Jianping Shi, Jiaying Liu, and Xiaodi Hou. Revisiting batch normalization for practical domain adaptation. Pattern Recognition, 80, 03 2016.
[21] Lin, Wei-Ming Chen, Yujun Lin, John Cohn, Chuang Gan, and Song Han. Mcunet: Tiny deep learning on iot devices. In In Advances in Neural Information Processing Systems, volume 33, pages 11711-11722. Curran Associates, Inc., 2020.
[22] Haolan Liu, Zixuan Wang, and Jishen Zhao. Cola: characterizing and optimizing the tail latency for safe level-4 autonomous vehicle systems. In 2025 IEEE International Conference on Robotics and Automation (ICRA), pages 3709-3719. IEBE, 2025.
[23] Aleksej Logacjov, Kerstin Bach, Atle Kongsvold, Hilde Bremseth Bårdstu, and Paul Jarle Mork. Harth: A human activity recognition dataset for machine learning. Sensors, 21(23):7853, 2021.
[24] Ilya Loshchilov and Frank Hutter. SGDR: Stochastic gradient descent with warm restarts. In International Conference on Learning Representations, 2017.
(25) Virchn maintainers and contributors. Torchvision: Pytorch's computer vision library.
https://gi thtb. pyttoch/viiiion...to... 2016.
[26) Baharan Mirzasoleiman, Jeff Bilmes, and Jure Leskovec. Coresets for data-efficient training of machine learning models. In Proceedings of the 37th International Conference on Machine Learning, volume 119 of Proceedings of Machine Learning Research, pages -950- PMLR, 13-18 Jul 2020.
[27] Eduardo Fernandes Montesuma, Fred Maurice NGOLE MBOULA, and Antoine Souloumiac. Optimal transport for domain adaptation through gaussian mixture models. Transactions on Machine Learning Research, 2025.
[28] Zachary Nado, Shreyas Padhy, D Sculley, Alexander D' Amour, Balaji Lakshminarayanan, and Jasper Snoek. Evaluating prediction-time batch normalization for robustness under covariate shift. arXiv preprint arXiv:2006. 10963, 2020.
[29] Shuaicheng Niu, Chunyan Miao, Guohao Chen, Pengcheng Wu, and Peilin Zhao. Test-time model adaptation with only forward passes. The International Conference on Machine Learning, 2024.
12

---

[30] Shuaicheng Niu. Jiaxiang Wu, Yifan Zhang, Yaofo Chen, Shijian Zheng, Peilin Zhao, and Mingkui Tan. Efficient test-time model adaptation without forgetting. In Proceedings of the 39th International Conference on Machine Learning, volume 162 of Proceedings of Machine Learning Research, pages 16888-16905. PMLR, 17-23 Jul 2022.
[31] Shuaicheng NIu, Jiaxiang Wu, Yifan Zhang, Zhiquan Wen, Yaofo Chen, Peilin Zhao, and Mingkui Tan. Towards stable test-time adaptation in dynamic wild world. In The Eleventh Interaational Conference on Learning Representations, 2023.
[32] NVIDIA Corporation. NVIDIA Jetson Nano, 2019. Accessed: 2024-11-20.
[33]
Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, Alban Desmaison, Andreas Kopf, Edward Yang. Zachary Vetito, Martin Raison, Alykhan Tejani, Sasank Chilamkurthy, Benoit Steiner, Lu Fang. Junjie Bai, and Soumith Chintala. Pytorch: An imperative style, high-performance deep learning library. In Thirly-second Advances in Neural Information Processing Systems, pages 8024-8035. Curran Associates, Inc., 2019.
[34] Mansheej Paul, Surya Ganguli, and Gintare Karolina Dziugaite. Deep learning on data diet: Finding important examples early in training. In Advances in Neural Information Processing Systems, 2021.
[35] Geoff Pleiss, Tianyi Zhang, Ethan Elenberg, and Kilian Q Weinberger. Identifying mislabeled data using the area under the margin ranking. In Advances in Neural Information Processing Systems, volume 33, pages 17044-17056. Curran Associates, Inc., 2020.
[36] Omead Pooladzandi, David Davini, and Baharan Mirzasoleiman. Adaptive second order coresets for data-efficient machine learning. In Proceedings of the 39th International Conference on Machine Learning, volume 162 of Proceedings of Machine Learning Research, pages 17848- 17869. PMLR, 17-23 Jul 2022.
[37] Joaquin Maliionero-Candee Masashi Sugiyama, Anton Schwaighofer, and Neil D Lawrence. Dataset shift in machine learning. Mit Press, 2008
[38] Raspberry Pi Foundation. Raspberry Pi 4 Model B, 2019. Accessed: 2024-11-20.
[39] Raspberry Pi Foundation. Raspberry Pi Zero 2 W, 2021. Accessed: 2024-11-20.
[40] Steffen Schneider, Evgenia Rusak, Luisa Eck, Oliver Bringmann, Wieland Brendel, and Matthias Bethge. Improving robustness against common corruptions by covariate shift adaptation. In Advances in Neural Information Processing Systems, volume 33, pages 11551111551. Curran Associates, Inc., 2020.
[41] Roy Schwartz, Jesse Dodge, Noah A. Smith, and Oren Etzioni. Green ai. Commun. ACM, 63(12):54-63 November 2020.
[42] Mattia Segu, Alessio Tonioni, and Federico Tombari. Batch normalization embeddings for deep domain generalization. Pattern Recognition, 135:109115, 2023.
[43] Junha Song, Jungsoo Lee, In So Kweon, and Sungha Choi. Ecotta: Memory-efficient continual test-time adaptation via delf-distilled regularization. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 11920-11929 2023.
[44] Ben Sorscher, Robert Geirhos, Shashank Shekhar, Surya Ganguli, and Ari S. Morcos. Beyond neural scaling laws: beating power law scaling via data pruning. In Proceedings of the 36th International Conference on Neural Information Processing Systems, NIPS '22, Red Hook, NY,
USA, 2022. Curran Associates Inc.
[45] Ardi Tampuu, Kristjan Roosild, and Ilar Uduste. The effects of speed and delays on test-time performance of end-to-end self-driving. Sensors, 2466) 2024.
[46] Mariya Toneva, Alessandro Sordoni, Remi Tachet des Combes, Adam Trischler, Yoshua Bengio, and Geoffrey J. Gordon. An empirical study of example forgetting during deep neural network learning. In International Conference Learning Representations, 2019.
13

---

[47] Cédric Villani. The Wasserstein distances, pages 93-111. Springer Berlin Heidelberg, Berlin, Heidelberg, 2009.
[48] Dequan Wang, Evan Shelhamer, Shaoteng Liu, Bruno Olshausen, and Trevor Darrell. Tent: Fully test-time adaptation by entropy minimization. In International Conference on Learning Representations, 2021.
[49] Haohan Wang, Songwei Ge, Zachary Lipton, and Eric Xing. Learning robust global represen- tations by penalizing local predictive power. In Advances in Neural Information Processing Systems, pages 10506-10518, 2019.
[50] Qin Wang, Olga Fink, Luc Van Gool, and Dengxin Dai. Continual test-time domain adaptation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 7201-7211, June 2022.
[51] Xiaobo Xia, Jiale Liu, Jun Yu, Xu Shen, Bo Han, and Tongliang Liu. Moderate coreset: A universal method of data selection for real-world data-efficient deep learning. The Eleventh International Conference Learning Representations, 2022.
[52] Shuo Yang, Zeke Xie, Hanyu Peng, Min Xu, Mingming Sun. and Ping Li. Dataset pruning: Reducing training data by examining generalization influence. In The Eleventh International Conference Learning Representations, 2023.
[53] Longhui Yuan, Binhui Xie, and Shuang Li. Robust test-time adaptation in dynamic scenarios. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pallern Recognition, pages 15922-15932, June 2023.
[54] Matthew D Zeiler and Rob Fergus. Visualizing and understanding convolutional networks. In Computer Vision-ECCV 2014: 13th European Conference, Zurich, Switzerland, September 6-12, 2014, Proceedings, Part 13, pages 818-833. Springer, 2014.
[55] Marvin Zhang, Sergey Levine, and Chelsea Finn. Memo: Test time robustness via adaptation and augmentation. In Advances in Neural Information Processing Systems, volume 35, pages 38629-3888 38642. Curran Associates, Inc., 2022.
14

---

A Experiment details
All experiments presented 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, the performance differences attributable the random seed are negligible. Latency measurements were mainly conducted on a Raspberry Pi 4 [38], equipped with 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 inplementations 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 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 fair comparison. To minimize overhead and maintain consistency with inference batches, we set the size CnDRM equal to the batch size. TTA is conducted in an online manner, with adaptation inference performed per batch. When there and certain components of the existing baseline methods, we prioritized SNAP's features for fair evaluation the STTA setting.
conflict between the implementation of SNAP
Tent [48] We update the BN affine parameters using the SGD optimizer [24] with learning rate of I = 1 - 3 for CIFAR10/10 10/100C and = 1e 4 for ImageNet-C. For separate experimentation on the ViT, we used learning rate of / 2e 4.
CoTTA [50] We update all model parameters using the Adam optimizer [15] with learning rate o = le - Furthermore, we set CoTTA's teacher model EMA factor to a = 0.99, the restoration factor to p 0.1, and the anchor probability Ahh 0.9.
EATA [30] We use the SGD optimizer with a learning rate of l 1e 4. We set the entropy threshold as Fn = 0.4 x In [V], where is the total number of classes.
SAR [31] We use SAM [5] with the base optimizer as SGD with a learning rate of | 1e- - 3. For fair evaluation, replaced the sample filtering scheme with SNAP's CnDRM.
RoTTA [53] We use the SGD optimizer with learning rate of l = 1e - we replaced RoTTA's RBN and CSTU with SNAP's CnDRM and loBMN. For the teacher-student structure, we set the teacher model's exponential moving average update rate
3. For fair evaluation,
1e 3.
Finally, we list the hyperparameters specific to the components of SNAP. The confidence threshold for CnDRM Feom is set to 0.4 for CIFARIO- 10-C, 0.45 for CIFARI00-C, and 0.5 for ImageNet-C. The entropy threshold for our ablation study Tentr is set to log(10) x 0.40 for CIFAR10-C and (og(10)) x 0.40 for CIFAR100-C C, as referenced in a previous work using entropy-based filtering [30]. Additionally, the parameters for the soft shrinkage function in loBMN are fixed with a for Tent, CoTTA, SAR, RoTTA, and 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 data- efficient learning and generalization under constrained adaptation settings. Under latency-constrained scenarios, models can only adapt intermittently. This raises the following question:
15

---

Which subset of streaming samples yields the greatest adaptation gain when only a. f.aactioon p n/N of them can be used for weight updates?
Selection ratio and phase transition. 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 p::
p= n/N (0. 1] denote the adaptation ratio, where
When p 0.6 (high adaptation rate), selecting low-confidence samples near decision boundaries provides maximal information gain.
When < 0.5 (sparse adaptation), selecting high-confidence, representative samples near class domain centroids leads to better generalization.
This dichotomy is supported analytically in [2], which shows that in underparameterrzeed regimes, boundary samples may inject noisy gradients and destabilize learning.
Illustrative example. Consider a binary classification task where inputs H; ~ NN(0, 7/ Ta), and labels are assigned by sign(x;1). The Bayes-optimal classifier aligns with e,, the first basis vector. Suppose we select a subset (X9, E Rdxaa x {- and compute the ridge regression solution:
Wis arg min llys wERd
w01²
As shown in prior work [2], in the sample-deficiett regime (n < d), the solution we aligns best with the true decision direction when trained on high-confidence samples. In contrast, in the sample- sufficient 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 C Dteat under << 1 can be defined as:
S arg max
Σ (1f(a)) 8.
pe,
s.t. c; arg max fz(24),
(8)
where Me. is the estimated feature-space class centroid. This motivates our use of class- and domain- representative memory (CnDRM), which prioritizes confident, centroid-alignede samples for parameter updates under low-frequency adaptation.
Under sparse adaptation (p < 1), selecting the most informative subset of test samples becomes critical. Our method prioritizes samples that are both semantically reliable cclass-representative and statistically aligned (domain-reprrseentttiv))
For the dlassteepreeentttive criterion, we follow insights from [2], which show that the sample- deficient regime, high-confidence samples, those far from the decision boundary, yield better general- ization than boundary samples. Rather than explicitly computing class centroids, we approximate class-representative samples by selecting those with the highest prediction confidence:
S Slasss
{oz E Drest Conf(2;)) T).
where Conf(x;; = max, fI;)) is the softmax confidence score and is a confidence threshold.
To additionally enforce domain- representativeeness, we compute the Wasserstein-2 distance between each candidate sample and the estimated domain distribution. Specifically, each domain d is modeled as Gaussian A( Ea), where:
Va
Σ f(x)), ILEDA
Σn
Σ (f(a)) va)a))-)(((())))) - va)T. I.EDa
(10)
Da
Da
Each sample x; is treated as an empirical distribution (ip,, E,) using a local batch of neighboring features. The closed-form squared 2-Wasserstein distance between two Gaussians given by:
W3 (N(n, N,s, Ex)) = ||l4 vall Tr E, E. (,"/"",>//""
(1))
16

---

Combining both criteria, our final selection strategy becomes:
S = arg
min
Σ Cliss B:ES
(H Ea));
(12)
SCS
i.e. we select 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 p < 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 diagonal covariance assumption. The detailed assumptions are as follows:
Gaussian assumption: Each channel's activations are assumed to follow Gaussian distri- bution N(u, o²), which simplifies the formulation since Gaussian distributions are fully determined by their mean μ and variance o². This approximation is commonly adopted in deep learning, where normalized feature activations tend to exhibit near- Gaus-an behavior in high-dimensional feature spaces.
Diagonal covariance: The covariance matrix for each Gaussian is assumed to be diago- nal, implying independence across channels. This assumption is widely used in domain adaptation and transport-basee methods, as it reduces the computational complexity of full covariance estimation while focusing per-channel variance shifts.
W-ssssesteiin distance for Gaussian distributions: Under these assumptions (independent Gaussian distributions), the squared 2- Wasserstein distance between two univariate Gaussian distributions N(1, of) and N o is given by:
W? = (P1 222 (a1 - ?
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 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 Batch Normalization (BN) statisties at inference time, our key contribution lies in systematically redesigning these components for sparse-update regimes resource-constrained environments, which impose fundamentally different computational and statistical constraints.
17

---

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.
loBMN 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 odaptation-involver 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 inherently domain-specific,, making these layers more sensitive shifts in input data distribution-44 critical challenge for tasks requir-
hew (Gn))
Wetherinww Dignal Eant)
PCA 104toa
ing domain adaptation and generalization [19, 42]. This sensitivity arises because early layers encapsulate domain-specific patterns that may not generalize 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.
Faaturr
Figure 7: PCA embedding of early layer features for one do- main from each of the four main CIFAR corruption categories, showing clear sep- aration between domains.
Visualizing early layer feature embeddings using 2D PCA on CIFAR- 10C domains reveals distinct domain-speciffe patterns, highlighting 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-sensinn 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 ran- dom sampling with high-confidence sampling across three benchmarks: CIFAR100 10-C. CIFAR 100-C, and ImageNet-C. Table shows that high-confidence sampling consistently outperformed random sampling, achieving significantly higher pseudo-label accuracy in all datasets. This result demon- strates the effectiveness of selecting high-confidence samples to improve the quality of pseudo-labels, thereby enhancing model adaptation under domain shift conditions.
Table Pseudo-label accuracy comparison between random and high-confidence sampling on three benchmakrs: CIFAR1O-C, CIFAR100-C, and ImageNet-C. Bold numbers are the highest accuracy.
CIFARIO-C CIFAR100-C
ImageNet-C
Random 69.9110.31
15.30.0000
23.90_019
HighConf
74.80
29238
59.40=004
18

---

B.6 Latency tracking of SNAP on diverse edge-devices
To evaluate the latency efficiency of SNAP on resource-constrainee edge devices, we measured
the adaptation latency across three devices: NVIDIA Jetson Nano [32], Raspherry Pi 4 [38], and
Raspherry 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. demonstrating the effectiveness of SNAP reducing adaptation lateney while maintaining competitive accuracy, Figure 8 illustrates the latency performance for each device. It is evident
Tent
Original TTA
Or ginal TTA
Original TTA
SNAP-TTA
ShAP-TTA
SNAP-TTA
EATA
EATA
EATA
BOTTA
BoTTA
RoTTA
COTTA
COTTA
CoTTA
10
15
10
20
30 Batch
50
0
200
400
600
500
Average Batch
Average
Awerage Latenty Batch (9)
(a) NVIDIA Jetson Nano
(b) Raspberry Pi 4
(c) Raspberry Zero
Figure 8: Latency comparison between SNAP-TTA and Original TTA across five state-of-the-ard 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.
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 87.5% on the Raspberry Pi 4, emphasizing the practical benefits of SNAP latency-sensitive environments. Additionally, similar trends were observed across other devices, including the resource- limited Raspberry Pi Zero 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.
Table 4: Latency Measurements (AR=1, 0.3, 0.1, 0.05) on Jetson Nano [32].
Methods
AR=1
AR=0.3
AR=0.1
AR=0.05
Tent
2.57
1.97 (-23.51%)
1.35 (-47 62%%
1.19 (-53.75%)
EATA
2.52
1.90 (-24.70%)
1.33 (-47.22%)
1.19 (-52.79%)
SAR
5.15
2,87 (-44.29%)
(-68.94%)
1.32 (-74.28%%
RoTTA
5.24
2.91 (-44.46%)
1.62 (-69.13%)
1.32 (-74.81%)
CoTTA
13.18
6.13 (-53.46%)
2.61 (-80.22%)
1.82 (-86.19%)
Table 5: Latency Measurements (AR=1, 0.3, 0.1, 0.05) Raspberry Pi 4 [38].
Methods
AR=I
AR=0.3
AR=0.1
AR=0.05
Tent
4.78
3.54 (-26.09%)
3.09 (-35.45%)
2.35 (-50.87%)
EATA
5.68
3.52 (-38.00%)
2.87 (-49.45%)
2.31 (-59.28%)
SAR
9.45
4.88 (-48.34%)
2,98 (-68.41%)
2.54 (-73.16%)
RoTTA
12.07
4.95 (-58.97%)
2.94 (-75.62%)
2.91 (-75.91%)
CoTTA
41.77
11.80 (-71.766)
4.93 19%)
3.64 (-91.29%)
Table 6: Latency Measurements (AR=1, 0.3, 0.1, 0.05) Raspberry Pi Zero 2 W [39].
Methods
AR=1
AR=0.3
AR=0.1
AR=0.05
Tent
34.96
24.67 (-29.42%)
25.06 (-28.32%)
17.07 (-51.16%)
EATA
50.72
27.01 (-46.75%)
28.43 (-43.93%)
17.00 (-66.48%)
74.64
47.79 (-35.96%))
29.56 (-60.40%)
18.64 (-75.01%%)
RoTTA
154.88
86.54 (-44.13%)
44.08 (-71.54%)
22.44 (-85.51%)
CoTTA
622.28
228.03 (-63.36%)
92.01 (-85.21%)
39,22 (-93.70%)
19

---

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, present both 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, includ- ing both feature statistics (mean and variance) and the raw image samples, and (2) the statis- ties required for Inference-only Batch-aware Memory Normalization (IoBMN). For batch size B, the total theoretical memory overhead can be expressed as: Memory Overhead (Image Size + x Feature Dimension x Bytes per Value) +Feaurre Dimension x Bytes per Value x 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.
B x
For ResNet18 on CIFARIO-C. CIFARIO images have resolution of 32 x 32 x 3 with each value stored as byte. For a feature dimension of 512 and batch size / 16, the total overhead is: Image Overhead = 16 x (32x) x 32 x x1)
1)- = 49, 152 bytes (48 KB), Feature Overhead (CnDRM) = 16 x (512 2 x 4) = 65, 536 bytes (64 KB), Feature Overhead (IoBMN) 512 x 2 x =
4, 096 bytes (4 KB). Thus, the total memory overhead is: Total Overhead = 48 KB + 64 KB
4 KB- 116 KB.
For ResNe150 on ImageNet-C, ImageNet images have a resolution of 224 x 224 x 3, stored as byte per value. For a feature dimension of 2048 and batch size B 16, the total
overhead is: Image Overhead = 16 x (224 x 224 x 3 x 1) = 12, 044, 928 bytes (11.5 MB), Feature Overhead (CnDRM)
262, 144 bytes (256 KB), Feature Overhead (IoBMN) = 2048 x 2 x 4 = 16, 384 bytes (16 KB). Thus, the total memory
16 (2048 x 2 x 4)
overhead is: Total Overhead = 11.5 MB + 256 KB + 16 KB 11.77 MB.
Table 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% 1.74%. Furthermore, while peak memory usage 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 eeemory-intensiie operation in TTA.
Table 7: Comparison of memory usage (Average Memory, Peak Memory, and Memory Overhead) between Original TTA and SNAP (adaptation rate 0.3) across various methods (Tent, EATA, CoTTA, SAR, and RoTTA) tested on Raspberry Pi 4. Bold numbers are the lowest memory usage.
Average Mem (MB)
Peak Mem (MB)
Mcm Overhead (MB)
Methods
Original TTA
SNAP
Original TTA
SNAP
SNAP Original
Tent
764.24
751.35
822,93
828.46
5.52 (0.67%)
CoTTA
1133.52
1099.64
1211.21
1227.99
16.78 (1.13%)
EATA
816.69
749.95
847.73
862.51
14.78 (1.74%)
SAR
786.65
753.69
863.77
865.18
1.41 (0.02%)
RoTTA
933.23
871.64
972.23
983.94
11.71 (1.20%)
These findings demonstrate that SNAP's memory overhead is negligible compared to its benefits in latency reduction and accuracy improvements. By leveraging 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 applications on edge devices.
20

---

B.8 Integration of SNAP with memory-efficient TTA algorithm
This section evaluates the integration of SNAP with MECTA [12], memory -emnory-efffiient 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 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.
Table 8: Comparison of classification (%) and memory peak (MB) in STTA with an adaptation rate of 1. MECTA significantly reduces memory consumption, and SNAP is applied alongside to boost the performance of sparse adaptation. The accuracy is the average over 15 corruptions in ImageNet-C.
Bold numbers indicate either the lowest memory usage or the highest accuracy.
Methods
Accuracy (%)
Mennory (MB)
Tent
35.21
6805,22 26
+MECTA
37.62=0.1
4620.25 (-32.10%) 4622.12
SNAP
39,52a015
(-32.08%)
EATA
35.55.0 19
6541 .00
+MECTA
41.41_037
4512.38
(-31.01% %)
+ SNAP
42.86::020
4535.44
(-30.66%)
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 results. The findings confirm that SNAP 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-constrrined environments such as edge devices.
Table 9: Evaluation of SNAP with MECTA on ImageNet-C through Adaptation Rates(AR) (0.3, 0.1,
and 0.05). Bold numbers are the highest accuracy.
AR
Methods
Gan.
Shot
Imp.
Def.
Gia.
Mot.
Zoom
Snow
Froo.
Fog
Drit.
Cont.
Clas.
Pis.
JPDG
Avg.
Teas + MECTA
+1..0
28:20
=3.41
30.13
20.08
29.58
211.2
23:07
=1147
23.35
20.13
34.09
20.13
45.95
20.15
40.97
=1141
35.68
+11.4
55.66
20.06
66.56
+0.47
14.72
+0.15
53.09
50005
57.16
50.15
50,74
=11.22
39.29
SNAP
10.26
30.49
31.98
31.66
20.21
26.29
10.32
26.19
20.30
38.47
47.38
:0.11
43.70
40.12
10.05
56.38
=0.07
66.81
28.87
20.26
20.09
53.53
57.61
20.10
50.86
20.15
42.83
EATA MFCTA
32.18
41.02
49.24
57.35
=t085
+11.0
55.38
41.11
SNNP
30.35
57.50
55.38
45.08
20.19
+0.10
20.11
20.06
=0.10
20.10
20.15
20.06
20.16
20.12
20.02
20.15
Teat MECTA
24.04
+6.15
+0.30
25.63
+0.07
21:11
+0.23
+0.18
+0.02
32.11
-0.19
44.05
38.22
53.92
#0.12
40022
66.48
50.80
+0.13
55.67
#0.18
48,33
37.62
+0.16
0.1
EATA + MECTA
SNAP
20.05
20.57
27.49
29.42
+0.30
=41.14
25.90
51.72
20.32
20
=0.16
28.26
24
23.49
20.17
10:74
24.41
40.45
+11.2
23.76
25.45
20.18
=0006
34,92
37.04
20.13
47.10
20.15
45.18
20009
43.60
20.19
40.21
20.38
20.18
38.40
39.43
+0.13
+11.4
55.95
53.78
20.14
66.42
2003
66.54
21.18
27.72
28.85
29.20
20.15
211.00
53.70
51,00
20.15
S7.34
2013
55.48
#0.36
51.20
47.51
20.17
20.37
20.13
41.41
39
SNAP
31.26
10.11
+0.17
32.71
+0.17
32.22
27.31
10.46
40.25
27.61
#0.28
38,88
47.83
$0.09
44.52
#0.14
10.05
41L5X
10.06
56.42
66.24
80.21
60.63
35.38
10.17
53.67
57.30
#0.13
50.83
10.20
42.86
Tex MECTA
21.22
21.13
23.19
21.90
10.18
18.69
19.39
29.89
20.10
42.02
36.53
35.23
#1.15
51.75
66.23
19.64
211.00
45.43
53.54
45.43
211.14
35.54
0.06
-SNAP
MECIA
23.93
$11.7
#1.42
+0.27
21.87
<3
=0.15
+0.90
21.19
10.18
+1145
=000
33.61
=0.16
20.1
42.68
=0.14
45.11
20.19
40,92
#1 11.10
+0.17
51.64
51.43
66.60
2017
23,00
+0.59
-0:35
51.87
56.60
20225
44.57
=0.23
+0.51
20.15
36.74
36.41
SNAP
20.57
28.39
+0.38
36,10
#0.22
29.45
10.20
24.32
10,07
25.12
#0.20
35.54
20.27
46.04
41.87
20.07
10.15
39,16
10,01
55.12
66,1
2009
30,34
19.34
20.24
51-06
10.1
36-42
20.07
49.11
20.20
40.64
21

---

Table 10: Classification accuracy (%) on ImageNet- C through SNAP (AR=0.1) using ViT-Base [4].
Method
Gau.
Shot
Imp
Def.
Gln.
Mot.
Ziom
Snow
Fro.
Fog
Brii.
Comt
Elas
Pis.
JPEG
Avg.
40.56
41.30
41.69
35.76
31.81
42.01
38,02
44.33
53.53
20.00
72.41
30.42
45.87
51,95
56.11
43,10
20.17
1:.29
10.19
+ SNAP
+0.08
40.98
+0024
41.72
+0.19
42.18
20.00
57.16
+0.27
32.30
=0.15
42.89
+0:13
38.44
+0.25
46.19
+0.20
52.50
+0.18
53.11
=0.12
72.25
+0.26
39.25
=0.14
46.77
#0.11
51,53
+:1.2
55.99
+0.09
46.22
COTTA
20.05
17.12
20.43
20.06
16,62
12.87
14.50
9.68
28.31
16.01
35.79
1.96
15.00
12.09
15.99
17.14
10.16
1.0.00
4.0.1
10.14
1.0.25
20.13
10.12
1.0.33
10.27
10.19
1.0 20
10.11
1.0.22
10.29
10.17
10.18
SNAP
34.85
33.35
36.11
25.77
35,57
42.23
51.63
5.86
42.18
52.27
39.41
40.28
1:006
#0:11
+0.25
+:0.27
=0.08
2:0.9
+0.21
20.13
EATA
20.12
+0.14
+0.17
21.52
+1.21
21.40
20,90
=0.00
+0.20
23:42
+0.10
15.71
+0.27
18.00
+1.11
16.12
+0.24
28.35
+0.16
22.24
=0.22
35.97
+0.15
11.33
=0.29
19.78
+0.18
20,22
+d.23
19.99
+0.12
21.00
SNNP
40.74
43.22
43:11
40.63
44.59
51.58
50.63
54.77
58.32
61,90
73.91
33.85
60.19
63.35
63.01
52.23
40.15
1:0.19
40.13
=0.27
10.11
=0.1
10.18
10.12
10.25
1:0.00
20.14
1.029
=0.10
1:.23
10.13
21.44
22.08
16.87
17.71
15,00
13.27
+0.14
+0.21
+0.13
+0.22
+0.09
+0.27
+0.15
+0.00
+0.24
+0.13
+0.20
+0.11
+0.25
+0.10
SNAP
35,68
+0.16
+0.17
34.60
+0.21
36.86
+0.13
31,20
+0.23
25.81
+0.09
36.24
+0.26
33.47
+0.12
42.72
+0.27
55,50
+0.18
$1.74
+0.15
71.84
+0.29
17.84
+0.14
42.86
+0.10
42.24
+0.24
$2.67
+0.11
40.75
Table 11: SNAP accuracy and lateney per batch, using Vit-Base [4]. Performance averaged over ImageNet-C. Values in parentheses show the performance difference from full adaptation.
Accuracy
Lalency per batch (s)
Methods
Original TTA
SNAP (AR-0.1)
Original TTA
SNAP (AR-0.1)
Tent
39.53 2014
46.22 18.33 (+6.69)
28.19
15.66
i (-44.43%)
41.25
10.3 (-183)
523.26
(-65.18%)
EATA
48.43 1
52.23 18.13 (+3.79)
28.69 10:00
16.44 1u0e (-42.71 %)
SAR
43,86 +013
47.77 =4.12 (4:391)
44.28
17.76 =007 (-59.90%)
42.93
+8.30
(-61.88%)
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
-instance distances, with subsequent adjustment of memory statistics match the target test batch using the Inference-only Batch-aware Memory Normalization (loBMN) method. Specifically, these calculations leverage the mean and variance across batches as follows:
1
1 E
Pe BXL
fo,et of -²=
EEE (fr.c. ub,0)2
(13)
BXL b=1 1=1
where represents the batch size, 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 feature vector fo belonging to the b-th instance, LN computes:
14b C E
1 E - mm)) Je. of -
(14)
where 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 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:
1
LN Me
Σ Mb,
2LN
2 6
(15)
M
M
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
22

---

each instance, but the procedure for aggregating these statistics to form domain centroid remains the same-by by averaging the group-level statistics across instances.
To maintain the core concept of selecting domain--epresenntativ samples with minimal modifications, continue to use the memory of high-confidence domainn-rerresentatvv samples in the Inference- only Batch-aware Memory Normalization (IoBMN) strategy. The adjustment for LN requires: 1. Calculating LN-specific centroids 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- rerraiinteereeetatiive 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 noomain-rpreesentaivv 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 bradeent-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.
Table 12: Performance comparison between T3A [13] and FOA [29] against Tent [48] + SNAP (adaptation rate 0.1) on ImageNet-C (i.id and non-i.i.d) Latency is measured on Raspberry Pi 4.
Thaross
Medted
Gas
Shoe
Irp
Def
CTa
Min
7atm
Snow
Pro
Frg
Cor
Flx
Pix
19P3
Ang
10000
RcNN410
14.50
-1.19
61.11
44.50
26.13
23:24
18:15
SNAP
40.14
27.85
40.00 PM
27.50
40 16
+0.10
23.62
40.1%
40
6611
40 17
42.19
+0.17
+0.30
$2.95
+0 18
GLET
+0.11
2623
40.77
08.56
+0
-6 13
47.09
-0.76
35.83
-0.10
-1333
VIT-Roo
$0.20
30.35
PUA (k-0)
20.30
37.53
35.52
20.12
$3.03
30.36
54.15
+0.27
39.10
27.45
20.10
37.85
34.43
20 12.12
43.65
#2000
36.10
20.11
02.54
20.10
20.16
71.79
50.35
+0.88
$0.12
44.25
20.00
41.33
20.05
53.05
43.54
20.37
$1.43
26.12
73.35
<0.24
RaNNd50
T3A
25.10
11:75
20.36
11.0%
20106
11.44
20.22
11.30
2005
10.5
20.17
19.35
11.44
$1.30
21.16
2011
20.20
2451
2010
58.35
20.15
56.31
21.00
10.15
$0.25
57.41
21.30
42:35
20.40
12.53
20.42
15.25
20.77
15:32
24.78
5L.7
45.99
25.10
(nvi--10 4b
(K-25))
35-36
26.25
10.41
30.67
4010
35.00
01.31
25.35
36.44
81.19
20.00
11:20
2230
10.14
25.45
61.67
101K
70.00
41.51
43.05
41.43
52.41
J1.16
43.50
60.17
00.00
0331
2110
20104
0016
4016
4019
0014
40.22
-1.00
a1133
45.84
Tenti SNAP
20.73
38.02
28.31
+0.50
09.33
6083
+0.11
55.77
36.38
10.00
80.17
18
37.30
+0.35
+0.54
41.57
+0.27
5478
63.01
60.77
73.19
40.22
40.35
24.8
30.47
85.64
3051
47.88
F5.66
20.33
40.33
4381
-0.5)
87.54
T3A maintains a fixed feature extractor and updates per-class prototypes using pscudo-labels from incoming samples. Although it avoids backpropagation, T3A accumulates growing support set of query features per pseudo-label to refine class-wise prototypes. This not only increases memory usage, but also incurs non-negliiible 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 test sample against all stored support features becomes increasingly costly in such settings. As shown 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.
Prototype-based.
Prompt-based. FOA [29] introduces learnable prompts to adapt ViT encoders without backpropa- gation. 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, 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 SNAP, while achieving similar accuracy. Reducing level, but results in substantial performance degradation, showing strong sensitivity to prompt update
reduces latency to a comparable
23

---

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 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 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 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.
Table 13: Performance of SNAP (AR=0.1) on ImageNet-R R and ImageNet- Accuracy and latency are reported as the mean standard deviation over 3 seeds (0, 1, 2). Latency measured by Raspberry Pi 4.
Method
Accuracy (1)
Net-oNet-R
Latency (5)
Accuracy (5)
ImoggNietSSutthh
Lusency
40.53 1 0:22
SNAP (AR=LLD)
3673:20021
150.0
1:
0:21
EATA (Pull)
42.88 0.18
29.22 1 0002
30.32 1: 0.20
32.99 0.08
+ SNAP (AR-ILI)
39:45 0.17
15.50 + 008
27:43 #: 0.18
17.53 0.23
SAR (Full)
40.37 0.22
7251 1 0.05
27.00 1. 0.19
16.37 0.05
SNAP (AR-ILE)
37.32 0:22::000
19.59 : 0.26
27.95 4: 0.17
22.52 0.06
RoTTA (Fall)
3008 0.21
7806 2 0.09
26.05 2
84.98 0.06
SNAP (AR-ILD
36.79 0.19
B.12 Efficient strategy for re-calculation of sample's distance
The domain centroid in framework is updated using 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 predefined significance threshold. Specifically, if the change in the domain centroid ACammiin surpasses a threshold TA- updated to reflect the new domain conditions. This
the distances of all samples in memory threshold-basee 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 long the threshold TA was not set too high, indicating robustness to the choice of threshold. Based on these observations, we set TA = 0.1 and used this value consistently for 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.
24

---

B.13 Strategy for continuous domain shift setting
In our proposed framework, the centroid used for selecting domainn-epresentaaiv 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 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 effectiivnness of SNAP under continual domain shift scenarios, we conducted ex- periments 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 controid-based sampling, allowing performance 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 z- score evaluation to enable even more responsive adjustments. For instance, a z-score-bases -asee approach could further refine the centroid's '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.
Table 14: Performance of SNAP under continual domain shift scenarios. The table reports the accuracy (%) for different datasets with incremental and abrupt shifts. Bold numbers are the highest accuracy.
AR
Method
Gos.
Shot
Imp.
Def.
Gia.
Mot.
Zooen
Snow
Fro.
Fog
Brit.
Cont.
Elas.
Pix.
JPEG
Avg.
Test
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
10.01
0.1
COTTA
+ SNAP
20.66
10.40
28.71
10.99
+1.82
10:04
12.21
22.91
10.30
12.25
11.54
10.13
#0.90
11.28
20.15
=0.20
11.13
1.62
20.13
10.07
22.08
0.87
20.18
34,80
=0.07
0.58
20.08
30.69
0.64
10
29.15
10.04
20.06
0.64
10.19
10.05
43.87
0.66
10.09
10.01
61.92
0.75
10.16
10.05
12.76
0.44
20.13
20.08
40.03
0,60
44.99
20.14
20.07
20.07
10.16
36.43
#0.43
27.61
10.15
-SNAP
15.19
15.60
46.77
30.21
+0.17
+0.11
+0.02
=0.04
=0.03
+0.07
=1..0
#0.06
+0.10
+9.14
+0.04
#0,02
=0.06
#01.12
+00.08
Tem:
10.37
23.31
11.13
27.08
12.50
22.71
13.35
9.72
23.00
4.14
11.53
2.03
10.75
1.16
10.22
0.56
10.12
0.45
10.09
0.47
10.16
0.61
10.09
0.33
10.08
0.47
10.08
0.47
10.07
0.46
10.90
6.27
SNAP
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
0189
0,84
11.39
+9.10
CoTTA
+0.38
+0.39
+0.42
11.73
+0.10
=0.50
#0.13
22,05
=0.13
34,89
+0.20
+0.17
20.50
10.18
44.09)
40.09
61.87
#0.18
12.87
=0.17
40.15
20.19
45.06
10.14
36.53
#0.23
27.71
+ SNAP
+0.15
15.20
+0.02
15.89
+0.10
15.93
+0.04
1331
+0.13
14.15
10.16
24.74
=0.27
36.68
#0.04
32.51
+0.20
31.71
+0.05
46.11
+9.09
63.48
+0.19
15.73
42.20
#1.12
=11.00
46.69
#0,04
38.05
+0.10
30.19
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, TTA) of work [11], which repeatedly cycles through non-i.i.d. CIFARIO-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], method specifically designed for continual test-time adaptation. While CoTTA alone initially performs well, we observe a steady degradation across rounds it accumulates shift-induced bias and overfits to recent domains. In contrast, combining
25

---

CoTTA with SNAP enables the model to preserve robust performance even after multiple adaptation cycles.
The key to this stability lies SNAP's architecture: (1) class-balanced memory to prevent lahel bias, (2) sparse but confident updates mitigate overfitting, (3) loBMN 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.
Table 15: Long-term TTA accuracy, cycling through all CIFARIO-C corruptions each round (R).
Method
R1
R2
R3
R6 m
R7
R8
R9
COTTA (Full adeçt)
58.49
2015
50.32
2009
48.71 2015
44.92
2010
31 86
29.81 2011
25.39
2016
21.43
20:1
28.46 200
16.97 2014
SNAP(AR-LU (AR-(UI)
50.50
19.32
2325
$2.57
2011
49.90
90.17
2032
50.58
2014
49.01
49.56
2233
54.16
$2,89 2009
Experimental results. Table and Figure shows adaptation accuracy over 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 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 per-sample basis, evaluate its performance in a single-sample adaptation setting. where the adaptation batch size is limited to 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, adopt the SAR [31] architecture, which natively supports batch size of 1 and sparse update routines. SAR allows us to test SNAP with an adaptation rate 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 single-sample (BS=1) adaptation scenario on ImageNet-C. Results are averaged over random seeds (0, 1, 2).
Method
Accuracy (%)
(single sample-sample)
52.21
STTA
8.06 + 0.12
11.80-2 +
SNAP achieves strong gains even when adapting from just one memory sample. When only one sample is used for adaptation, method still selects the representative sample with high prediction confidence and low Wasserstein distance to the domain centroid, enabling stable model updates.
60
CcTTA (Full SNAP (AR=0.1)
Accuracy
10
2
10
Adaptation Round
Figure 9: Long-term TTA accuracy over 10 adaptation rounds. Shaded regions indicate std over seeds. SNAP maintains stable performance, while original CoTTA alone degrades over time.
26

---

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 loBMN 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 implica- tions 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, con- ducted experiments on ImageNet-C under Gaussian noise corruption, using Tent + SNAP(adaptation rate 0.3) with 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 prox- imity to class and domain centroids. The saturation in accuracy suggests that a carefully aligned memory size to the batch size is suf- ficient to balance computational efficiency, performance, and privacy considerations.
Table 17: Performance com- parison with varying memory sizes on ImageNet-C.
Memory Size
Accuracy (%)
16 (Base)
26.60 #0.11
32
28.44 10.17
28.89 10.06
128
28.60 =0,09
In conclusion, to minimize computational overhead while ensuring robust test-time adaptation, the memory size in SNAP is designed privacy and memory overhead risks by limiting the number of stored samples without compromising adaptation effectiveness.
to align with the batch size. This configuration addresses
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 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 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 x 10-1 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.
27

---

Table 18: Accuracy with varying learning rates on ImageNet-C Gaussian noise adaptation rate 0.5.
Bold numbers are the highest accuracy.
Tent
CoTTA
FATA
Leurning rate
Full
naive STTA
SNAP
Full
naive STTA
SNAP
Full
naive STTA
SNAP
2 10m3
2:31 ioos
4.16 2017
6.88 1014
13.31 1a1
12.03 1010
14.58 10
0.36 2e05
0.48 go0
0.69 1:m
10-3
4.54
10.19
16.37
13.18
11.98
14.63
1.31
1.36
22.11
5 10-4
10.22 20112
18.43 =0.33
28.36 =0.0
13.15 =00
11.95 =0,0
15.17 +0.11
21.96 10.34
13.97 =0.22
25.42 =013
10
27.03
25.24
28.05
13.12
11.99
15.16
29.42
28.62
30,00
5x
26.34 20.00
22.62 =0.30
26.32 s001
13.34
23.10
12.10 =0,07
14.93 10.0
29.37 40.33
27.30
=0.1
28.76 =002
Table 19: Accuracy with varying learning rates on ImageNet-C Gaussian noise adaptation rate 0.3. Bold numbers are the highest accuracy.
CoTTA
EATA
Leurning rate
Full
naive STTA
SNAP
Full
naive STTA
SNAP
Full
naive STTA
SNAP
10-3
1ios
1011
1015
10:0
_0o0
10m
1
4,54 s10z
16.13 20134
27.63 2011
13.18 20m
11.86 so1r
14.68 10.10
1.31 :006
0.95 sou
24.35 =014
10
24.96
15.11
21.96
20.96
1 10
27.03 20.10
23.63 :0.1
26.60
2012
13.12 =007
11.74 20.00
15.26 10
29.42 10.00
27.35 =009
29.48 =0.00
5 10
26.34
20.94
24.87
13.34
11.92
14.85
29.37
26.07
27.90
Table 20: Accuracy with varying learning rates on ImageNet-C Gaussian noise adaptation rate 0.1. Bold numbers the highest accuracy.
Tent
CoTTA
EATA
Learning
naive STTA
SNAP
Full
naive STTA
nai've
STTA
SNAP
x 10-3
2.31 #0000
18.06 =0.14
27.41 2012
13.31 =008
10.93
14,80 +0.11
0.36 =003
1.86
9.59 =0.15
1x
4,54 10.11
25.46 =0.33
31.12 20.14
13.18 =om
10:93 =00r
14.73 10.00
1.31 =005
2,86 =bos
24.95 =013
3 10
10.22
24.71
28.01
13.15
10.92
15.18 10.0
21.96 40.12
18.76 =0.1
28.09
10
22.00 =m12
26.21
2013
13.12 2008
10:0
1:
29.42 i
22.43 20.1
2012
x 10
26.34 jince
16.72 10333
19.31 1012
13.34 1.00
10.92 1.00
14.76
101
29.37 Jum
20.32 in1o
23.28 Lo0
In conclusion, selecting an appropriately high learning rate for sparse adaptation significantly en- hances 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 other real-world domains, we further test SNAP HARTH [23], a human activity recognition dataset that collects data from two three-axial accelerom- eters attached 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 composed of four mie-immnsioonll convolutional layers followed by fully- layer, and 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
Table 21: Performance of SNAP (AR=0.1) on HARTH. Accuracy is averaged over all target domain users.
Method
Average Accuracy
Tent (Naive STTA)
19.64
SAR (Nalve STTA)
21.10
28

---

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 CIFARIO-C, CIFARI00-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 ffate-o--hhe-a (SOTA) TTA algorithms: Tent [48], EATA [30], SAR [31], CoTTA [50], and RoTTA [53]. This comprehensive evaluation resulted a total of 150 combinations (3 datasets, adaptation rates, 5 algorithms).
The results demonstrate that, regardless of the adaptation rate, dataset, the TTA algorithm, integrat- ing SNAP consistently outperforms the baseline methods. Specifically, SNAP achieved the highest accuracy across nearly all of these 150 combinations, effectively demonstrating both high and low adaptation settings. For CIFARIO-C and 100-C SNAP showed substantial performance improvements compared 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.
robustmess in
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.
29

---

C.1 CIEARIO-C
Table 22: STTA classification accuracy (%) comparing with and without SNAP on CIFARIO-C through Adaptation Rates( (AR) (0.5, 0.3, and 0),,, including results for full adaptation (AR=1). Bold numbers are the highest accuracy.
AR
Medhods
Gau.
Shot
Imp.
Def.
Gla.
Mot.
Zoom
Snow
Fro.
Fog
Bril.
Cont.
Elus.
Fi..
JPEG
Avg.
Source
22.13
40.00
+0.00
29.25
+0:00
22.55
54.54
+0.00
+0.00
55.10 10
67.45
40.00
64.37
+0.00
+0.00
76:25
69.93
40.00
74:26
-0.00
91:29
+0.00
+0.00
35.45
77.20
-0.00
46.00
46.56
40.00
73.38
+0.00
57.65
63.23
65.67
57.14
62.73
78.9%
76.95
53:32
88.46
84
73.96
76.61
68. 7V.7V
75.60
+0.46
-0:25
+0.23
+0.50
30
+0.08
-0.17
+0.16
+0.37
-0.18
+0.02
+0.24
Texs
40.88
73.66
68.04
=1.32
20.50
a0.76
67:12
20.09
86.34
82.34
81.56
$9.64
56.02
=0:18
89.09
20.16
87.16
+2.50
76.40
20.15
K2.95
76.45
20.45
13.71
80443
COTTA
A0.32
71.95
+0.45
67.03
20:56
20.30
#0.05
66.75
K2.64
20.19
79-92
40.09
79.49
20.13
=0:23
82.41
20.18
20.37
80.14
20.09
75.39
20.07
79.24
20.25
73.42
78.00
231233
75.82
69.65
09:41
15.96
83.42
56.58
77.62
K3.35
77.37
$1.56
+0.57
20.08
+0:27
=0.41
+0.17
20.39
+0.32
#0.20
+9.33
SAR
20.35
20.53
3501
20.37
s11.7
54.10
20,00
61.20
74.84
79:05
ROTTA
40.23
20.46
60.27
40.63
64.84
40.36
80.15
40.56
75.02
=0.09
54.13
59.00
84.91
10.15
77.96
73.00
Text
4061
73.44
+0.44
75.91
67.18
+0.78
86.52
+0.17
+1.77 76
67.25
+0.49
65.25
86.35
+0.43
62.24
40.77
80.35
55. 59
-0.30
+0.78
39.50
87.77
+0.27
77.00
+0.65
62.08
40.65
75.55
40.60
60.14
+0.55
+SNAP
$8.00
75.17
=0.76
77.66
#1.26
68.78
20.38
68.25
#0.51
69.18
#0.18
87.11
88L19
20.13
20.29
84.21
$1.45
82.72
20.51
87.34
91.63
s0.12
86.30
$1.07
20.25
78.76
K3.43
10.18
20.50
71.18
K1.74
10.44
OSTTA
20122
65.06
=0.21
66.67
61.31
20.16
20.18
77.50
61.36
20.15
77.70
20.37
77.37
16.37
74.05
20.22
72.86
211.4
17.43
=0.19
$2.69
20.30
72.44
s11.72
70.52
20.07
20.27
70:94
s0.10
69.77
+3.29
71.85
+SNAP
20.45
71.99
20.33
74.15
20.19
66.92
55.46
20.33
20.26
67.57
14.27
#0.23
8491
20.18
20.09
N1.10
24146
MB.62
20.24
$4.86
20.17
90.16
82.14
+0.33
76.75
20.16
28.35
50.23
20.50
75.98
20.28
79.05
0.5
EATA
+SYAP
#0.22
7485
73.95
40.51
30.18
75.82
+0.46
77.63
68.00
20.70
+0.43
68.43
56.35
$8.53
20.25
#0.17
67.83
$0.50
09.78
+0.69
85.27
87.19
+0.35
20.39
$6.48
88.16
#0.15
+0.18
82.63
+0.50
R388
40.42
30.99
82.44
20105
A0.33
20.16
$7.18
35.45
.8.15
39.56
20.18
91.54
#0.12
87.61
89.62
+01.3
40.36
20.31
20.4 65.8
75.91
77.01
#0.14
$2,13
20.15
K3.76
40.55
40.22
76.11
77.36
$1.97
+0.32
80.40
$0.33
SAR
69.10
+1.63
+1.05
72.33
63:12
+0.44
$5.18
-0.25
64. 50
+1:07
81 51.94
1012
8507
+0445
80.1
+0.17
+0.60
69
$3.01
-0.33
$6.64
+0.10
84:1
+0.30
-0.34
75.70
70.
-0.5
+0.02
72.90
+0.50
77.63
SMAP
10.48
73.98
+8.65
75,45
=1.26
66.41
20.15
3661
68.15
$0.15
85.50
86533
20.10
81.62
20.39
80.20
29.17
85.06
=0.27
91.46
29.03
87.04
29.11
77.22
29.45
K1.16
20.27
20.23
75.53
N0.13
21.32
RoTTA
65.02
4000
66.84
40.53
58 3%
+0.33
35.26
+044
(3.5)
2018
83,81
4015
36,66
+0:20
40
79.26
76.76
10.49
$3.46
-0.21
38:27
+0.04
85.47
10.05
-0. 16
74.43
-0.29
77.39
69.13
10.4]
40.25
75.95
SNNA
66.03
10.14
68.09
58.88
10.06
64.55
20J17
R5,70
86.8
20.02
80.97
10.22
78,87
10.20
85.29
=0.22
90.28
86.22
10.10
76.85
=0.22
78.76
10.22
10.35
70:51
77.88
10.16
Tesa
71.18
65.44
+1.17
66:01
20.97
54,37
20.17
20 40
81.31
20.09
79.80
$4.50
20.25
89.5%
20.23
84.01
+0.30
75.96
=0.30
10.39
50.46
74.09
20.51
78.95
13147
SNAP
10.54
77.29
+0.46
67.59
40.26
67.46
87.44
20,16
83.46
$1.45
49.19
56.72
19.19
87.79
78.36
+0.36
K2-61
+0.32
75.79
+0.39
81.23
CoFTA
58.95
59,15
(541
71-25
70:35
75.52
50.94
70.35
57.81
07.55
09.75
20
SNNAP
66.29
10.10
s0.19
$4.06
15.15
10.34
16.27
75.09
78.75
EATA
70.06
65.75
86.10
$4.48
30.58
80.66
73.04
70.02
SNNA
74.19
10.38
76.64
20.19
67.59
#0.20
68.56
20U5
$1350
10.30
N3.56
83.20
20.33
8894
78.30
10.20
K3.03
20.43
75.05
20.30
N1.50
SAR
11.65
69.10
$1.05
63.22
20.44
21.02
64.30
83.94
2015
90.11
20.17
5964
10.00
$3.91
20.51
20.10
20.30
84.21
20:34
10.52
79.10
20.09
72.92
77.83
SNAP
72.73
75.25
65.78
86.53
66.19
85.53
86.00
81.61
80.33
85
91.11
86.44
77.33
K1,00
74.52
79.71
40.94
+0.30
61.06
+0.16
40.60
40.26
10.17
40.45
40.64
-0.23
+6.14
10,68
40.41
+0.37
+1.04
40.46
ROTTA
10.44
64.09
30.13
66.07
21.53
57.58
20.30
$4.97
20.15
67.00 16
20.15
83.05
20.17
20.34
78.60
20.36
76.40
$2. 36
20.01
8805
20.22
83:1
20.34
20.55
74.14
20.47
76.35 25.35
20.17
68.25
$9.29
75.5
SNAP
10.18
6583
#0.19
67.57
+0.29
58.39
$6.97
50.33
20.16
64.22
85.63
#0.18
86.36
20,09
96.75
20.15
7899
20.08
$5.21
20.17
50.19
50.16
8592
30.21
75.92
50.09
#0.05
73,91
+0.37
70.42
77.41
#0.18
Tenx
67.92
+0.93
69.30
+0.96
+0.36
60
85.14
-0.34
63.62
#0.41
81.52
H0113
84.70
10.15
70
10:41
72.79
+0.50
63.05
10.08
88.53
+0.49
83.12
+0.66
75.18
-0.68
77.83
+0.69
71.47
+0.44
76.81
+0.48
SNNP
10.44
70.22
=0.91
71.45
630M
20.04
87.35
20.20
20.26
66:74
#0.25
K5,99
=0:33
21:33
20:11
85.62
24.14
91.14
20.22
87.47
29.11
20.12
76.44
20.14
79.63
20.39
72.72
21127
78.95
CSTTA
20.45
59.11
20.56
60.26
20.55
36.07
20,59
72.15
20164
56.77
20165
73.55
7220
20:52
6646
28.56
72.54
21.15
77.66
6595
21.17
65.67
20.83
20.95
64.12
65.
20.55
11173
66.42
SNAP
20.40
71.70
+0.21
73.54
66.70
+0.02
20.19
35.16
66.83
20.39
2008
84.90
$128
#0:30
25
+0.24
$4.20
20.23
39254
20,06
M1.71
20,20
76,64
20.30
20.14
79.66
10.25
75.71
10.20
75,83
RATA
10:45
65.65
40.47
65.96
15:15
5975
8455
+0.27
10.3
61.26
81,10
+024
36:3
20.5
20
72
25
+0-42
71.4b
=0.13
33
36.12
+0:09
82:46
10:24
74,40
=0:30
10.69
77.65
20.25
70.43
+0.30
76.29
SNAP
69.29
$0.30
70.09
+0.37
61.71
87.32
s0.42
65-48
20.38
R5.06
8664
#0.21
81.44
10.34
79.56
10.47
85.47
s8.23
90.50
10.38
86.84
10.36
76.32
=0.21
#0.12
79.64
+0.32
72.51
+0.34
78.61
SAR
66.11
40.59
68.18
=0.73
50
#0:27
61.87
81.53
84.27
20.13
#0.32
20
+1.43
77.58
53:21
=0.18
10:00
$8.19
82.60
+0.57
74.65
=0.46
70.77
75.92
$0.40
70.79
10.45
76.01
SNNAP
67.76
$0.32
#0.14
6082
+1.08
20.36
20.43
64.73
NE.29
20.11
86.32
MAN2
+0.33
79.30
+0.48
$4.95
=0.28
91.33
20.17
86.39
#0.34
20.36
75.72
+0.35
78.72
20.46
71.34
#1.31
78.06
ROTTA
63.12
36.72
02.15
81,53
7k
76.13
82.58
87.48
81.49
73.75
76.04
68.24
74.78
+SNAP
5K00
19.18
#0.18
63,3
W0.54
:0.43
$4.99
8530
10.06
78.14
10.23
70,05
75.07
30

---

Table 23: STTA classification accuracy (%) comparing with and without SNAP on CIFARIO-C
through Adaptation Rates(AR) (0.05, 0.03, and 0.01). Bold numbers are the highest accuracy.
Gau.
Imp.
Gb.
Zeom
Snow
Fog
Plc.
JPRG
Text
04.65
67.08
s3.42
58-48
55.00
+3144
62.61
82.76
54.63
79.01
s1..74
17.66
53.32
20.45
82.34
74.16
20.60
77:11
690.43
s11.77
75.75
+SNAP
69.84
59.53
+1.10
+0.25
64.66
N0.68
29..33
78.92
85.60
20.05
78.86
70.95
77.43
CoTTA
20.06
20.06
56.35
=1.43
21.10
57.37
11.66
41.02
70.05
08.68
+0,52
74,52
23.05
61.13
+1.27
65.
10.95
67.22
21.05
SNNAP
71.42
40.29
40.12
73.31
65.91
20.13
85.23
10.11
#0.21
67.01
84.19
40.20
20.14
$4.91
80.50
40.19
$0.56
60,34
84,19
+6.14
90,00
66.21
+0.35
82,09
+0.05
79.79
40.29
75.18
40.21
78.73
40.20
0,15
EATA
SNAP
64.65
$1,33
67.36
40:31
=0.26
+0.37
68.73
67.01
+0.34
29.37
59.35
58.07
50.23
$7.05
$4.50
+0.52
#8L18
+0.33
64.36
67.56
85.62
SILIN
82.64
+0.6
26.35
$6.48
$4.57
+0.61
81.31
20.34
76.77
+0.71
511.22
+0.92
79.73
77.16
+0 04
+8.15
K5.33
K3.06
s8.34
87,60
90.03
+0.47
+0.99
$1.02
=0.07
66.31
28.12
74.05
+0.25
76,04
18.27
78.79
76.99
40.41
69.33
70.96
HIL38
+0.71
+1L23
77.76
+0.51
75.55
SAR
64.79
20.13
20.86
66.32
20.50
$7.5%
$4.66
20.72
28126
62.46
81.42
+1.52
$4.13
20.34
76.87
28.36
21.51
77.20
21.24
62.62
20.41
58.10
62.12
20.74
20.05
74,04
10.50
75.38
+1.52
69.13
21162
75.25
SNAP
65,00
M0.17
68.85
+0.75
58.47
10.42
$6.54
20.25
+1.28
63,66
85.26
$6.13
20.38
N0.38
40.89
78.17
29.27
95.17
+8.13
=0.36
90,93
85.96
20.20
75.27
+0.11
77.37
10L28
70.61
77.21
RoTTA
63.21
*0.37
#0.62
64.87
56
s0.28
$4.64
20.53
62.16
81.31
2063
$4.15
20.56
76.16
10.71
76.39
=0.95
=0.62
K2.90
=0.46
67.44
81.47
=0.65
20.42
73.50
76.02
66.19
11125
20.52
74,80
SNAP
65.28
20.32
10.23
66.91
20.06
57.5M
36.75
20.25
21.13
63:51
85.45
21113
20.10
36.17
M0.46
20.23
291.6
7W.38
N5
20.13
28.23
$9.991
55.82
20.03
20.16
75.66
20.19
77.98
21129
70.15
21L18
77.15
Tex
64.36
40:43
M5.21
40.15
#1.0
57.65
$4.73
20.48
62.95
4052
81.07
1050
20.3
$4.50
+0.22
7844
+0:30
76.99
-0. 10.36
53,00
$3.00
+0.61
$2,62
-0.54
73.90
46.23
10.6
16.00
68.82
10.4
40.66
75.95
SNAP
66.32
10.1
65.35
+0.53
39.00
86.81
10:24
64:04
$6.35
16/15
80.78
10.00
78A8
20.92
+0.05
R5.34
90.08
86.19
75.77
78.37
70,49
1008
77.49
10.23
COTTA
60.36
+1.71
61.26
=2.47
56.77
72.44
+1.55
=1.4
7464
72:3
+2.0
68
68.34
=2.00
67.18
=1,80
+3.77
64-22
f6.12
11.33
+1.98
SNNA
20.47
71.13
66.34
20:12
66/64
#8:3
$4555
40:15
80.11
20.15
20.14
54.06
20.37
76.27
20.19
79.77
20.26
#U08
75.35
21121
78.05
57.39
62,66
83,11
56.44
78 4244
7643
$2.97
73.45
76.45
65-91
75.24
40.87
#062
40.75
20-26
20.26
20.47
#3.56
$0150
SNAP
06.16
56.81
64.06
80.70
7865
75,88
78.48
70.56
77-42
#6117
10.01
10.15
SAR
57.50
61:45
5246
SNAP
58.37
s0.16
6311
79.33
20.17
$4.92
26.22
69.07
ROTTA
56.64
62.41
20.79
5435
76
20.25
K2.60
10.44
76.09
sh.31
SNAP
65.27
20.32
EX.05
10.18
63.45
K5.46
M0.39
29.08
20.15
78.34
10.19
M5.19
90.30
75.04
10,09
69.75
77.05
Text
+1.70
62:43
+1.51
64.13
55.55
+1. 35
$4.00
+1077
62.21
+1.20
82.47
+0.86
83.87
+0.01
77.71
40.4
+0.18
76.55
40. 14
R2.75
87.35
+1.11
+1.81
81.83
+1.31
73.24
41 1118
75.34
67.73
+1.50
74,
+1.10
SNAP
+0.24
05.51
+0.31
67.26
20.34
58.85
50.25
56.89
=4J17
63.53
K5.44
#0.33
$5.97
26.30
+0.12
N0.55
21112
78.35
85.12
16.16
56.21
90.09
85.86
20.11
20.05
75.66
#0.21
75.38
70.12
+0.35
+0.21
77.12
COTTA
59.75
14.69
15.21
59.04
54.47
25.55 57
25.10
71.12
14.35
57.11
72.47
$5.52
72X3
$4.00
66
65.14
27.65
06.33 75
29.3 79
75.12
25.3 79
64.31
26.06
56.22
$4.50
02 62.65
25
64.75
15:36
65.51
15.91
SNAP
71.79
40.22
+0.29
73.61
68.98
60.58
+6.36
$5.34
#1.26
66.76
84.26
40.12
$493
#0.21
40.45
R0.64
50.36
+0.30
#0.42
$3.94
#6.06
$0.96
82.47
.0.64
#8.26
76.88
79.61
A1.24
75.66
78.79
11.31
0.01
EATA
+SNAP
20.29
+1.73
62.36
65.49
+0.04
67.19
63.93
+1.66
+1.30
20.00
57.93
55.75
:8.41
=1.10
36.92
$4.05
21.18
=1.18
62.24
63.65
85.42
87.35
1085
35,97
$3.00
=6.34
=0.93
M0.46
20.18
+1.72
73.66
29..77
=0.15
7X.13
76.48
N5.07
=0.17
28.13
K2.67
=8.10
=1.12
90.03
67:34
81.32
85:87
=0..00
=1.81
+1.24
28.11
75.69
71.30
x1
20.13
75.20
75.31
#tL46
67.76
70.03
+1.52
211.33
+1.12
77.17
74.46
SAR
#1.69
62:50
41:83
64.13
21.38
35
23.37
$2.30
21:21
62.22
26:3
77.21
25119
20.11
20:30
77.66
20.34
76.75
23,25
79.12
39.45
21.79
=1.97
31.97
23.21
73.39
69.39
15.48
11.65
67.83
22.57
75.31
+NNAP
$0.17
65.06
+0.11
(6.93
57.66
+0.51
20.29
36.76
20:24
61.78
#621
85,05
1
-6:45
$594
79.95
40.18
20.37
7744
#0.21
84,65
90.72
=0.03
35.48
=0.38
75.34
18.13
+1.35
75.73
20:25
69.61
10.36
76.62
ROTTA
62:25
$1
63.71
11.68
14 /6
35
1111
11
11
1083
-0.
77 2h
10.55
76.19
-0.24
K1.64
80,23
11
-14
$1.75
+1:31
73.21
75,
15.
61:25
1113
74.36
+SNAP
65.32
$0.25
66.94
+8.12
37:85
10.29
1691
6344
10.24
85.2
11122
#0.14
80.49
10:34
78.22
20.30
83.04
10.15
9691
#8.06
85.77
20.34
76.76
#8.11
78.15
10077
7006
10.47
77.02
11.21
31

---

C.2 CIEAR100-C
Table 24: STTA classification accuracy (%) comparing with and without SNAP on CIAFRI00-C through Adaptation (Ates(AR) (0.5, 0.3, and 0),,, including results for full adaptation (AR=1). Bold numbers are the highest accuracy.
AR
Medhods
Gau.
Shot
Imp.
Def.
Gla.
Mot.
Zoom
Snow
Fro.
Fog
Brtl.
Cont.
Elus.
Fi..
JPEG
Avg.
Source
40.00
10.25
40.00
11.87
+0.00
6.48
+0.00
35.16
+0.00
20:33
64.42
+0.00
42.13
+0.00
45.99
+0.00
+0.00
34.84
-0.00
41.12
+0.00
66.37
+0.00
19:56
50.59
-0.00
46.00
22.68
40.00
45.48
+0.00
33,15
36,90
57.96
12:13
90 14
61:16
50.65
54.81
60:35
50.48
51.40
41.08
$0.44
+0.10
-0:44
=0.36
+0.19
+0.05
+0:15
+0.09
-0.34
+0.05
+0.12
-6.34
+0.11
+0.49
+0.21
Texs
46.71
20.13
40.08
20.40
=044
44.10
20.23
36
55.46
$0.49
59
=0:30
67.43
20.17
+0.42
20.15
20.32
50.40
20.65
49:91
55.76
+31.3
COTTA
42.14
+0.44
37.92
20.18
55.40
20.12
#0.39
41.01
#0.10
20.58
40:25
40.63
50.61
20.31
50.56
61.35
+0:27
47.4L
+0.37
48.69
20.15
54.38
20.65
48.11
+3.33
49.39
32.64
38.73
61.07
50.50
50.79
55.30
49,06
53.62
43.02
50.74
+1.71
#0.33
20.19
=0.23
#0.12
+0.13
=0.30
+0.41
#0.20
SAR
45122
48
=0.40
20.25
M1.5
50.72
ROTTA
40.24
+0.37
33.75
40.32
40.74
20.09
51.61
51.75
20.31
56.20
20.22
54.42
10.35
20.22
51.55
Text
43.96
40.85
45.43
+1.34
36.57
+0.13
60.28
+2.97
36.57
40.59
59.96
+0.48
61.00
+0.72
53.25
53.14
+1.70
57.36
-0.23
+0.30
65.20
60.14
+2.77
-0.08
49.72
57,62
40.61
40.52
46.83
52.66
40.96
+SNAP
18.00
49,06
20.13
50.43
19.50
41.49
s0.34
65.55
20.06
44,09
63.31
#0.53
65.62
$0.37
20.99
ST.62
56.81
$0.31
20.48
60.75
68.72
s0.31
$0.64
67.52
20.19
54.08
=8.14
61.15
#0.11
51.54
$7.18
+0.29
OSTTA
20.00
34.31
35.16
20.46
20.28
31.42
47.7%
20.15
20.40
34.99
20.45
45.91
47.79
20.46
20.86
41.27
211.37
41.42
=0.57
43.77
52.16
20.27
38.30
201.6
42.25
20.49
44.12
20.41
41.55
20.22
sh.42
41.68
+SNAP
20.46
41.28
#0.16
42.23
20.19
37.17
59.24
20.21
20J15
40.70
20.12
57.32
57.78
20.09
#0.38
49.85
11.11
50.82
20.25
52.21
20.18
63.69
+0.23
51.30
20.14
49.41
28.09
55.15
20.25
47.92
20.20
50.34
0.5
EATA
+SNAP
#022
38.02
39.75
10.11
20.15
+0.26
41.14
39.05
32.77
20.17
+0.10
34.15
20.38
61.48
63.75
+0.23
20007
+0.21
38,42
00.55
20099
59.11
61.09
#0086
62.81
#0.18
A0.19
20.25
50.15
$1.12
40,05
30.67
52.12
A0.30
J9.92
20.13
14,00
20.18
$6.47
63.45
65.75
20.21
+0.23
58.70
61.85
20.44
40.34
20.22
49.42
$1.14
20.25
20.20
#0.15
53.08
55.75
10.21
#0.81
42.62
$1.86
50.13
$1.21
20.24
40.22
SAR
40:00
+061
50.00
+0.47
42:99
+0.33 30
65.10
-0.44
45:21
+0.1
+020
64.45
+0.3
55.78
H022
56.59
+0.46
60.21
-0.45
67.15
-0.44
65.17
+0.66
$3:50
-0.50
10.21
-0.29
$1.28
+0.25
+0.00
$6.65
SMAP
51.71
10.46
=0.08
52.79
44.95
+0.54
20.10
66.59
47.84
64.40
10.18
20.28
66.15
20.20
59.02
59.12
211.37
62.62
:0.16
29.06
69.15
68.20
29.16
55,89
29.26
18.21
62.66
53.77
20.23
58.99
21L23
RoTTA
37.12
40.99
35.34
40.20
+0:22
32.54
62.15
10:00
10113
35.91
10.19
59.52
61.19
10.21
30.22
40.5
40.56
49.91
-0.1
54.69
63.74
40.10
59.40
10.42
50.32
-0.20
-0.29
53,20
41.94
40.55
50.22
20.25
SNNP
38.33
10.30
39.12
32:93
10.28
64.01
20.44
40.36
61,30
62.96
10.16
51.77
10.22
51.54
10.19
56.15
=0.28
66.13
61.67
10.17
31,40
=0.34
54.90
10.23
10.36
43.14
51.73
10.25
Tesa
38.72
+1.17
20.38
40.92
39.79
20.33
76
20.65
57.47
20.62
20.39
$2.70
20.00
58.21
20.81
20.43
47.23
53.36
$7.77
SNAP
42.19
40.75
$1.15
45.12
40.51
57.45
57.13
+0.37
60.72
-0.17
+0.31
$1.52
+0.54
61.35
$1,90
57.27
CoFTA
38.57
16
35.55
40.71
15.12
39.11
40.53
SNNAP
37.08
10.37
10.12
51.00
-0.22
50.90
54.75
20.13
EATA
10.04
32.69
s0117
60.50
10.05
40.33
=0.41
54.63
30.41
$3.17
30.44
43.40
20.25
SNAP
A0.26
40,03
34.91
20.25
40.29
63.56
10.25
51.M5
51.78
56.13
=0.01
20.25
55.25
10.17
44,90
52.19
SAR
49.00
10.61
20.30
42.99
20.44
#0.11
45.21
$0.20
64.5
20.33
20.27
56.59
10.46
=0.05
60.21
67.35
20.44
20.46
55,90
20.50
20.29
60.22
20.23
51.24
10.40
56.65
SNAP
58.63
$2.03
44.99
66.28
47.06
64.31
6530
S7.96
58.99
61.88
69.17
67.82
55.47
62.02
$3,09
58.44
40.31
40.32
10.54
#0.13
+6.26
40,99
16.11
40.27
$0.40
+0.24
+0.62
40.29
20.29
40.31
40.15
40.29
ROTTA
10.18
36.3
40.23
57.94
20.05
32.00
20.30
61.00
20.10
33.0 67
20.14
%6
20.34
60:9
20.25
40
211338
32
20.21
54.00 62
63.71
20.18
10.11
56.11
20.22
40.33 0079
20.34
57.65
20.27
41. 1.55%
20.21
49.84
SNAP
20.13
38.11
=0.25
39.21
+0.14
32.80
63.72
50.13
20.23
40.01
#0.13
61.51
62.74
20.16
10.15
51.37
$1.49
20.30
20.25
55
65.90
20.13
61.56
$0.29
51.50
20.05
#0.15
$4.67
#0.19
43,01
#0.18
51.55
Tenx
43.55
+0.66
44.25
+0.54
37.95
+0.72
60.56
-0.47
41.80
+0104
+0.20
50.45
62.13
+0.21
$3.04
+0.44
$1.60
+0.39
-0.15
56.76
+0.56
64
+1.68
61.19
51.01
-0.30
$6.43
+0.27
46-28
+0.49
+0.51
$7.84
SNAP
10.35
46.51
+0.25
47.68
20.48
30.92
20.11
65.30
20060
44.34
63.29
10.18
20.38
64.53
10.47
55.20
55.55
21.11
20.33
59.71
68,05
20.17
64.90
20.50
53.91
20.30
20.16
59.25
20.75
49.54
21137
55.84
CSTTA
10.90
25.55
20.86
29.53
20.50
26.45
21.19
42.19
20.77
30.54
#1007
44.99
41.48
10
34.44
33.95
21.07
20.89
39.03
45.49
21.36
21.17
20.500
37.25
20,00
11.20
36.17
20.71
36,84
35.86
11190
SNAP
+0.25
41.73
40.60
42.62
20.13
37.46
20.13
58.33
+0.21
41.24
1007
57,33
20.90
$7.96
20.38
50.34
20.18
51.17
20.16
52.29
63.59
20.30
51.32
20.36
20.31
49.68
10.25
54.75
+0.35
47.89
50.53
10.25
RATA
40.53
38.1
40.45
39.03
+0.32
32:29
61,07
20.36
40129
33.45
59.21
40.57
60/2
10.56
+0 30
89 59
+0.34
1919
-0.90
34.25
62.46
+0:28
57.39
10,02
20.65
49.00
#0,60
53.01
10.15
42,00
10.42
89.20
SNAP
10.26
48.62
41.53
34.31
10:34
64,08
s0.30
a0.21
40.29
61.32
63,04
16.16
$1.00
10.53
51.77
$0.40
56.88
#0.43
65.08
61.96
$0.34
51,85
=0.09
55.67
+0.28
+0.15
64.80
$1.35
+0.28
SAR
43.02
40.52
=0.28
68
63.36
=0.25
=0144
62.78
#0.23
#0.8
90
+0.28
52.15
57.5
=0.33
65.41
60
+0.55
52.07
=0.90
10.13
20.20
47.16
+0.43
$1.49
46.29
39.95
65.26
44.00
55.05
55.17
39.73
64.72
53.54
58.98
49.54
55.76
$0.68
20.06
#0:31
20.18
+0.22
20.36
10.34
+1.17
=0.34
20,09
#0.44
20.31
20.35
10.65
#1130
ROTTA
36.25
37.12
31.38
61.20
35.56
49.20
45.21
33.54
56.7%
49.61
52.25
41.26
49.11
+SNAP
37.83
20.20
31.38
20.38
39.72
10.18
51.38
55.61
20.07
30.34
54.51
51,35
32

---

Table 25: STTA classification accuracy (%) comparing with and without SNAP on CIFARI00-C
through Adaptation Rates(AR) (0.05, 0.03, and 0.01). Bold numbers are the highest accuracy.
Imp.
Gh.
Zoom
Snow
Fog
Pts.
JPBG
Avg.
Text
40.69
41.55
15:14
+1.38
62.26
.0.23
40.26
101.5
51.21
50.00
55.5 52
=0.33
58.45
50.50
10.25
54,63
30.69
44.56
20.54
$1.24
+NNAP
42.87
101.37
29.08
37.60
+0.35
42.22
40.31
20.46
54.13
53.68
=0.47
58.03
67.05
63.08
57.67
46.94
54.13
ColTA
10.00
25.15
26.89
25.26
20.44
39,48
40.74
28.34
49.76
40.85
52.05
20.05
30.84
E1.12
35.5
61.36
41.60
34,59
20.82
33,60
20.54
34,54
$0.75
33.20
SNNAP
42.02
40.21
+6.13
42.70
49.31
37.67
58.30
60.36
+0.37
41.57
40.14
57.47
58,02
69.15
40.27
58.55
$1.31
40,32
52.34
+0.17
6363
60.16
40.49
51.25
49.76
+8.05
54,94
#0.12
47.96
50.63
40.22
0,05
EATA
SNAP
$0.21
40.12 14
40.49
38.46
+0.56
:8.43
41.64
39.05
34,37
+0.23
33:47
20.15
20.30
61,77
64.28
+0.53
20.51
+0.29
40.36
38. 50
61.52
$0.30
58.16
+0.45
63.17
20.18
+0.48
60.59
+0.53
49
$1.66
+0.55
52.12
$1.52
49
+0.47
=0.21
$6.50
-0.24
54.41
65.15
66883
+0.49
50.36
62.01
+1:37
s0,32
57.06
20.12
49.09
51.76
-0.58
58.23
55.66
52.67
40.42
20.32
40.
42.49
44.83
$0.29
$2.43
49.61
+0.50
SAR
00.25
10.07
=0.62
41,02
35:35
20.04
62.54
10:26
10.61
40.57
20 36
59.51
61.68
50.28
51.29
10.11
50.65
10.38
20.3 80
55,00
64.45
50,02
58.49
+0.82
50.50
20.64
40.27
54.22
40.63
44.54
51.50
40.43
SNAP
41.76
18.29
+0.44
64.24
36.89
10.21
64.34
20.38
+6.37
41.54
62.13
#0.15
63.9
=0.24
K3.24
H0.33
$2.91
10.02
$7.54
s8.23
66,99
=0.60
62.41
50.50
52.70
20.15
57.23
+0.47
=0.57
46.83
53.89
+1.33
RoTTA
#0.12
36.36
+0.42
57.38
11.7%
+0.45
61.44
20.06
38.25
20.20
=0.42
55.18
60.19
20.53
48.95
10.18
+0.28
46.30
=0.17
53.50
62.75
=0.42
+0:50
56.52
49.57
20.40
20.19
$2.19
20.25
41.60
+1.34
40.12
SNAP
20.12
37.67
20.21
38.66
20.12
32:47
63.95
20.16
20.20
40.15
#0.47
61.33
62:52
20.35
20.14
51.47
$1.32
291.36
=0.21
55.67
29.24
65.99
61.24
29.15
20.14
51.47
20.15
54,53
20.35
42.84
$1.41
21.23
Tex
40.17
38,55
10.15
39.28
33.27
40.1
61.64
20.25
+0.3
39.86
58,83
40.88
60.29
+0.29
89 85
10.1
39.51
+0.08
-0.0
54.64
65.48
+0.58
57.29
10.33
50.34
-0.54
+0.38
53.64
40.25
43,28
50,27
+0.37
SNAP
10.33
41.23
42.20
10.36
35.31
64.88
10.06
30.60
49.82
61.96
63.50
10.40
51.84
$2.36
10.40
+0.33
57.18
10.02
66,30
02.17
10.41
52.12
-0.17
+0.18
56.48
+0.40
45.72
18.28
51.99
COTTA
27.11
+1.11
27.73
=1.4
25
40.35
20.50
39.00
42
+1.71
#2.50
54.51
+1.75
35.96
+2.05
$4.21
41.77
37.50
41.15
50.45
51.34
52.72
48.14
50.70
40.34
20.08
20.33
#0.16
#0.65
+0.20
H1.61
20.17
20.13
#0.36
#11.66
32.00
39:08
33.59
52.93
42.11
49.56
+0:91
=0.53
20.44
#3.47
SNAP
3987
38.48
50.37
51.37
$1.36
40.42
16.11
#0.26
SAR
23.43
20016
10.54
20.31
53.67
SNNA
39.84
20.07
+0.75
41.83
20.28
34.94
50.26
26.16
30.49
10.28
51.27
10.51
51.11
20.17
=0.25
56.69
56.06
20.18
#0.16
44.95
20.28
52.41
ROTTA
20.05
36.24
36.94
20.09
31.15
20.14
40.5
20.36
40:52
38,
10.61
48.17
=0.67
53.32
20.46
-0.39
10.51
52.12
10.61
41.24
10.35
43.67
SNAP
37.85
40.20
+0.20
35.08
+0.31
32.78
63.97
60.34
#0.17
19.75
40.16
61.41
62.57
+0.52
$1.83
40.27
$1.36
40.28
+0.37
58.68
68.56
60.30
61.25
40.33
#0.19
51.53
48.26
$4.84
40.33
42.96
$1.45
40.25
Text
20.42
36.05
=0.21
56,95
20.47
31.31
61.08
20.51
20.56
35,00
20.53
57.63
26.31
58.76
20.47
46.24
21157
45.65
20.19
53.45
20.49
62.14
55.07
$2.13
20.25
48.59
51,82
20.55
20.04
40.68
20.54
45.57
SNAP
20.06
38.40
20.16
39.90
20.10
33.26
63.85
20.11
20.36
40.36
#0.34
61.23
20.34
62.79
20.06
51.92
541.00
51.73
20.34
56.20
65,83
20.17
20.24
60.95
51.82
20.00
20.30
54.75
#0.16
43,53
51.73
#0.18
CSTTA
$1.64
26.59
31.79
27.92
+1.51
24.36
41.34
52.21
$1.96
23.91
$2.85
23.00
$2.87
40.11
11.11
34.33
$2.67
33.32
37.99
+2.00
46.78
53.61
$2.1 18
25.30
36.20
21.50
21 15
$4.70
+1.47
35.67
12.13
34,55
NNAP
42.05
4008
+0.17
42.91
37.50
40.08
$8.70
20.12
41.22
+0.36
$7.35
#0.17
58.14
+0.33
$0.39
H0AR
$1.13
+0.43
$2.23
a6.12
63.42
#0.35
51.74
+0.17
49.87
20.50
$4.84
#8,00
#0.25
47.77
58.62
+1.26
0.01
EATA
SNAP
20.14
38.54
+0.27
36.10
20.15
39.75
+0.59
57.05
+0.34
33.11
28.22
31.03
63.82
20.10
60:56
=0.50
20.53
39:98
20.37
33.83
#0.20
61.33
+0.57
S7.64
62.53
20:34
20.32
58.77
20.12
51.76
48.02
+0.50
211.32
51.56
*1.26
46.75
56.03
-0.09
=0.44
51.57
65:94
29.19
62.18
=0.3
54.95
61.16
20.11
+2.22
51.47
48.55
29.04
-6.15
54,51
20.27
20.65
$1.80
20,04
20.02
43.67
40.75
51.68
48.51
=1.21
+0.55
SAR
36,04
40.00
+0.26
57.02
+0:30
31.38
61.13
+6.35
+0144
38.07
55,00
59.06
+0.44
48.44
+0-77
45.84
+0.92
-0.16
53.52
62.57
+0.50
55.19
+2:30
48.57
-6.15
+0.57
$2,01
40.71
19
45.72
+0.90
SNAP
10.30
37.91
31.92
10.38
63.17
20.45
39.35
62,01
20.36
51.11
10.11
50.4K
10.28
55.47
-0.41
65.07
20.16
59,69
10.15
31,34
20.15
10.47
54,10
#0.06
42,90
50.08
11.28
ROFTA
35.55
20133
=0.31
20:45
30.55
66.76
20.50
37.42
58.57
#0.30
40.28
47.87
+0:97
46.11
-0.23
53.11
61.00
20,02
54.70
#1.98
48.25
20,00
20.02
51-37
=0.11
40:20
s1.52
45.16
37.83
32.60
39.90
51.42
51.33
55.71
65.44
31.50
54.27
42.92
51.36
20.16
20.10
29.01
#0.49
20.33
20.06
20.12
+0.42
20.14
20.38
20.18
#0.19
20.47
#0.21
33

---

C.3 ImageNet-C
Table 26: STTA classification accuracy (%) comparing with and without SNAP ImageNet-C through Adaptation Bates(AR) (0.5, 0.3, and 0),,, including results for full adaptation (AR=1). Bold numbers are the highest accuracy.
AR
Medhods
Gau.
Shot
Imp.
Def.
Gla.
Mot.
Zoom
Snow
Fro.
Fog
Bril.
Cont.
Elus.
Pi..
JPEG
Avg.
Source
40.00
3.00
+0.00
3.20
+0.00
2,54
17.50
+0:00
+0.00
9.74
44.00
14.72
22.45
+0.00
+0.00
15.60
23.06
+0.00
24:00
-0.00
+0.00
59.11
+0.00
5:37
-0.00
16.50
40.00
20.85
40.00
32,63
+0.00
13.15
stuts
+0.05
14.20
15.06
-0:88
14:89
=0.08
13.90
+0.08
19.58
+0.05
23.78
+0.06
+0.04
31.78
+0.07
30.26
46:40
-0.14
=0.11
15.14
+0.05
40.42
-6.10
+0.04
45:25
36.59
20:07
+0007
Texs
$0.05
27.03
28.98
28.64
=0120
24.66
z0.27
20.25
23:63
38.70
45.77
20.12
+0.08
44:82
38.06
40.35
=0.08
14.59
=0.10
#1.51
16.44
51.64
20,10
20.15
55.54
20.07
49.38
21124
39.53
COTTA
40.08
13:12
20:01
13.94
20.10
12.44
20.04
12:18
#0.04
23.74
20.00
45:05
31.78
30.26
40.06
20.14
44.40
62.40
20.11
#0,00
15.13
40.42
20.04
45,26
20.15
36.53
28.72
20007
29.62
31.17
26.59
26.30
36.29
40.75
55.57
3600
52.66
56,00
50.26
42.56
40.15
$0.09
10.05
=0.08
20:30
20.04
#0.15
#0.10
SAR
25.97
20:25
55.13
89.35
ROTTA
19.51
40.25
10.10
40.27
20.18
39.66
=0.23
46.08
47.47
40,67
20.21
31.20
Texk
40.10
25.24
+0.27
26.86
26.35
+0.08
+0.06
23:26
22.41
+0.05
40.00
35.99
+0.10
46.60
42.96
40.5
40.17
37.68
-0.15
53.60
64.40
+0.12
+0.94
21.35
-0.17
50.35
$4.32
40.15
47.91
40.04
38.68
+0.17
+SNAP
18.00
2K05
20.04
29.97
29.19
20.39
25.73
20.15
20.06
23.39
35.49
#0.17
20.03
45.65
10.09
44.21
10,10
39,57
20.10
53.90
64.52
=0.00
34.39
=1,83
20.14
49.99
+0.0T
54.8%
$0,09
48.72
+1.21
48.72
OSTTA
21113
11.99
20.20
13.04
20.10
12:56
20.07
11.00
2011
11.64
20.12
22.92
35.06
20.06
31.20
20.09
21106
20.07
=0.07
44.28
62.16
20.07
14.02
20.00
40.39
20.09
45.29
20.12
36.55
st.09
25.22
+NNAP
20.14
15.16
=0.02
15.9%
20.14
15:86
20.04
13.98
20,00
14.13
20099
24,60
20.07
36.51
20.16
32.59
241.66
31.71
20.09
45.9H
20.05
63.62
20.04
15.72
42.85
20.00
20.24
46.71
20.14
37.93
20099
36.17
0.5
EATA
+SYAP
+0.10
25.62
38,00
20.10
30.12
31.88
20.14
29.96
31.47
26.93
25.24
20.30
20.54
24.43
26.64
#0.10
39.16
33,944
47:15
36.35
20.25
45.20
#0.12
45.36
10.01
39.75
38,05
20.06
55.30
15.04
64.34
64.52
20.07
34.48
33.75
20.41
$2.06
$2.29
20.24
20.13
55,57
55.66
20.05
50.48
49.85
20.16
41,42
42:03
40.29
+0.17
+0.13
a0.21
+0.25
#0.15
+0,07
40.15
10.14
e0.14
10.10
+0.07
.0,09
#8.15
#0.05
$0.18
SAR
26.74
+0.25
23.56
+1.75
26.77
+0.13
+0.21
19:50
21.50
+0.38
+0.10
90.97
44.%
+0.12
45.90
+0.17
34.22
+0.80
-0.05
55.04
63:05
+0.00
+0.64
6:58
-6.10
$2.50
+0
55.95
+0,09
48:71
+0.33
S8.29
SMAP
10.38
31.58
33.23
+2.44
33.77
+0.56
21,00
26.47
=0.94
26.36
#0.10
44.01
47.94
20.04
10.12
48.77
211.99
42.51
56.96
=0.13
64.86
20.10
=10.99
28.31
54.23
20.08
57.55
28.16
51,90
20.19
=1.20
43.22
RoTTA
4005
18.17
10.0%
19:90
40.0 10
18.49
12:32
10.11
20113
11.79
23.56
1015
34.62
20.14
37.84
+0.1
32.91
10.00
-0.05
47.56
63:94
10.10
18.68
10.42
-0.08
43.21
25.25
48.54
40.23
40,20
$1.45
#0.14
SNNA
20.43
1003
21.08
10.11
15.47
14.49
20.17
26.36
10,06
36.46
20.10
38.98
10,09
34.15
10.12
48.41
20.13
64.02
20.13
10.33
43.66
=0.10
49.16
18.10
#0.15
41.05
3310
11.11
Tesa
23.63
20088
24:80
20:28
2000
20:97
20.15
34,11
20:04
41.41
20:05
36.95
10.04
52.66
20:15
20.13
20.16
20.07
53.46
46,50
20.09
37.42
20112
SNAP
25.21
+0.33
27:94
#0.12
22.39
#0.13
10.07
42.64
40.15
38.54
=0,00
52.91
48.58
16.14
$3,90
#0.11
47.41
#0.17
39.47
CoFTA
11.24
12.66
11.02
31.05
29:11
45,19
36.71
23.09
SNNAP
14.13
31.58
=0.21
46.04
36,05
EATA
27.35
28.22
$0.60
23.45
45.05
54.52
=0.01
55.00
40.27
20.21
21.21
SNNA
29.45
30.69
25.00
38.34
46.60
44.62
39.31
54.92
55.41
49.75
19.11
20.25
20.06
20.06
10.06
10.14
SAR
20.15
25.12
20.89
29.65
20.17
40.33
23,88
39.34
45.36
10.18
45.69
10.79
36.75
54,91
=0.00
20000
10.96
20.19
10.13
55.76
20.05
10.34
39.20
SNAP
32.63
34.09
34.26
18.91
27.96
13.11
47.99
25.27
42.41
56.45
64.77
32.76
53.74
57.21
$1,67
43,80
10.11
+0.25
10.18
+0,27
16.29
40.14
10.11
40.13
+0.09
+0,00
63.64
20.13
46.28
40.12
40.35
ROTTA
#1.15
16.00
20.11
17.68
20.00
17.25
20.17
12.59
20115
12.51
2001
23.96
20.16
35
2001
36,2
20.07
32.92
20.02
47.25
20.13
63.96
17.46
42.77
20.09
20.24
48.3
20.15
20111
$0.05
SNAP
10,07
18.63
=0.05
19.94
19.06
19.35
20.08
14,88
20.05
14,34
25.88
20013
3647
50.03
#0.02
37.15
33.32
10.11
=0.17
47.74
63.96
30.06
#0.21
19.08
50.07
42.96
#0.17
48.73
#0.20
40.37
#0099
32.15
Tenx
22.00
+3.47
+3.92
29.51
23
+3.85
+2.50
19.98
+2.06
18.96
+3.40
31.15
42.19
+2.45
30.20
+3.27
+0.60
34.93
-2. 30
51.60
63.70
+0.20
15.99
+4.61
47.74
-2.64
+3.27
$0.35
45 54
+2.9%
+2.71
35.47
SNAP
24.92
26.21
25.36
27.85
+5.30
27.30
24.33
23.62
24.11
22.73
1557
36001
23:72
44.11
14.49
42.19
x3.37
36.15
52.95
23.47
21.18
64.57
30.23
25.15
24.29
48.56
23,31
53.71
24.09
47,09
24.17
39.13
CSTTA
20.32
13.97
20.32
11.92
20.14
11.9%
20.04
11.45
20.34
11.34
2002
21.29
34556
25:15
20
30.85
20.09
29.89
20.23
44.09
61.56
20:05
20128
13.0%
40.21
28.18
20.15
45.27
20.10
36.71
21L17
27.81
SNAP
10.06
15.13
+0.09
16,03
20.04
15.91
20,00
13:66
20007
14.02
4005
2499
20,05
36.51
10.66
33.56
20.12
31.81
=0.0 06
46.02
63,60
20.10
15.99
+0.04
41.91
20.09
10.09
46.75
20.12
35,03
10007
38.19
RATA
$0.5
22:45
10.15
23.78
25:26
+0:43
20.25
19:38
40.1
19:42
1031
32.18
4522
20.10
10
20.5
10.16
36.64
-0.27
52.38
65.57
+0,05
24.59
#1.50
20.40
45.15
10.12
51,89
40
46.33
+0.32
36.61
SNAP
2610
40,09
10.13
27.29
27.13
+0.30
22.38
30.14
22.15
10,08
43.92
10.16
48.96
36.68
$0.81
+0.09
52.71
63.77
10,10
27.03
10.18
48.47
=0.34
53,23
+8.10
+0.17
47.46
38.24
$I.15
SAR
25.12
+0.17
=0.01
27.56
26.05
:0:11
22.51
+0.34
#0.21
23:55
46.48
20.00
43. 19
+0.09
37.26
#1.32
=0.21
53.52
=0.11
19:87
#2.10
=0.12
50.78
10.18
$4.78
=0,07
48.43
$0.28
38.62
+NNAP
30.28
20.16
=0.12
31.30
26.67
20.34
=0.37
36.31
#0.25
20,44
10,00
45.43
+1.13
40.26
54.76
=0.23
64.22
20,05
36.12
#1.67
31.36
20.06
=0.20
55.42
20.06
49.63
=0.20
41.99
ROTTA
14.77
15:33
13.17
13.19
31.73
30.77
45:22
63.08
15.22
41.05
46.15
37.19
29.54
-0.10
+SNAP
16.01
x0,07
=0U77
13,66
33.04
31.02
20.11
45.38
1896
30,07
46.14
29,85
34

---

Table 27: STTA classification accuracy (%) comparing with and without SNAP on ImageNet-C C
through Adaptation (ates(AR) (0.05, 0.03, and 0.01). Bold numbers are the highest accuracy.
Gau.
Imp.
Gb.
Zeom
Snow
Fog
Ptc.
JPEG
Text
23.77
24.65
24.44
00.53
30.54
+31.69
20.27
52.73
43.57
s1.15
40.3
35.92
20.12
50.78
15.05
40.33
53.46
10.09
+1103
47.19
111.35
36.62
+SNAP
29.12
30.45
20.45
30.30
40.25
25.22
38.21
44.29
20.13
39.95
20.15
54,65
65.47
=1.10
20.10
55.59
49:21
211.35
41.27
ColTA
10.30
11.05
40.57
20.33
11:75
11.00
20.46
13.20
22.30
34,56
20.08
30.87
=0.01
29.78
20.11
43.99
20.06
61.57
=0.36
12.92
40.26
+0.17
45.23
36.63
20.07
27.72
10.21
SNAP
40,06
1522
40.11
15.97
+9.03
15.93
+0.06
13.91
20.12
14.05
24.87
40.04
60.00
36,48
32,60
40.07
3145
+0,04
+6.03
46,09
63,59
68.07
20.05
+8.03
40.09
46.71
37.96
40,09
30.18
40.06
0,05
EATA
SNAP
$1,10
40:31
19.53
22.33
20.34
+0.65
23,95
20.85
29.30
+0.75
23.62
20:72
50.09
+0.41
19.43
16.34
20.19
+0.58
19.70
16.95
s1.56
30.34
29.11
+0.49
28.18
41.23
+0.27
41.59
37 96
10.11
+0 18
38.06
211.11
+0.33
35.06
34.84
18.15
+0.21
50.98
50.75
28.13
63.29
63.30
+0.11
+1.26
23:72
20.30
19.50
s8.16
45.90
40.35
46.36
10.16
51.52
51.15
40.17
SIL18
44.13
+0.09
45.46
+1L21
35.72
+0.41
34.19
SAR
20:21
23.25
20.34
24.23
20.30
23.66
20.09
19.58
#8.16
20.58
33.05
20.30
43.04
20.16
20.02
40.75
21.112
36.06
20.09
52.61
64.59
20.07
20.54
20.17
20.11
49.00
20.10
$3.35
s1.11
46.75
20120
36,69
SNAP
27.54
10.16
29.13
28,66
20.04
24,05
20.16
23.42
36.25
H0.12
20.10
44.12
42.89
H0.11
10.87
38.54
53.34
+8.07
=6.15
64.25
31.83
=0.24
a6.23
48.79
54.04
47.90
39.63
RoTTA
10.06
14:42
+005
15.23
20.10
15.00
20.11
13:25
20117
13.51
23.79
+0.3
35.27
20.08
+0.25
32.09
=0.07
30.43
20.13
44.71
62.64
20.14 14
=0,00
15.24
20.10 10
40.63
45.55
+0.7
#0.16
36.75
29.22
#1109
SNAP
20.06
1466
+0.02
15:45
20.18
15:29
20.09
13:43
21.19
13:45
21013
2393
20.05
35.33
32.18
20.04
211.6
30.53
:0.16
44.71
28.10
62.54
20.04
15.41
20.09
40.64
20.10
45.55
36.11
#1L14
1100
29.33
Texx
21.26
40.17
40.35
22.76
20.1 17
22.58
+0.04
19:06
2012
13.90
2085
1022
42.34
20.12
38.96
+0:26
35.53
+0.31
20.18
51.58
63,42
20.11
-0,91
18.61
47,96
40.25
52.41
10:21
45.55
10.0
35.08
40:55
SNAP
26.42
40.14
+0.26
25.20
27.81
+0.37
+0.46
23,79
20:21
21-81
35,77
11111
44,50
r6.16
41:37
40.34
38.81
20.14
+8.06
53.34
64.95
#6.11
+0.63
30,85
49.28
+0.17
$4.16
11009
47-57
10:22
39,24
COTTA
+0.18
1061
+0.36
12.36
=0.57
11.75 1..78
11,66
20.57
11:52
2111
35/01
20.18
+0
30.55
=0.07
29.84
=0.11
44.09
61.83
20.16
=0.12
12.00
20. 19
40:36
45
+1.11
1109
36-56
11122
22:27
SNAA
20,00
15:29
16.00
=0.09
=0.07
=0:11
14106
24.78
=040
3654
31.62
20:06
31.70
-0,08
=0.01
46.01
63,49
=0.04
15,69
=0.04
20.15
42,05
#0.19
46-75
#U0
37:97
#1008
30,20
17.17
17.94
15:04
2621
29.47
35.51
23:41
49.16
63.06
44.16
49.90
42.47
32,30
40.41
+0.36
20.52
#0:22
20:33
20.33
=0.19
=0.05
20.59
#0.09
#9.31
211.55
SNAP
21.38
17.90
3954
36.37
33:54
49.50
39.97
43.33
33.90
+0.35
+0.34
+0.34
10.16
40:13
:0.11
+0.12
40,03
SAR
20:36
18.24
4163
36.57
51,19
47.50
52.02
44.81
SNAP
26.00
20.56
21.25
10.16
40.83
28.15
52.63
45.80
37.64
ROTTA
20.04
14:36
20.00
14.05
20105
13.54
20.04
31.89
=0.07
30.33
=0.11
44.52
15:20
45. 45.36
20.07
36.63
sh.17
29.13
SNAP
14.45
20.05
15.06
20017
13.42
23,33
35.26
49.02
31,92
30.36
19.19
44.53
10.08
45.39
20.16
36.65
29.18
Text
40.14
17.09
40.1 10
17.20
+0.13
17.00
+0.21
14.91
+0.09
15:25
+0.35
25.23
+0.27
38.06
+0.27
36.15
+0.31
32.26
40.21
48,14
+0.16
60,65
+0.48
15.76
40.21
43.44
89.
00.04
41.18
+0.10
31.55
+0.19
SNAP
20.02
20.66
20.13
21.73
20.18
21.55
20.34
18.46
24.35
15.25
20112
29.85
56.14
40.63
36.97
#0.21
211.10
34.89
20.36
49.85
50.10
64.29
20.14
22.64
20.29
45.13
58.77
+0.07
#0.51
4X.17
$0.19
34,59
COTTA
10.1
11.11
20.12
13.24
20.55
11.56
20.99
10.35
10.95
10.97
22.15
20.55
34.66
20.18
20.14
30.35
20.21
29.55
20.21
44.05
61.71
50.23
20.53
12.51
50.20
40.16
25. 14
+0.2
36.75
10.12
20.34
27.75
SNAP
15.09
40,04
$0J09
16,00
10.14
15.83
+0.09
15.84
+0.02
14.06
24.70
#0077
36.47
#6.02
32.59
10.11
31.66
+0.83
+8.15
46.10
63.62
=6.07
+0.06
15.00
42.03
10.10
36.74
+0.01
38.17
H0.20
M6.17
0.01
EATA
+SNAP
20.12
16.75
#0.13
1485
20.10
+0.21
17.55
15.61
20.19
=0.21
17.30
15.40
28.09
14.35
-0.04
13:26
z1.10
14.64
+006
13:57
23.72
24.13
z1136
+0.19
=0.23
36,53
=0.13
36.18
32.81
+0.09
32:57
31.14
21.86
20.10
31.09
28.19
=0.20
46.06
46.63
=8.1P
62.35
62.20
20.16
=0.54
15.26
-0.35
15.88
20.12
41.91
20.17
42.34
+0.15
21.18
47.44
43.00
211.4
39.81
+1.09
35.85
21L19
*0.15
29.76
38.61
SAR
20.8
16088
40.07
17.04
20.10
16.59
20.16
14.72
20112
14:75
20113
25.92
20:05
27,45
34.07
20124
20.11
32.25
20.13
47.66
63.15
20.05
17.20
20.15
20.20
43.05
2010
45.75
11120
26.14
21113
31.29
+SNAP
1889
19:45
19.70
16,70
16:55
27.69
38.57
35.34
33,09
48.08
63.04
20.29
42.95
35.76
38,99
32.08
10.15
+0.15
#0.12
26.14
20.15
#0.16
#6.11
40.32
20.09
#0.31
=0.07
=0.12
$6.29
#0.26
+0.33
10.18
ROTTA
$0.05
14.30
10.0%
15.05
+0:07
14.39
+0.00
13.30
40.8
13.37
23.78
10.04
+0.05
35.23
10.04
31.79
+0.06
30.27
+0.
44,40
62,40
-0.11 11
15.16
+0.06
40,42
40, 10
85:21
+0.05
36.54
10.6
29.08
40.07
SNNP
10.06
14.30
20.08
14.92
13.30
atJ17
13.38
23.78
36.23
#0.06
10.04
31.78
=0.07
30.26
10.14
44.41
62.40
=0.11
15.18
#0.05
$0,09
40,43
45.27
10,04
36.84
11.15
29.08
10.07
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 loBMN components in SNAP. Specifically, we measured the average accuracy across 15 corruption types on CIFARIO-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 loBMN across these adaptation rates. The results indicate that the combination of CnDRM (Class and Domain Representative sampling) and loBMN (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 distinet positive effect, as evidenced by consistently higher accuracy compared to using no adaptation or only 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 loBMN results in improved robustness against various corruptions.
35

---

Table 28: STTA classification accuracy (%) of ablative settings on the CIFARIO-C, adaptation rate
(AR) 0.3, 0.1, and 0.05. Averaged over all 15 corruptions. Bold numbers are the highest accuracy.
AR
Methods
Tent
CoTTA
RATA
SAR
RoTTA
Naive
78.86
69.75
79.02 20.14
77.83 #0.11
75.39
Random
78,90
66.04 =0.10
78.97 +0.13
77.77
+0.12
75.06
LowFntropy
78.68 =0.11
63.74 10.16
78.42 1:009
76.21 +0.10
72.83 +:
0.3
CRM
80.32 #:007
66.50
#0.12
80.1 4008
75.78
+0.13
75.49 +0.06
CnDRM
79.62 10.13
77.68 1:010
79.63 10.12
78.22 1.009
75.85 10.0
CnDRM+EMA
80.96 #0.06
72.42 ::014
80.27 +0.11
78.19 +0.13
76.73 +0.00
CaDRM-HOBMN
81.23
78.75
81,30 +:007
79.77
77.41
Naive
76.81 10.18
1:012
76.29 1:011
76.01 1:007
74.78 1:015
Random
77.08
65.61
76,59
76.33 +0.13
75.01
LowEntropy
75.66 1.009
63.19 10.14
74.89 1.0.12
74.41 1.0188
72.60 1.0.10
0.1
CRM
77.77 20.05
65.71
::019
77.18 1:008
74.36 2:011
75.27 #:017
CnDRM
77.46 10007
77.69 10.10
77.17 1:0.06
76.85 1.009
75.64 1.008
C&DRM+EMA
78.02 10.12
72.19 1:015
77.05 1:0.11
76.84 1:013
76.18 1:0.05
CnDRM+1oBMN
78.95
1:006
1:0.13
78.06
1:007
77.07 1:0100
Naive
75.75 1.018
67.22 1.012
75.55 1.0.44
75.25 10.17
74.80 1.0.11
Random
10.13
=031
75.56
1:016
75.27
1015
74,91 1:0 10
LowEniropy
74.07
64.08
73.73
73.58
72.83
0.05
CRM
76,55 10.11
66.14 1.017
76.06 1.0.13
74.02
1..15
75.23 1.009
CnDRM
76.53 10.14
77.67
76.29 1:018
76.18 10
75.61 1:.13
CnDRM+EMA
76.86 +0.10
71.69 =0.19
75.98 +:015
75.43 +0.14
75.95 +0.11
CaDRM+1oBMN
77.93 10000
78.73 13
77.76 10012
77.21 20.1
77.05 2008
Table 29: STTA classification accuracy (%) of ablative settings on the CIFAR100-C, adaptation rate (AR) 0.3, 0.1, and 0.05. Averaged over all 15 corruptions. Bold numbers are the highest accuracy.
AR
Methods
Tent
CoTTA
BATA
SAR
RoTTA
Naïve
53.36 10:32
39.11 10.7
49.97 10.19
56.65 20
49.84 1: 18
Random
10.24
33.49 :021
49.24 10.17
56.06
10026
49.00 1: 16
LowFatropy
53.53
32.29 =028
45.51 2023
55.84 20
44.77
0.3
CRM
54,21 10.18
32.86 =024
47.42 1:020
56.40 10.19
46.68 10
CnDRM
55.15 #0.11
50.02 #0.14
$1.36 #0.16
57.72 +0.18
50.74 +0.15
CnDRM+EMA
55.39 10.16
41.34 10
50.11 1:019
57.68 +0.21
49.88 +0
CaDRM+HoBMN
$7.27 #0.13
50.32 #:015
$2.19 +:014
58.44 +0.16
51.55 +0.12
Naive
52.84 +0.19
35.86 23
49.70 +:018
53.49 +0.1
49.11 +0.17
Random
52.68 #022
33.18 10026
49.39 4:020
53,42 4-018
48.84 4:0.4
LowEntropy
51.76
32.30
46.03
52.15
45.18
0.1
CRM
52.43
32.54 20:5
47.68
10:21
53.12 2:020
47.01 16
CnDRM
54.46
50.06
$1.41 1:019
55.24
50.47
CnDRM+EMA
54.36 10.15
41.63 1.022
50.21 1.0.18
54.84 10.17
49,95 1.0.1
CnDRM+1oBMN
55.84 20.14
50,52 1:.11
52.35 1:0.55
55.76 1:0.33
51.33 1:0.00
Naive
51.24 10.18
33,20 1::25
49.81
1.0.6
$1,50 10211
49,12 100.99
Random
51.35 1:0.0
33.71 1:022
49,57
10.17
$1.48 1:000
48.98 1.0.15
LowEntropy
49.79 =0.24
32.36 #0026
46.65 +:019
49.51 4:22
45.41 40.18
0.05
CRM
50.17
32.74
47.47 4:020
50.49
46.58 +0.16
CnDRM
52.86 10.14
$1.47 10:17
$3.09 10
$0.44 1: 13
CnDRM+EMA
52.68
41,43
50.32 10.18
$2.80 1.0
50.04
CnDNM+HOBMN
54.13 10.11
50.63 1..14
$2.43 1.0.16
53,59 10.12
51.41 10.10
D License of assets
Datasets CIFAR1O/CIFAR 100 (MIT License), CIFARIO-C/CIFARRIO- (Creative Commons
Attribution 4.0 International), ImageNet-C (Apache 2.0), and ImageNet-R/Scken (MIT License).
Codes Torchvision for ResNet18, ResNet50, and VitBase-LN (Apache 2.0), the official repository of CoTTA (MIT License), the official repository Tent (MIT License), 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 T3A (MIT License), official repository of FOA (NTUITIVE License) and the official repository of MECTA (Sony AI).
36

---

NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification: The claims in the abstract and introduction accurately reflect the paper's contributions and are supported by the presented results.
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or
NA answer to this question will not be perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.
is fine to include aspirational goals as motivation as long as is clear that these goals not attained by the paper.
2. Limitations
Question:
Does the paper discuss the limitations the work performed by the authors?
Answer: [Yes]
Justification:
Limitations are discussed in Section 6.
Guidelines:
The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.
The authors are encouraged to create a separate "Limitations" section their paper.
The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect how these assumptions might be violated in practice and what the implications would be.
The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on few datasets or with few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.
The authors should reflect on the factors that influence the performance of the approach. For example, facial recognition algorithm may perform poorly when image resolution is low images are taken in low lighting. Or speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon.
The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.
If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness.
While the authors might fear that complete honesty about limitations might used by reviewers as grounds for rejection, worse outcome might be that reviewers discover limitations that aren't 't acknowledged judgment and recognize that individual actions in favor of transparency play impor- tant role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations.
the paper. The authors should use their best
3. Theory assumptions and proofs
Question: For each theoretical result, does the paper provide the full set of assumptions and complete (and correct) proof?
Answer: [NA]
37

---

Justification:
No theoretical result.
Guidelines:
The answer NA means that the paper does not include theoretical results.
All the theorems, formulas, and proofs in the paper should be numbered and cross- referenced.
All assumptions should be clearly stated or referenced the statement of any theorems.
The proofs can either appear the main paper or the supplemental material, but they appear in the supplemental material, the authors are encouraged to provide short proof sketch to provide intuition.
Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix supplemental material.
Theorems and Lemmas that the proof relies upon should be properly referenced.
4. Experimental result reproducibility
Does the paper fully disclose all the information needed to reproduce the main ex- perimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?
Question:
Answer: [Yes]
Justification: Experimental details for reproducibility are provided Section and Ap- pendix A. Also, we provided source code in the supplemental material.
Guidelines:
The answer NA means that the paper does not include experiments. If the paper includes experiments, No answer to this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.
If the contribution is dataset and/or model, the authors should describe the steps taken to make their results reproducible or verifiable.
Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is novel architecture, describing the architecture fully might suffice, or if the contribution is a specific model and empirical evaluation, it may be necessary to either make possible for others to replicate the model with the same dataset, or provide access to the model. In general. releasing code and data is often one good way accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model (e.g.. in the case of large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.
While NeurIPS does not require releasing code, the conference does require all submis- sions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example
(a) If the contribution is primarily a new algorithm, the paper should make it clear how reproduce that algorithm. (b) If the contribution is primarily
model architecture, the paper should describe the architecture clearly and fully.
(c) If the contribution is a new model (e.g., a large language model), then there should either be way to access this model for reproducing the results or way to reproduce the model (e.g., with an open-source dataset instructions for how to construct the dataset).
(d) We recognize that reproducibility may be tricky in some cases, in which case authors are welcome deseribe the particular way they provide for reproducibility, In the case of closed-source models, it may be that access to the model is limited in some way (e.g., registered users), but it should be possible for other researchers to have some path to reproducing or verifying the results.
5. Open access to data and code
Question: Does the paper provide open access to the data and code, with sufficient instruc- tions to faithfully reproduce the main experimental results, as described in supplemental material?
38

---

Answer: [Yes]
Anonymized source code and instructions are provided in the supplemen- tary material. The complete codebase and scripts will be made publicly available upon publication.
Justification:
Guidelines:
The answer NA means that paper does not include experiments requiring code.
Please see the NeurIPS code and data submission guidelines (https://nips.. cc/
for more details.
While we encourage the release of code and data, we understand that this might not be possible, so "No" is an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (e.g., for open-source benchmark).
The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurlPS code and data submission guidelines (https:
/ httpssccccpbccccccccpcccc gww//uuieee//eee /Coee//udebumimi ssi aisionPolicyy for more details.
The authors should provide instructions data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.
The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. only subset of experiments are reproducible, they should state which ones are omitted from the script and why.
At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).
Providing as much information as possible in supplemental material (appended to the paper) recommended, but including URLs to data and code permitted.
6. Experimental setting/details
Question: Does the paper specify all the training and test details (e.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
Answer: [Yes]
Justification: Details are provided Section 5 and Appendix A.
Guidelines:
The answer NA means that the paper does not include experiments.
The experimental setting should be presented the core the paper to level of detail that is necessary to appreciate the results and make sense of them.
The full details can be provided either with the code, in appendix, supplemental material.
7. Experiment statistical significance
Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
Question:
Answer: [Yes]
Justification: All experiments were conducted using three random seeds (0, 1, and 2), and the corresponding standard deviations are reported and visualized as error bars. Note that standard deviations omitted from Table are reported Appendix C. Detailed descriptions are provided in Section and Appendix A.
Guidelines:
The answer NA means that the paper does not include experiments.
The authors should answer "Yes" if the results are accompanied by error bars, confi- dence intervals, statistical significance tests, least for the experiments that support the main claims of the paper.
The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall with given experimental conditions).
39

---

The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.)
The assumptions made should be given (e.g.. Normally distributed errors).
should be clear whether the error bar is the standard deviation or the standard error of the mean.
It is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have 96% CI, if the hypothesis of Normality of errors is not verified.
For asymmetric distributions, the authors should be careful not to show in tables figures symmetric error bars that would yield results that are out of range (c.g. negative emror rates).
If error bars reported in tables plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables the text.
8. Experiments compute resources
For each experiment, does the paper provide sufficient information on the com- puter resources (type of compute workers, memory, time of execution) needed reproduce the experiments?
Question:
Answer: [Yes]
Justification: Details are provided Section 5 and Appendix A.
Guidelines:
The answer NA means that the paper does not include experiments.
The paper should indicate the type of compute workers CPU or GPU, internal cluster, cloud provider, including relevant memory and storage.
The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute.
The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn't 't make it into the paper).
9. Code ethics
Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics https: : /ttp///ee.i///eeeeee/eeeeeeeeeee httpp/lcc/ttiiceciieeeeeee
Answer: [Yes]
Justification: Ensure that our work adheres to the NeurlPS Code of Ethics.
Guidelines:
The answer NA means that the authors have reviewed the NeurIPS Code of Ethics.
If the authors answer No, they should explain the special cireumstances that require deviation from the Code of Ethics.
The authors should make sure to preserve anonymity (e.g., if there is special consid- eration due to laws or regulations in their jurisdiction).
10. Broader impacts
Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
Answer: [Yes]
Justification: Potential socictal impacts are described in Section 6.
Guidelines:
The answer NA means that there is no societal impact of the work performed.
If the authors answer NA or No, they should explain why their work has no societal impact or why the paper does not address societal impact.
Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.
40

---

The conference expects that many papers will be foundational research and not tied particular applications, let alone deployments. However, if there is direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster.
The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology being used intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology.
If there negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms monitor how system learns from feedback over time, improving the efficiency and accessibility of MI..
11. Safeguards
Does the paper describe safeguards that have been put in place for responsible release of data models that have high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
Question:
Answer: [NA]
Justification:
No such components.
Guidelines:
The answer NA means that the paper poses such risks.
Released models that have high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere usage guidelines or restrictions to access the model or implementing safety filters.
Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.
We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make best faith effort.
12. Lieenses for existing assets
Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper. properly credited and are the license and terms of use explicitly mentioned and properly respected?
Answer: [Yes]
Justification: All licenses and credits are described in Appendix D.
Guidelines:
existing assets. The authors should cite the original paper that produced the code package or dataset.
The answer NA means that the paper does
The authors should state which version of the asset is used and, if possible, include URL.
The name of the license (c.g., CC-BY 4.0) should be included for each asset.
For scraped data from a particular source (c.g., website), the copyright and terms of service of that source should be provided.
If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, paperswi thcode. com com/datasets has curated licenses for some datasets. Their licensing guide can help determine the license of dataset.
For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided.
41

---

If this information is not available online, the authors are encouraged to reach out to the asset's creators.
13. New assets
Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
Answer: [NA]
Justification:
No new assets introduced.
Guidelines:
The answer NA means that the paper does not release new assets.
Researchers should communicate the details of the dataset/code/mmoel as part of their submissions via structured templates. This includes details about training, license, limitations, etc.
The paper should discuss whether and how consent obtained from people whose asset is used.
At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file.
14. Crowdsoureing and research with human subjects
Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well details about compensation (if any)?
Answer: [NA]
Justification:
No crowdsourcing or human-subject experiments were required.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.
Including this information in the supplemental material is fine, but if the main contribu- tion of the paper involves human subjects, then as much detail as possible should be included the main paper.
According the NeurIPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector.
15. Institutional review board (IRB) approvals or equivalent for research with human subjects
Question:
Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or institution) were obtained?
Answer: [NA]
Justification:
No IRB approvals were required.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.
Depending the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.
We recognize that the procedures for this may vary significantly between institutions and locations, and expect authors to adhere to the NeurlPS Code of Ethics and the guidelines for their institution.
For initial submissions, do not include any information that would break anonymity (if applicable), such the institution conducting the review.
16. Declaration of LLM usage
42

---

Question: Does the paper describe the usage of LLMs if it is important, original, or non-standard component of the core methods this research? Note that if the LLM used only for writing, editing, or formatting purposes and does not impact the core methodology, scientific rigorousness, or originality of the research, declaration is not required.
Answer: [NA]
Justification: No LLMs were used in this research components.
Guidelines:
The answer NA means that the core method development in this research does not involve LLMs any important, original, non-standard components.
Please refer to our LLM policy fattps://neet /ttpss:://ee.p..eeeeee http//rrpp..ccoooffeeeeeee////// ccc///oofeerreccee222///11/ for what should or should not be described.
43


Reviews:
[{"review_id": "5X5oOvPB5J", "reviewer": "Reviewer_GNGJ", "summary": "This 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.", "questions": "See weaknesses and try to address all of my concerns.", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths:\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", "was_revised": true, "final_justification": "As most of my concerns have been addressed, I will raise my score.", "rebuttal": "**Weakness1 (W1).** Thank you for the insightful comment. We have conducted additional evaluation on the **HARTH**[r1] dataset, a realistic *health monitoring* benchmark consisting of three-axial sensory inputs and human activity recognition labels. 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***, providing a complementary scenario to validate SNAP.\n\nWe compared the naïve Sparse TTA (STTA) baseline and our proposed SNAP module under an adaptation rate (AR) of 0.1, using Tent[46] and SAR[30] as TTA methods. The source domain is the data collected from the back (15 users), and the target domain is the data collected from the thigh (from the remaining 7 users). Table A shows that SNAP improves accuracy even with sparse updates, demonstrating its effectiveness under realistic shifts.\n\n*Table A. Performance on HARTH[r1].*\n| Method | |Average Accuracy | \n|-|-|:-:|\n| Tent | naïve STTA (AR=0.1) | 19.64 |\n| | **SNAP (AR=0.1)**|**30.67**|\n| SAR | naïve STTA (AR=0.1) | 21.10 |\n| |**SNAP (AR=0.1)**|**26.63**|\n\nFor other motivating scenarios, such as autonomous driving and high-frame-rate video, we believe that these are aligned with the main evaluations of ImageNet-C's 2D frame-based corruptions. Given the shared methodological assumptions, we expect similar gains for SNAP. We will conduct additional validation on these scenarios and include the results as resources permit.\n\n---\n**W2.** Sparse TTA scenarios, including SNAP, require at least one adaptation (model update) cycle before achieving effective performance, regardless of batch size. After the first sparse update, SNAP functions as intended and exhibits robust performance. Specifically, our Class and Domain Representative Memory (CnDRM) is designed to be batch-size agnostic. For domain-representative sampling, the domain centroid is computed using a moving average of early-layer feature statistics, stabilizing quickly even under bs=1. For class-representative sampling, CnDRM selects samples based on per-sample prediction confidence and class balance. While small batches can slow down class distribution balancing (particularly under skewed distributions), we found empirically that this has a limited effect on overall adaptation (*Appendix C.12*). In practice, as shown in *Appendix C.13*, SNAP maintains robust performance even in bs=1 scenarios. We will clarify this and add such visualizations in our final manuscript.\n\n---\n**W3.** We agree that memory-based sampling and BN correction have been partly explored in prior TTA work. Our key contribution lies in re-designing these components specifically for the sparse update regime, which differs significantly in its constraints and requirements.\n\n**CnDRM vs. Prior Memory Sampling (RoTTA[51], NOTE[6], SAR[30], EATA[29]):**  \nPrevious methods assume frequent adaptation (≥50% of test samples used for update) and focus on selecting time-wise fair and low-entropy samples (e.g., RoTTA, NOTE, SAR, EATA). In contrast, our target is *Sparse TTA* (e.g., 10% adaptation rate), where such filtering leaves too few useful samples for effective adaptation. Hence, SNAP's CnDRM (1) does **not** rely on low-entropy filtering, and (2) selects *representative* samples based on domain centroids and class confidence, enabling efficient adaptation with minimal latency. We provided theoretical analysis (*Appendix C.1*) and ablation results (*Table 2, Appendix D.4*) that showed our entropy-based filtering performs worse than even random selection under sparse settings.\n\n**IoBMN vs. Instance-wise BN Correction (NOTE):**  \nNOTE corrects BN statistics per instance, incurring high latency proportional to sample count. In contrast, our IoBMN uses the memory (CnDRM)-derived domain-class statistics to correct batch BN stats efficiently, maintaining compatibility with batch inference. Additionally, we shift the memory stats toward batch stats to mitigate skew from sparse updates. This design not only improves computational efficiency but also leverages adaptation-involved samples for normalization, generating performance gains (*Table 2, Appendix D.4*).\n\nWe will emphasize these distinctions in the manuscript to better position the novelty of each module.\n\n---\n**W4.** Thank you for the pointers to the related work. In our manuscript (*Intro* and *Appendix C.8*), we included a discussion and empirical comparison against recent and representative **training-free TTA** methods T3A [14] and FOA [28]. These studies and your suggested papers are standalone TTA algorithms that generally augment a memory bank for a KNN classifier [r2], adapt model outputs directly through regularization [r3], improve batch normalization statistics to handle reduced class diversity [r4], and use instance-guided statistics and prototypes for semantic segmentation [r5].\n\nIn contrast, **SNAP is a modular extension that addresses the challenge of making computationally intensive, backpropagation-based TTAs fast and efficient for edge deployment.** These model-adaptation methods are widely used due to their ability to perform deeper, feature-level updates, which offer improved robustness under complex and evolving distribution shifts. However, their practicality is often limited by latency and resource constraints. SNAP makes such methods viable in real-world scenarios by enabling them to operate sparsely, thus preserving their adaptation benefits while significantly reducing computational cost.\n\n---\n**W5.** We address the two claims as follows.\n\n**Feature distribution correction:** In sparse update settings, memory-based statistics are computed from a small and outdated subset of data, leading to skewed normalization. To mitigate this, IoBMN shifts the memory statistics toward each incoming batch direction, correcting skew adaptively. As the adaptation rate decreases (i.e., updates become sparser), this correction becomes more effective—demonstrated by consistent performance gains when IoBMN is added (*Table 2, Appendix D.4*). Compared to prior BN correction-only methods, including EMA [27,39,24,46,30,48,51], IoBMN outperforms them under sparse TTA by leveraging representative memory statistics with minimal overhead.\n\n**Diverse and reliable sample selection:** Diversity is achieved by maintaining prediction-balanced sampling (as validated in prior works[51,6]). Reliability is ensured by selecting high-confidence samples, whose pseudo-label accuracy is empirically verified to be significantly better than random (Appendix C.3). The ablation in the Evaluation section (\"Contribution of SNAP individual components\") further supports this: CRM outperforms Rand, and CnDRM+IoBMN outperforms CnDRM alone.\n\nTo further back up, we will incorporate additional validations, such as the analysis of the proportion and magnitude of IoBMN correction, as well as the distribution of memory samples, in our final manuscript.\n\n---\n\n*Reference*\n\n[r1] Logacjov A, Bach K, et al. \"Harth: A human activity recognition dataset for machine learning\", Sensors, 21(23), 2021\n\n[r2] Zhang, Yifan, et al. \"AdaNPC: Exploring Non-Parametric Classifier for Test-Time Adaptation\", ICML 23\n\n[r3] Boudiaf, Malik, et al. \"Parameter-free Online Test-time Adaptation\", CVPR 22\n\n[r4] Su, Zixian, et al. \"Unraveling Batch Normalization for Realistic Test-Time Adaptation\", AAAI 24\n\n[r5] Wang, Wei, et al. \"Dynamically Instance-Guided Adaptation: A Backward-free Approach for Test-Time Domain Adaptive Semantic Segmentation\", CVPR 23"}, {"review_id": "GciGNGpA4D", "reviewer": "Reviewer_wZnu", "summary": "This 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.", "questions": "Please refer to the weaknesses.", "limitations": "Yes. The authors have addressed the limitations in Section 5.", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\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.", "was_revised": true, "final_justification": "The authors have addressed my previous concerns. Hence, I raise my score accordingly.", "rebuttal": "**Weakness1 (W1).** Thank you for pointing this out. We acknowledge that the explanation of domain-representative sampling was unclear, and we appreciate the opportunity to clarify.\n\nA *domain-representative sample* is a sample whose early-layer feature distribution lies close to the domain centroid—computed as a moving average of incoming sample features. Wasserstein distance measures the proximity between a sample’s distribution and the domain centroid. We maintain a fixed-size memory by continuously replacing the furthest (i.e., high-distance) samples with new ones that are closer to the centroid. This ensures that the memory retains only the most representative samples under dynamic distribution shifts (as described in lines 163–166, 191–196, and 201–202).\n\nIn our final manuscript, we will explicitly define domain-representative samples and clearly describe the replacement mechanism based on Wasserstein distance ranking. \n\n---\n**W2.** While \"Remove domain-centroid farthest sample\" and \"Update domain-centroid\" were described in lines 201–202 and 184–186, respectively, we acknowledge that the connection between *Algorithm 1* and the operations “Remove domain-centroid farthest sample” and “Update domain-centroid” was not sufficiently clear in the original manuscript, and we appreciate the reviewer’s attention to this point.\n\nTo clarify:\n- **Farthest sample removal**: As described in lines 201–202, the “farthest sample” refers to the memory sample with the largest Wasserstein distance to the domain centroid, as defined in Equation 1 and discussed in lines 191–196. This sample is considered the least representative and is removed when the memory pool exceeds its capacity.\n- **Domain centroid update**: As noted in lines 184–186, the domain centroid is updated after every batch using a momentum-based moving average over early-layer features. The momentum coefficient is fixed at 0.9 throughout all experiments, allowing the centroid to adapt to the evolving feature distribution.\n\nWe will revise the manuscript to explicitly link these procedures to *Algorithm 1* and clarify their implementation details to enhance reproducibility and reader understanding.\n\n---\n**W3.** We apologize for the confusion. \n\nTo clarify:  \n- **Adaptation Rate** refers to the frequency of model updates in Sparse TTA, as described in lines 116–118, and noted in the caption of *Figure 1*. It is the ratio of batches that trigger an update over the total number of test batches.  \n\n- **Sampling Ratio** denotes the proportion of samples (across complete data) that are used for model updates. This term follows the convention used in data-efficient learning literature[2,49].\n\nIn cases where the memory size equals the batch size and updates occur batch-wise, these values coincide. However, they are conceptually distinct and can diverge depending on the implementation. We will clarify this in the final manuscript.\n\n---\n**W4.** Thank you for pointing this out. The results presented in *Table 1* were obtained using **ResNet-50** for the ImageNet experiments. We will revise the main text and the table caption to explicitly state this in our final manuscript."}, {"review_id": "tnFyVb2KB3", "reviewer": "Reviewer_aqRo", "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.", "questions": "Please refer to the above.", "limitations": "yes", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "1. Strengths\n\n- 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.\n- 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.\n- 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.\n\n2. Weakness\n- This work adopts a fixed adaptation rate/CnDRM safeguard. Can the authors provide dynamic tuning (i.e., learning this rate) and efficiency metrics?", "was_revised": true, "final_justification": "Thanks for the author's rebuttal. Since other reviewers also considered raising their score, I will also keep my positive score here.", "rebuttal": "**Weakness 1.** Thank you for your insightful comment. The fixed adaptation rate is currently used as a baseline, and dynamic tuning of the adaptation rate would improve flexibility and responsiveness, which is future work.\n\nOne direction is to use the **Z-score**, which measures how much a feature's value deviates from its mean, normalized by its standard deviation. By tracking Z-scores between consecutive batches, we can adjust the adaptation rate: if the shift in Z-score exceeds a threshold, we increase the adaptation rate for more frequent updates. Otherwise, the adaptation rate could be reduced to save computational resources. This would help the model respond quickly when there is a significant domain shift while conserving resources during stable periods.\n\nAdditionally, we could incorporate **dynamic accuracy estimation**. If accuracy on a validation set starts to drop, the system could trigger an increase in the adaptation rate to improve performance. This could be done similarly to the method used in **AETTA** [r1].\n\nWe will explore these ideas further to balance adaptation rate, efficiency, and performance in future work.\n\n---\n*Reference*\n\n[r1] T. Lee, S. Chottananurak, T. Gong and S.-J. Lee, \"AETTA: Label-Free Accuracy Estimation for Test-Time Adaptation\", CVPR 2024."}, {"review_id": "0H3wXuqiJ7", "reviewer": "Reviewer_Vzgx", "summary": "This 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.", "questions": "- 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?", "limitations": "Yes.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "# 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.", "was_revised": true, "final_justification": "The author did a good job in the rebuttal providing additional clarification and details. My concerns are fully solved.", "rebuttal": "**Weakness 1 (W1).** Thank you for your questions. \n\n(1) **Does IoBMN require two forward passes for adaptation?**  \n\nNo, IoBMN does **not** require an additional forward pass. The prediction and confidence scores used in CnDRM sampling are obtained during the *same* forward pass used for inference. The normalization statistics used by IoBMN are computed from the memory (CnDRM) that stores samples involved in sparse model updates. These statistics are reused without extra passes.\n\n(2) **Why not use standard BN with a moving average over all feature maps?**  \n\nRather than relying on all feature maps at inference, IoBMN uses the memory-derived statistics—representative of previously adapted domain-class conditions—as a stable reference. During inference, these memory statistics are shifted toward the current batch statistics using a shrink function. This *memory → batch* directional correction helps compensate for outdated memory statistics from infrequent updates, and improves normalization stability under sparse adaptation. *Table 2* and *Appendix D.4* show that IoBMN outperforms standard BN and batch-stat-only approaches across various adaptation rates and datasets.\n\n---\n**W2.** The closed-form expression in Equation 1 indeed assumes a Gaussian distribution with diagonal covariance. Here we clarify both the assumptions and the derivation.\n\n(1) **Distribution definition**: The distribution in Equation 1 refers to the empirical distribution of scalar **feature activations per channel**, not the input data distribution. We consider each channel's activation statistics (mean and variance) in a deep layer’s feature map.\n\n(2) **Wasserstein approximation and assumptions**:  \nTo compute the Wasserstein distance efficiently, we approximate the feature distributions as **univariate Gaussian distributions** for each channel. The assumption is that the feature distributions can be well-approximated by Gaussians, and we assume these distributions are independent (i.e., **diagonal covariance**). The detailed assumptions are as follows:\n\n(2-1) **Gaussian assumption**:  \nWe assume that the feature activations across each channel follow a Gaussian distribution $\\mathcal{N}(\\mu, \\sigma^2)$, simplifying the problem as Gaussian distributions are fully defined by their mean $\\mu$ and variance $\\sigma^2$. This assumption holds in many deep learning applications, particularly where feature activations are approximately Gaussian, especially in high-dimensional feature spaces.\n\n(2-2) **Diagonal covariance**:  \n   We assume the covariance matrix for each Gaussian is diagonal, meaning features across different channels are independent. This is a common assumption in domain adaptation and transport-based methods, as it reduces the complexity of computing full covariance matrices and instead focuses on the variance of each channel (i.e., no correlation between channels).\n\n(2-3) **2-Wasserstein distance for Gaussian distributions**:  \n   Given these assumptions (independent Gaussian distributions), the squared 2-Wasserstein distance between two univariate Gaussian distributions $\\mathcal{N}(\\mu_1, \\sigma_1^2)$ and $\\mathcal{N}(\\mu_2, \\sigma_2^2)$ is given by:\n\n   $$\n   W_2^2 = (\\mu_1 - \\mu_2)^2 + (\\sigma_1 - \\sigma_2)^2\n   $$\n\nThis simplification enables efficient computation of the Wasserstein distance without requiring a full covariance matrix, which is computationally expensive.\n\nThis approximation is widely used in domain adaptation literature [r1, r2] as it balances **computational efficiency** and **empirical performance**. The simplification allows us to avoid the complexities of full covariance matrices while providing meaningful distance measurements for aligning feature distributions.\n\nIn the final manuscript, we will explicitly state these assumptions, the detailed derivations, and the rationale behind using this approximation.\n\n---\n**W3.** Thank you for pointing this out. The subscript m is not an index, but indicates that these statistics are derived from the memory. We will revise the text to avoid any confusion. \n\n- In Equation 2, as we compute per-channel statistics, the averaging is correctly done over the batch $B$ and spatial dimensions $L$, not over channels. \n\n- In Equation 3, there was a typo. As correctly noted around line 218, the denominator should be L×M, not C×M. We apologize for the mistake. The division by L×M is necessary as the sample mean and variance are computed over L spatial locations for each M memory samples. Assuming i.i.d. features across spatial dimensions, the total number of independent observations per channel is L×M. Therefore, when estimating the variance of the sample mean and variance, the correct normalization factor is LxM, following standard results in sampling theory. We will revise the notations and equations accordingly in our final manuscript.\n\n---\n**Question.** One might think there is a contradiction between our domain-centric sampling strategy (criterion 2 in CnDRM) and the approach used in EATA [29], which discards test samples whose predictions are close to the prediction mean. However, these **two strategies differ fundamentally in context, granularity, and update regime**:\n\nIn EATA, the sampling occurs at the *prediction* level (final logits), and the update is applied at **every batch**. This setting favors more challenging samples by dropping the samples whose prediction is too close to the testing sample mean. \n\nIn contrast, our method targets the **Sparse TTA (STTA)** scenario, where only ~10% of test samples are selected for model updates. In such a setting, choosing **reliable and representative** samples near the **feature-level domain centroid** (early-layer statistics) leads to better stability and performance, as shown empirically in *Figure 4* and theoretically supported in *Appendix C.1.*\n\nWhile both methods use centroid-based criteria, they operate at different representation levels and serve different adaptation strategies: EATA prioritizes informativeness under high-frequency updates, whereas CnDRM prioritizes reliability under sparse updates. The strategies are therefore complementary, not contradictory.\n\nRegarding the integration of EATA and SNAP (as in our EATA+SNAP evaluation), we first apply SNAP’s sample selection criteria (CnDRM) to identify a reliable subset, and then apply EATA’s strategy to that subset. This design ensures compatibility between the two methods.\n\nWe will clarify this distinction and sampling logic more explicitly in our final manuscript.\n\n---\n*Reference*\n\n[r1] Y. Li, N. Wang, J. Shi, J. Liu, and X. Hou, “Revisiting Batch Normalization for Practical Domain Adaptation.” ICLR 2017.\n\n[r2] E. F. Montesuma, F. M. N. Mboula, and A. Souloumiac, “Optimal Transport for Domain Adaptation through Gaussian Mixture Models.” TMLR 2025."}]

Author rebuttal:

Meta-review: The paper presents a test-time adaptation method which is demonstrated to work on edge devices. The paper received 2 accept and 2 borderline accept votes. The reviewers appreciate the work for addressing an important and practical problem (from real-world deployment perspective) and for the comprehensive experiments. The reviewers raised some concerns in their original reviews and the rebuttal provides responses to most of them, which the reviewers largely seem to be satisfied with. From my own reading of the paper and considering the reviews, rebuttal, and discussion, I agree with the general consensus of the reviewers. I recommend the paper for acceptance. The authors are also advised to incorporate the changes they promised to make in the rebuttal.
Decision: Accept (poster)