Feature-Based Instance Neighbor Discovery: Advanced Stable Test-Time Adaptation in Dynamic World
Authors: Qinting Jiang
Chuyang Ye
Dongyan Wei
Bingli Wang
Yuan Xue
Jingyan Jiang
Zhi Wang
Venue: NeurIPS 2025 poster ()
Keywords: Test time adaptation
domain adaptation
continual learning
Primary area: deep_learning
TL;DR: Design the test time adaption algorithm for dynamic data streams

Abstract: Despite progress, deep neural networks still suffer performance declines under distribution shifts between training and test domains, leading to a substantial decrease in Quality of Experience (QoE) for applications. Existing test-time adaptation (TTA) methods are challenged by dynamic, multiple test distributions within batches.  We observe that feature distributions across different domains inherently cluster into distinct groups with varying means and variances. This divergence reveals a critical limitation of previous global normalization strategies in TTA, which inevitably distort the original data characteristics. Based on this insight, we propose Feature-based Instance Neighbor Discovery (FIND), which comprises three key components: Layer-Wise Feature Disentanglement (LFD), Feature-Aware Batch Normalization (FABN) and Selective FABN (S-FABN). LFD stably captures features with similar distributions at each layer by constructing graph structures; while FABN optimally combines source statistics with test-time distribution-specific statistics for robust feature representation. Finally, S-FABN  determines which layers require feature partitioning and which can remain unified, thus enhancing the efficiency of inference. Extensive experiments demonstrate that FIND significantly outperforms existing methods, achieving up to approximately 30\% accuracy improvement in dynamic scenarios while maintaining computational efficiency. The source code is available at https://github.com/Peanut-255/FIND.

Feature-Based Instance Neighbor Discovery: Advanced Stable Test-Time Adaptation in Dynamic World
Qinting Jiang
Chuyang Ye Courant Institute of Mathematical Sciences New York University chuyang ye@nyu.eeeuem edu
Shenzhen International Graduate School Tsinghua University
jqt:23mmails tsinghua, edu, en
Dongyan Wei CSDAI Department Institut Polytechnique Paris dongyan. wei@ip-paris....
Bingli Wang College of Information Engineering Sichuan Agricultural University sangbingli@stu sicau. edu. cn
Yuan Xue
Shenzhen International Graduate School Tsinghua University pxzu20220gmaill com
Jingyan Jiang"
Zhi Wang" Shenzhen International Graduate School Tsinghua University wangzhi ēsz. tsinghua edu, cn
School of Artificial Intelligence Shenzhen Technology University jiangj ingyansztu.nn.z....mmmm. edu.
Abstract
Despite progress, deep neural networks still suffer performance declines under distribution shifts between training and test domains, leading to a substantial decrease in Quality of Experience (QoE) for applications. Existing test- time adaptation (TTA) methods are challenged by dynamic, multiple test distributions within batches. We observe that feature distributions across different domains inherently cluster into distinct groups with varying means and variances. This divergence reveals critical limitation of previous global normalization strategies in TTA, which inevitably distort the original data characteristics. Based on this insight, propose Feature-based Instance Neighbor Discovery (FIND), which comprises three key components: Layer-Wo Layer-Wise Feature Disentanglement (LFD), Feature-Aware Batch Normalization (FABN) and Selective FABN (S-FABN), LFD stably captures features with similar distributions at each layer by constructing graph structures; while FABN optimally combines source statistics with test-time distribution-specific statistics for robust feature representation. Finally, S-FABN determines which layers require feature partitioning and which can remain unified, thus enhancing the efficiency of inference. Extensive experiments demonstrate that FIND significantly outperforms existing methods, achieving up to approximately 30% accuracy improvement in dynamic scenarios while maintaining computational efficiency. The source code is available at htttts:://gtthhhh FIND
waam//Pantt-.. -555
*Correponniigg author: wangzhi @ www.sssggu...uuu..o.oom jiangingyann@zzuu.co
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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1
Introduction
The remarkable advancements in deep neural networks have not fully resolved the challenge of domain shift. When deployed in real-world scenarios, neural networks often encounter significant performance degradation as testing environments deviate from training conditions I 2 3 To mitigate these challenges, researchers have developed test-time adaptation (TTA) approaches, which enable models to dynamically adjust to new domains during inference without accessing the original training data or target domain labels [4]
Existing TTA approaches can be divided into two main categories: lest-time fine-tuning
6.
8.9 [0] and test-time normalization [T B 14. The former methods adapt model parameters during inference
4 3 5 [3]. While effective, these approaches demand considerable computational
resources. The latter methods, altermatively, focus adapting batch normalization (BN) statistics to address distribution shifts. These approaches correct the statistics of source batch normalization (SBN) by leveraging either test-time batch normalization (TBN) or its variants during inference B [6]
The effectiveness of previous TTA methods primarily relies on the assumptions of ideal test condi- tions-test examples are homogeneous and originate from single distribution over period, which we refer to as the static scenario [4] 17 3 5 However, real-world data streams often exhibit more complex trends: distribution shifts no longer gradually evolve over time; instead, multiple distinct distributions may emerge simultancously, which we refer to as the dynamic scenario. For instance, due to variations in network conditions and device capabilities, clients may upload images of different compression rates. This results in the model receiving samples with varying levels of quality degradation that are drawn from multiple distinet distributions. Our investigation (Figure 2a reveals that existing methods exhibit significant performance degradation in dynamic scenarios (an average accuracy drop of 15%). Surprisingly, the test-time fine-tuning approach not only fails improve performance compared to test-time normalization but even decreases accuracy by approximately 0.4%. This finding highlights essential revelation: in dynamic scenarios, mitigating performance degradation depends primarily on carefully adjusting normalization methods. We observe that feature distributions in dynamic scenarios naturally form distinct clusters with varying means and variances (Figure 3a). However, current TBN- based normalization approaches employ a global normalization strategy across all features, inducing interference between different distributions (Figure
This brings us to a crucial insight: in dynamic scenarios, effectively addressing performance degradation hinges on a "divide and conquer" " normalization approach, which naturally raises two two fundamenttal questions-how to divide and how to conquer? To address these challenges, we start by performing preliminary experiments and motivation analyses to explore potential so- lutions (Section 3). We find that: 1) Adopting layer-wise feature partitioning instead of direct classification on raw input samples leads to supe- rior efficacy. 2) Integrating generic knowledge from the source domain enhances normalization stability and compensates for missing general- izable patterns (e.g., class correlations) across partitioned groups.
CiBerriccaannie unaall cicka rubidaaai bunin
The Camaess
X
Source
fg Xg
Opnentcc Soieets
Test
X Noisy
fo X
Collupse
66%
based methods
LFD
FABN
Moh0 Somna's Average Accuracy
italined
Ey X.
Collapen
72.7%
(b) Faature-Based Inatance Naighbor Discovary (ours)
Figure 1: (a) In previous TBN-based methods, batch-level statistical values are computed holisti- cally across all features, leading to erroneous nor- malization of cross- cross-distribution features. (b) Our FIND framework introduces layer-wise divide- and-conquer strategy for intra-batch feature pro- cessing, synergistically integrating source domain knowledge to achieve reliable normalization.
Based on the above insights, we propose FIND (Feature- Instance Neighbor Discovery), fine-grained test-time normalization framework tailored for dynamic scenarios, comprising three key components: layer-wise feature disentangle- ment (LFD), feature-aware batch normalization (FABN) and selective FABN (S-FABN), as il- lustrated in Figure Dp. The core innovation of FIND lies its layer-adaptive feature separation for multi-distribution samples and layer-specific distribution alignment, which precisely models the un- derlying statistical characteristics of each layer. For LFD, we establish graph-based feature modeling through the exploitation of inter-feature correlations, which enables systematic reorganization of

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features across heterogeneous distributions. For FABN, we integrate the group-specifie knowledge from each partitioned cluster with the generic knowledge derived from the statisties of the source domain to achieve robust normalization. Finally, we employ S-FABN to determine which layers require feature partitioning and which can remain unified, thereby enhancing inference efficiency. Our contributions can be summarized as follows:
We introduce the pioncering test-time normalization framework specifically designed for re- alistic dynamic scenarios, addressing the limitations of current mie-size-fits-al normalization approaches practical applications.
Our method employs instance-level statistics to identify and cluster features with similar distributions, achieving robust dynamic adaptation through the aggregation of group-specific knowledge and generic knowledge from the source domain.
Our method demonstrates versatility across architectures equipped with batch normalization layers, including both transformer-base models (ViT) and classical convolutional networks (e.g., ResNet). Remarkably, we are the first BN-based method tested VIT structures with outstanding performance in TTA.
Comparative analysis benchmark datasets validates method's effectiveness, showing a 30% accuracy gain over current state-of-the-art solutions in dynamic scenarios.
2 Preliminary
Test-time adaptation addresses the challenge of model adaptation when deploying pre-trained model in novel environments. Consider a deep neural network fo x - that has been trained on source domain data Ds. During deployment, this model encounters target domain containing N unlabeled test samples, denoted as Dr, { E Dr. While Dy and Dr may exhibit different distributions, they share the same output space for prediction tasks.
The fundamental objective of TTA is enable real-time model adaptation using streaming test samples. This online adaptation process operates sequentially: at any time step f, the model processes a batch of instances X, simultaneously performs adaptation and generates predictions Y. A key characteristic of this setup is its streaming nature: when processing the subsequent batch X at step t + 1, the model must adapt and make predictions without retaining or accessing historical data X1-1- This constraint reflects real-world deployment scenarios where memory and computational resources are limited, and past data cannot be stored indefnntell.
In the TTA framework, target domain distribu- tions evolve across time steps, with samples at each moment adhering independent and iden- tically distributed (i.i.d.) properties: X, E Dr and D, * D.-1. However, following ear- lier discussion, real-world applications com- monly present situations where the inference process must handle mixed samples from vary- ing distributions. To address this scenario, we model the target domain D, at time step t as set comprising one or multiple distributions: D. = (Dr, Dr,...... .... Dr, where M 2 1. This formulation, termed the Dynamic scenario, reflects that X, may originate from either single or multiple distributions.
Stalis
S0ape
(a) TTN VS. FT
(b) Gradient of cach step
Figure 2: (a) demonstrates the performance gains of test-time normalization (TTN) versus test-time fine-tuning (FT). (b) shows how gradient changes across fine-tuning steps under different scenarios.
3 Observations of TTA in Dynamic Scenario
Precise normalization is pivotal for effective TTA. To disentangle the contributions of test-time normalization (TTN) and test-time fine-tuning, we conduct ablation studies by sequentially applying TBN and fine-tuning (SAR 7 on the source model. As shown in Figure 2a] TBN demonstrates significantly greater contribution (5%-20% performance gains) compared to fine-tuning (-0.4%-19 % gains by building upon TBN). Notably, fine-tuning introduces negative impacts in dynamic scenarios. Our gradient convergence analysis in Figure reveals that in dynamic environments, conflicting

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gradients from multi- dintriiiistibttion samples hinder convergence and degrade model performance, whereas static environments allow stable convergence beyond 1,000 adaptation steps. These findings establish the inefficacy of fine-tuning in dynamic scenarios, emphasizing the necessity of developing precise normalization strategies for robust performance enhancement.
A divide-and-conquee strategy is essential in dynamic environments. Figure 3 reveals in- trinsic cluster patterns in BN layers when using domain as labels, where each cluster exhibits unique distribution characteristics (varying cen- ters and variances). Conventional test-time nor- malization methods that compute global statis- ties inevitably distort feature distributions, as shown in Figure B and 3p: In static scenarios, different classes exhibit well-separated feature boundaries, whereas in dynamic scenarios, im- proper normalization induces feature coupling. This phenomenon motivates our core design principle: features from divergent distributions require separate normalization pipelines.
(a) Domain (Dynamic)
(b) Class (Static)
(c) Class (Dynumie)
Figure 3: Feature distributions across domains (a) and classes (b and c) under different scenarios. The domains are gaussian noise, zoom blur, snow, and pixelate from CIFAR 100-C in (a). In (a) and (b), the feature distributions are clearly partitioned; in (c), they are entangled.
Replace processing the input samples directly by layer-wise feature partitioning. Direct parti- tioning input samples is infeasible due to missing domain labels and domain-class feature couplings. Inspired by Neyshabur al. [88] and Lee et al. (8) who demonstrated that visual features inher- ently decompose into domain-relevan features (DRF, e.g., backgrounds) and class-relevant features (CRF, e.g., object structures), and that various network layers exhibit distinct preferences for these feature types, we propose layer-wise processing for BN layers. This strategy achieves: 1) reduced cross-feature interference during partitioning, and 2) fine-grained alignment with layer-specific normalization needs.
Enhance normalization stability via generic knowledge from training data. When the "divide-and-conquer" strategy implemented. the features of the BN layer will be divided into multiple clusters. The sizes of these clus- ters are much smaller than the original batch sizes, resulting in biases in the distribution of class-relevant features. As shown in Figures 4a 4bd while TBN exhibits sensitivity to batch size and domain quantity, SBN maintains sta- ble performance across these variables. This robustness stems from SBN's integration of generic knowledge (e.g., class-relevant knowl- edge) compreensivee statistics derived from large-scale training data. These domain-shareable characteristics facilitate stable normalization by preventing the loss of generic features in clusters. A more specific analysis on the introduction of SBN in TBN is in Appendix M
Acquracy (8)
40
Accuracy (%)
20
Savic SDN
10
TBN
Syramic SBN
16
Domain
(a) DN vs. accuracy
(b) BS vs. accuracy
Figure 4: (a) and (b) display the inference accuracy with different domain numbers (DN) and batch sizes (BS). Static and Dynamic represent different scenarios.
Method: FIND
As shown in Figure 5) the proposed FIND involves three novel designs, including layer-wise feature disentanglement (LFD), feature-aware batch normalization (FABN) and selective FABN (S-FABN). Here introduce them in the following parts.
4.1 Layer-Wise Feature Disentanglement
In previous methods, the monolithic statistical computation- applied uniformly across all batch samples-inevitably skews feature representations toward erroneous distributions, particularly under dynamic multi-domain shifts, thereby compromising the overall reliability and accuracy of model inference during test-time adaptation. Our analysis reveals that divide-and-conquer strategy essential for normalizing multi-domain samples. However, directly partitioning input samples faces

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Step é
Feature-Basd Instance Noighbor Discovery (FIND)
Step
Comv
LFD
S-FABN
Loge
NEB
Canaud
FABN
Layer Eipu
Inference
Figure 5: Overview of the proposed FIND (FIND*). We design layer-wiss wise feature disentanglement (LFD) divide multi conli-dditributiinn feature maps within each layer into different subsets. Features in each subset have similar cosine distances, ensuring distribution consistency. Next, we combine the test-feature-seecifi normalization (TFN) statistics calculated for each subset with SBN statistics to improve normalization stability, Finally, layers requiring LFD partitioning can be selected through sensitivity score to enhance efficiency.
For supervised clustering algorithms, the lack of relevant domain labels and domain information poses challenges; for some unsupervised clustering algorithms, it is difficult to determine the number of clusters, while category features, domain features, and other characteristics in the samples inherently entangled. Disentangling these features may require additional training steps. Inspired by [18] and our observations that BN layers exhibit layer-speeific feature preferences (e-g., shallow layers focus edges/textures while deeper layers prioritize semantic structures), propose ayeerwiie feature disentanglement (LFD). Unlike sample-level segregation, this neighbor- search-based approach achieves fine-graine ane-ggained feature separation tailored each layer's distributional characteristics.
practical limitations:
For certain BN layer in the network, we analyze the feature map F E |BXC*XX of all samples at this layer, where B represents the batch dimension, C' denotes the number of channels, and spatial dimensions spatial dimensions the identification and re-grouping of feature maps that exhibit similar feature characteristics. This grouping process is performed based instance-level statistical representations ju' RC, which capture the essential features of each sample in the batch. The computation of these instance-level means je and the methodology for assessing feature similarity between samples can be formulated as follows:
represented by L (L HW). Central our approach is
11e 1
Σ ProeLe
Sim(i,j) =
(2)
||ttell |//ell
where Fic:L and FjEe2L represent feature maps of sample and sample j. Utilizing the Sim metric to measure the similarities between instance-level statistical representations across samples, LFD partitions the feature maps F of all samples into distinct subsets at this BN layer.
Drawing inspiration from FINCH [19]. LFD approach partitions F based on first-neighbor relationships of instance-level statistics. For each BN layer, we compute similarity metric Sim between different yt' pairs, where Sim quantifies the feature affinity between instances at the current layer. Each ye identifies its first neighbor by selecting the instance with the highest similarity score. Following this neigh-oe initialization, LFD constructs an adjacency matrix as follows:
(i, = 1, if of = or at =i or at = a
O, otherwise
where each sample's feature map at the layer constitutes the node of the adjacency matrix. a! represents the first neighbor of the th node. After obtaining the adjacency matrix First, LFD proceeds with feature map F partitioning. By traversing the adjacency matrix First, nodes i and are assigned to the same connected component when First(i, 1. This operation reconstructs F into graph structure with multiple connected components, thereby grouping features exhibiting high similarity measures. The detailed algorithm is provided Appendix A The analysis of clusters of each layer by LFD is provided in Appendix
5

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4.2 Feature-Aware Batch Normalization
After partitioning, the original feature map in the BN layer is divided into subsets, ie.. (F',², F ..... }r ...
where F* E R L. and represents the number of instance-wise feature maps included in that set. Similar computing batch-wise statistical values, we calculate the (TFN) statistical values udp and o for each subset:
1 pp bL
Σ b.b
F be o'p
Σ bL
Fioe - 14/)
Based on the preceding analysis, TFN computations enable the capture of fomain--specife feature distributions within each BN layer. However, since TFN operates smaller subsets compared to the original batch size, the missing or incomplete representation of generic features (e.g.. insufficient class diversity in subsets) in these subsets may introduce statistical bias to TFN estimations. Therefore, we introduce SBN (generic knowledge) to supplement TFN. We thus propose Feature-Aware Batch Normalization (FABN), which utilizes SBN to correct the TFN statistics:
MAARN = ats + (1 - a)pp
(5)
TAABN2 2 = ao; + (1-a)opp-
(6)
a determines the relative contributions of each component. This hybrid approach leverages pre- trained model knowledge through SBN while utilizing TFN to mitigate domain-specifie feature perturbations. The final FABN output can be expressed as:
(Fi: - (FABN)
FABN' (HEABN. FABN) = pp. VOTABN +
+ B, 1 1sisr,
where y and 3 represent the affine parameters of the BN layer, and is small bias prevent division by zero.
4.3 Selective Feature-Aware Batch Normalization (S-FABN)
As noted carlier, different layers exhibit varying preferences for features, meaning layers with minimal focus on domain characteristics remain insensitive to domain shifts. Consequently. feature map partitioning becomes unnecessary for these layers since their feature distributions across domains show minimal divergence and align closely with the source domain. To quantify the distribution gap, calculate the KL divergence between source domain Ds and current target domain Dy for each BN layer:
KC(DD Ds) = of (1T ms)
0S
+ +ln
(8)
20²
2
where KLC MT= BL EB. FBee, and or = V BL EB,L (F HT)² 2 We calculate the mean KL divergence K.Cmean across all channels in the current BN layer based on K.C. However, averaging across all channels risks diluting critical signals from highly sensitive ones. We address this by:
1
Score (1 I JKCmmans
where K.L.st is the standard deviation of KI. divergence in the current BN layer. The introduction of K.Cat as a weighting factor mitigates potential oversight of highly sensitive channels.
In this process, introduce additional data but conduct cold-start phase. Specifically, leverage the initial batches fed into the model to compute the average Score for each layer. followed by Score normalization. Throughout this phase, the divide-and-conquee strategy remains applied to all layers. Upon obtaining the scores, partitioning is deactivated for layers exhibiting lower sensitivity. We set threshold 7. If Score y, we retain the FABN. Otherwise, deactivate the partitioning and replace the TFN component in FABN with (HT, dT).
We denote the selectively partitioned FIND as FIND* We conduct sensitivity analysis on y in the experiments. The details of the cold-start process and the sensitivity analysis of y are given in Appendix G and Appendix

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Experiments
5.1 Experimental Setup
We evaluate our proposed FIND using the Test-Time Adaptation Benchmark (TTAB) (0). All reported results represent averages across three independent runs with different random seeds. Full implementation details and experimental configurations are provided in the Appendix.
Environment and Hyperparameter Configuration. Our experiments were conducted using an NVIDIA RTX 4090 GPU and a V100 GPU with PyTorch 1.10.1 and Python 3.9.7. For our FABN module in FIND, we set the aggregation parameter a to 0.8, We set the threshold y to 0.1 for FIND* A detailed analysis of a, y and the cold-start phase of FIND is available in the Appendix. The details of hyperparameter settings are provided in Appendix F
Baselines. We consider the following baselines: (1) Test-time fine-tune. SAR 7.. EATA 21 DeYO
8. TENT 4. NOTE [3, ROTTA and ViDA ( (2) Test-time normalization. TBN Q-BN 23 and IABN B We evaluate all methods under the online test-time adaptation (TTA) protocol,
where source training data is inaccessible. Detailed experimental configurations are provided in Appendix
Following standard protocols 20 3
we conduct experiments with test batch size of 64 and one adaptation epoch. Method-specifs hyperparameters are adopted from their respective published
configurations (20].
Datasets. We evaluate on three corrupted datasets from the TTA benchmark 20 CIFARIO-C (10-C), CIFAR100-C (100-C), and ImageNet-C (IN-C) (24] Similar to previous studies (20). all experiments use severity level 5 corruptions and ResNet-50 25 models pre-trained on their respective clean datasets. To demonstrate the transferability of our approach, we extend
evaluation to
transformer-bant -based architectures, specifically using Efficient [26) as an additional backbone. We are the first BN-based method tested on VIT. Details of datasets provided in Appendix B
Scenarios. In contrast to existing approaches that assume static data patterns, we shift our attention to TTA in dynamic data patterns. In experiments, we employed three scenarios based on dynamic data patterns: CrossMix. Each batch contains samples from multiple domains (15 domains). Shuffle. Batches alternate between containing samples from single domain and multiple domains. Random. The number of domains represented in each batch entirely stochastic.
All three scenarios involve abrupt distribution shifts between consecutive time steps. Detailed scenario specifications are provided in Appendix
5.2 Performance Comparison under Dynamic Scenarios
Table presents the comparative results of all test-time adaptation methods under dynamic scenarios. Our method consistently outperforms existing approaches in all scenarios. Most importantly, in the CrossMix scenario, we achieve accuracy gains of 17% and 7% over RoTTA (worst baseline) and DeYO (best baseline), respectively. This superior performance demonstrates our method's effectiveness handling multi-diistrbbution batch data, attributed to FABN's ability effectively partition features into distribution-specine subsets while maintaining their statistical integrity. The performance advantages persist in both Random and Shuffle scenarios, where we surpass the strongest baseline (a-BN) by 3% in three datasets. These results validate our method's ss robustness across various distribution shift patterns, regardless of whether the test batches contain single, multiple, or transitioning distributions. Notably, there is almost performance gap between FIND* and FIND, which better reflects each layer's individual sensitivity to distribution shifts. For insensitive layers, avoiding feature partitioning can reduce additional time consumption. The results under different domain scales of batch are provided in Appendix K Appendix and + respectively.
The results in other scenarios are provided in
5.3 Performance Comparison under Transformer Backbone
We use EfficientViT 26 as additional backbone. EfficientViT is an architecturally optimized vision transformer that replaces the conventional layer normalization with batch normalization layers to achieve computational efficiency. We are the first BN-based method tested on ViT. Table 2
7

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presents the comparative results. Our method consistently outperforms existing approaches across all scenarios. Most notably, in the CrossMix scenario, we achieve accuracy gains of 10% and 5% over NOTE (worst baseline) and Source (best baseline), respectively. The performance advantages persist in both Random and Shuffle scenarios, where we surpass all the baselines. It demonstrates our method has versatility across architectures equipped with batch normalization layers, including both transformer-base models (VIT) and classical convolutional networks (e.g., ResNet).
Table 1: Comparison with state-of oftt--of-the-art methods on CIFARIO-C, CIFARIOO-C, and ImageNet-C datasets (corruption severity 5, batch size 64). Results show accuracy ( (%) across CrossMix, Random, and Shuffle scenarios using ResNet-50. Best and second-best results are shown in bold and underlined, respectively.
CrossMix
Random
Shuffle
Method
Venue
10-C
100-C
IN-C
Avg.
10-C
100-C
IN-C
Avg.
10-C
100-C
IN-C
Avg. Avg-AAl
Source
CVPR16
$7.39
28.59
25.64
37.21
$7.38
28.58
25.93
37,30
57.38
28.58
25.80
37.25
37.25
TEST- TIME FINE-TUN:
TENT
CVPR21
62.77
31.57
18:45
40,96
23.15
45.20
40.73
45.36
EATA
ICML22
61.97
32.74
19.68
38.13
68.25
42.15
24.26
44.89
67.83
41.37
24.50
44.57
42.55
NOTE
NIP822
63.03
32.96
17:44
37.81
62.81
33.19
21.64
39.21
65 34
35.12
22.98
41.15
39
SAR
ICLR23
61.70
31.45
37.27
40.92
45.19
39.58
23.50
RoTTA
CVPR23
43.70
24.05
21.85
29.87
48.
23,80
20.39
30.96
54.79
29.29
22.71
35. 60
MID
ICLR24
61.97
32.14
18.52
37.54
67.96
39.48
23.33
43.59
67.96
39.48
23.06
43.50
41.54
DeYO
ICLR24
68.85
30.43
19:13
39.47
75.63
36.67
24.32
45.54
75.62
35.45
25.21
45.43
43.44
TEST-TIME
NORMALIZATION
TBN
ICML20
61,96
32.12
18.72
37.60
67.75
39,16
22,99
43.30
67.63
39.22
23.35
43.40
41.43
o-BN
arXiv20
62.41
33.22
21.92
39.18
69.88
41.59
27.57
46.35
69.87
41.60
27.78
46.42
43.98
JABN
NIPS22
62.63
24.54
9.73
32. 90
64.59
26.40
10.75
33.91
64.59
26.40
10.79
33.93
33.38
FIND
Proposed
71.54:0.2
39.7540.2
29.21=0.0
46.83
73
23.09=0.2
42. 42.56+0.2
30.1240.2
48.59
72.74a0.1
42.87=0.3
30
30.00+0.22
48.54
47.87
FIND*
Proposed 70.75 75405 40.48+0.1
30.3ee0.1
47.19
23 68.600
43.05+0.0
30.62+0.0
49.12
73.6040.0
43.88ef.2 30.24+0.4 49.23
48_50
Table 2: Comparison with state-of-tth-art methods on CIFARIO-C, CIFAR100-C, and ImageNet-C datasets (corruption severity 5, batch size 64). Results show accuracy (%) across CrossMix, Random, and Shuffle scenarios using Efficient bold and underlined, respectively.
Best and second-best results are shown in
CrossMix
Random
Shuffle
Mothod
Venue
10-C
100-C
IN-C
Avg.
10-C
100-C
IN-C
Avg.
10-C
100-C
IN-C
Avg.
Avg-All
Source
CVPR16
74.57
42.87
26.05
47.83
74.62
43.14
27.39
48.38
74.62
43.06
27.36
48.35
48.19
TEST-TIM
FINE-TUNE UE
TENT
CVPR21
74.22
42.54
20.37
45.71
77.98
44,70
23.58
48.75
77.97
44.86
23.67
48.83
47.76
EATA
ICML22
74.50
41.79
20:75
77.93
45.28
45.47
24.11
48.83
47.92
NOTE
NIPS22
68.45
36.42
20.10
41.66
67.05
35.19
18.95
40.10
65.56
34.24
18.50
39.43
40.550
SAR
ICLR23
75.17
41.39
20.
45.58 58
78.29
44,50
23.62
48.80
77.80
45.76
23.43
49.00)
47.79
RaTTX
CVPR23
75.84
43.35
20.10
42.58
20.99
46.03
23.63
47.93
VIDA
ICLR34
75.05
41.37
12.45
42.96
78.13
44.73
14.30
45.72
78:20
44.67
15.51
46.13
44.94
DeYO
ICLR24
75,10
42.50
20.35
45.98
78.01
44.54
24.45
49.00
78.35
44.65
20.83
47.94
47.64
TEST-TIME
NORMALIZATION
ICML20
41.26
20.06
45.42
43.84
23,10
48.22
44.75
48.42
47.35
a-BN
arXiv20
75.50
43,90
22.97
47.46
78:47
46.95
28:44
$1.29
78.94
46.92
28.55
51.47
50,07
JABN
NIP822
68.47
37.63
20:21
42. 10
67.08
34,66
19.20
40.31
66.68
35.04
18.52
40.08
40.83
HND
Proposed
78 02.60002222
28.690022
29
29.03300.0
52.17
79 5450.1
48.7550.2
30.94:000
53.08
58.58.011
48 47:0011
30.9560.2
(3.00)
52.75
FIND
Proposed
78.7240.2 49.30=904
30.5=001
$2.69
79.61=011
49.1050.3
31,17+0.2
53.29
79.60H002
48.89:012
31.24a0.3
53.24
53,07
5.4 Efficiency Analysis
To evaluate the efficiency of dif- ferent methods, we compare their
Table 3: Comparison of memory (GB) and latency (s) of different methods.
Overhead
|BBN
c-BN
TENT
IABN
DeYO
RoTTA
SAR
EATA
VIDA NOTE FIND FIND
Latency (s)
0.07
0.07
0.17
0.22
0.23
0.60
0.30
0.17
5.62
1.84
0.21
0.15
Memory (GB)
0.86
0.86
5.59
1.73
6.20
12.72
5.59
5.64
7.02
10.94
1.44
1.21
memory usage and latency on ImageNet-C using a V100 GPU and ResNet-50. Table Table shows that our proposed methods, FIND and FIND*, achieve significantly lower memory usage and latency compared to most of the baselines.
As shown in Table 3 our method demonstrates strong computational efficiency, ranking top-3 in inference speed (30x faster than ViDA) and memory usage (12x more efficient than RoTTA), confirming its practical deployability.
8

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5.5 Sensitivity analysis o
compress the score of each layer FIND* to the range [0, 1] through normalization, with score proximity to 0 indicating lower distribution shift sensitivity of the layer. As shown in Figure when y varies within 0-0.1, 1, accuracy fluctuation remains below I % while inference efficiency improves by 17%-32% demonstrating robust model performance. When exceeds 0.1, accuracy drops by 2%-6% with unstable model behavior. Therefore, setting 7 between 0-0.1 achieves inference acceleration while preserving model performance.
31
0.20
0.22
Besti 72,
0.20
Accuracy
30
20.33%
BR 179
0.16 0
0.18
Accuracy
70
6:1 3.
0.18
0.16 5
0.14
0.14 E
28
602
0.6
1/9
5.7 6.6 60
0.12
0.12
66
Accuracy
Accuracy
0.10
27
Time
0.10
Time
0.08
0.00
0.10
0.20
0.30
0.40
0.00
0.10
0.20
0.30
0.40
Y
(a) ImageNet-C & ResNet-50
(b) CIFARIO-C & ResNet-50
Figure 6: (a) and (b) demonstrate the sensitivity of model inference performance (Accuracy (%) to y variations, along with the associated changes in inference efficiency (Time (s)).
5.6 Performance Comparison Between FIND (Ours) and Other Clustering Algorithms
Table 4 displays the performance of LFD in our method
Table 4: Comparison of substituting our LFD in FIND with other clustering meth-
and other clustering algorithms on ImageNet-C. Requires
no predefined cluster count: HDBSCAN [271. DB-
ods. The model is ResNet-50
SCAN [28] RecCluster [29], and DSets-DBSCAN (30]
Method
Acc (%)
Time Mem (GB)
are density-based algorithms, while Agglomerative [3] and Birch 332 are hicrarchy-based Requires predefined
HDBSCAN
24.66
0.50
333. Our method demonstrates supe- rior performance and computational efficiency compared to alternative clustering approaches. This demonstrates that LFD can effectively aggregate distribution--rllvann features with high similarity, thereby providing a cleaner representation. In conclusion, FIND achieves fully auto- matic perception and dynamic grouping. Other clustering algorithms depend on hyperparameters can only partition the feature space globally, lacking the capability for fine- ane-grained perception in complex scenarios.
cluster: K-means
Agglomerative
25.77
0.33
1.56
Birch
26.09
2.12
ReeCluster
DSet-DBSCAN
25.13
DRSCAN
25.71
1.34
2,01
K-means
26.71
9.74
15.91
FIND (Ours)
29.21
0.21
1.44
5.7 Performance under Diffferntt Batch Size
Figure demonstrates our method's stability across varying batch sizes in the CrossMix scenario. While base-
Acourety (66)
Accurarr (96)
line methods exhibit significant per- formance degradation with smaller batches, particularly on CIFAR 100-C where accuracy stabilizes only beyond batch size 64, our approach maintains consistent performance regardless of batch size. This batch-size invariance highlights our method's 's robustness.
8
36
80
DaYO
DuYO
1
2
16
64
128
16
64
128
Baich Size
Betch Size
(a) CIFAR-10
(b) CIFAR-100
Figure 7: Batch size sensitivity analysis. Our approach demonstrates batch-size invariant performance.
5.8 Ablation Study on
We conducted two sets of ablation studies on a with 7 = 0.1 in FABN, separately for clustered and non-clustered layers (Table (). We observe that in both cases, performance is better when

---

Table 6: Ablation study of a for clustered layers (CL) and non-clustered layers (NCL) the CrossMix scenario, where a for one layer type is varied while a for the other is fixed at 0.8. The dataset is CIFARIO-C (severity level 5, batch size 64) and the model is ResNet-50.
(CL.)
(NCL)
0.2
0.4
0.6
0.8
0.2
0.4
0.6
0.8
Acc (9)
57.48
62,98
66.81
69.49
70.75
60.39
67.20
67.47
68.29
69.36
70.75
70.80
the SBN ratio is higher (>0.5). Clustered layers are sensitive to the SBN ratio (13% change in accuracy), while non-clustered layers are not (3% change in accuracy). The ablation study on a provides strong evidence supporting several conclusions in our paper: 1. The generic knowledge (SBN) dominates during inference. 2. The sensitivity of a is much lower in layers that do not require clustering compared to those that do, because TFN only provides domain-specifer distributions rather than the full generic knowledge distribution (as discussed in Section 3] Observation 4).
Table 5: Ablation study cor- rupted datasets using ResNet-50 (severity level 5, batch size 64) in the CrossMix scenario.
5.9 Ablation Study on FIND
We conducted the ablation study on the components of FIND, which consists of three key modules: LFD, FABN, and S- FABN. LFD performs hierarchical feature partitioning derive new normalization statistics, referred to as TFN. FABN com- plements TFN by incorporating SBN to supply the missing generic features. Table 5 reveals that neither SBN nor TFN alone achieves optimal results. SBN lacks relevant distribution information from the target domain, while TEN's small-batch computation limits its ability to capture generic feature distributions. Our proposed FIND leverages the complementary strengths of both approaches, thereby enhancing overall performance.
100-C
Avg.
SBN
57,39
28.59
25.61
37.11
TFN
45.78
18.90
10.65
25.11
SBN+TEN (FIND)
71,54
39.75
29.21
4633
FIND
20.75
40.48
30.33
47.19
6
Related Work
Online TTA and Continual TTA. Test-time adaptation (TTA), a form of unsupervised domain adaptation, enables model adaptation without source data. Initial work by Schneider al. (34 demonstrated the effectiveness of updating batch normalization statistics during inference. Subsequent approaches incorporated tackpropagation-baset optimization, with Wang al. focusing on batch normalization parameters through entropy minimization, while Zhang et al. full model optimization with test-time augmentation. Continual TTA addresses sequential domain shifts in real-world deployments. While TENT 4 can handle continuous adaptation, it risks error accumulation. COTTA [17] specifically targets this challenge through weighted averaging and restoration mechanisms. EATA (21] further enhances adaptation stability by incorporating entropy- based sample filtering and Fisher regularization.
35 extended this to
TTA in Dynamic Wild World. Real-world test data often exhibits complex characteristics, including data drift and mixed imbalanced distributions. SAR 7 examines model degradation under such wild data, NOTE 3 tackles non-i.i.d. distributions through IABN and balanced sampling, and Yo leverages feature decoupling for enhanced category learning.
However, TTA in dynamic environments remains largely unexplored. We present the first dedicated analysis of distribution shifts through BN statistics correction, introducing a backward- -reee adaptation framework. More details can be found in Appendix
7 Conclusion
In this paper, we propose FIND, divide-and-conquer strategy enhance TTA performance in dynamic scenarios. FIND combines LFD for feature map partitioning via instance normalization statistics, and FABN for consistent representation through SBN aggregation. Our approach demon- strates robust performance across diverse distribution shifts in dynamic data streams compared with existing methods. More discussions are Appendix U
10

---

8 Acknowledgements
This work is supported in part by the National Key Research and Development Project of China (Grant No. 2023YFF0905502), National Natural Science Foundation of China(Grant No. 92467204 and 62472249), Shenzhen Science and Technology Program (Grant No. JCYJ202208 18101014030 and KJZZD20224003330300000) and Natural Science Foundation of Top Talent of SZTU (Grant No. GDRC202413).
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Contents of Appendix
The Layer- Lise Feature Disentanglement Algorithm
22
B Details of Datasets
22
Details of Baselines
23
D Extension of Related Work
24
Details of Our Scenarios
25
Hyperparameter Settings
25
Cold-Start Mechanism and Layer Sensitivity
26
Analysis of Cluster Numbers of Each FABN Layer by LFD
26
Sensitivity analysis
27
Compatibility Evaluation with Temt-Time Tuning
28
Performance under Different Domain Scales
28
Performance under Different Model Structures
28
M Extension of Motivations
29
Performance under Static Scenario
30
Performance under Different Batch Size
30
Experimental Results and Analysis under Wild Scenario
31
Q Experimental Results and Analysis on Simulated Lifelong Adaptation
32
R License and Asset Attribution
33
S Broader Impacts
33
Limitations
33
Conclusion and Future Work
33
21

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A The Layer-Wiil Wise Feature Disentanglement Algorithm
Algorithm is the proposed layer-wise feature disentanglement (LFD) Algorithm this paper.
The identification of semantically similar samples is achieved through cosine similarity computations between feature map representations specific batch normalization layers. This similarity-bases approach enables precise detection of nearest neighbors that share comparable distributional charac- teristies. By constructing an adjacency matrix (detailed in Equation 3 that connects each sample both its primary neighbor and secondary connections, we establish hierarchical clustering structure. This clustering mechanism naturally groups samples with analogous feature distributions.
Our analysis reveals an interesting architectural phenomenon: the distribution of clusters exhibits a clear pattern across network depth. Specifically, observe higher cluster density in the network's earlier layers compared to deeper ones. This observation suggests a functional specialization where shallow layers adapt to domain-speciff representations, while deeper layers develop features that remain stable across different contexts.
Algorithm LFD Algorithm
1: Input: Feature map F; = 11,2. ... B} in the BN layer j. FJ E BRCxL 1 iijs 4 N, where
N is total number of BN layers in the model.
2: Output: Feature map Fj ( F2,.... F*) after clustering, F RbXCXL sisr.
3: Begin LFD Algorithm:
4: Compute first neighbors integer vector at BBx1 via exact distance (the distance metric is defined by Equation 2).
5: Given a get adjacency matrix First of the feature map Fj via Equation 3
6: Generate connected components from matrix First.
7: END
B Details of Datasets
We evaluate adaptation performance under covariate shift using three benchmark datasets: CIFARIO- C, CIFAR100-C, and ImageNet-C (24). These datasets simulate real-world distribution shifts through systematic perturbations at varying intensities, ranging from level 1 to 5, with higher levels represent- ing more severe distribution shifts. The CIFAR-based corrupted datasets maintain their original class structures, with CIFARIO-C containing 10 categories (50K/10K split for train/test) and CIFAR100-C encompassing 100 categories (maintaining identical data volume). For large-scale evaluation, utilize ImageNer-C, which spans 1,000 categories with approximately 1. 1.28M training samples and 50K test instances. As shown in Figure 8 each dataset contains 15 types of corruptions, which are: Gaussian Noise, Shot Noise, Impulse Noise, Defocus Blur, Glass Blur, Motion Blur, Zoom Blur, Snow, Frost, Fog, Brightness. Contrast, Elastic Transformation, Pixelate, and JPEG Compression. These three datasets are sufficient to effectively reflect the performance of different methods in dynamic data streams and mixed domain scenarios.
Table 7: Comparison with state-of-the-ar methods ImageNet-R and ImageNet-C datasets (batch size 64). Results show accuracy ( (%) under CrossMix scenario using ResNet-50, Best
results are shown in bold.
Dataset
Source
o-BN
JABN TBN TENT RATA SAR DeYO VIDA RoTTA
NOTE FIND
ImageNer.R
27.94
31.60
21.63
31.12
31.36
31.65
31.22
32.05
31.12
30.78
21.20
34.74
ImageNet-C)
33.78
38.01
23.35
38.63
38.69
39.00
37.90
38.42
38.49
39.62
24.48
41.91
To show the high extensibility of our method to other datasets. We compare our FIND with other methods on additional datasets ImageNet-R (36) and ImageNet-C (37]. Based on the previous setup, we tested the performance of different methods under the CrossMix scenario (where all domains are mixed as input), with specific details as follows:
Style transfer-based dataset ImageNet-Re R: ImageNet-R reflects style shift, where images are transformed from real photographs into various artistic styles (e.g., cartoons, sketches, etc.). Such shifts mainly affect low-level features such as edges and textures, resulting
22

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in milder perturbations compared to typical corruptions. As shown in Table 7 our FIND achieves state-of-the the-art performance, with improvements of 13% over existing methods.
Human-made corruption dataset ImageNet-C:: Compared to ImageNet-C, ImageNet-CC includes large variety of human-designed corruptions, such Blue Noise, Plasma Noise, and Caustic Refraction. This allows for a more thorough evaluation of model robustness against structured, frequency-relatee and complex synthetic corruptions. As shown in Table our FIND still achieves the best results, outperforming the previous SOTA by 2.5%-17999
Gaussian Noise
Shot Noise
Impulse Noise
Defocus Blur
Glass Blur
Motion
Frost
Fag
Brightness
Contrast
Elastic Transform
Pixelate
Jpeg Compression
Figure 8: Visualization of the 15 types of corruptions in CIFARIO-C, CIFARI00-C and ImageNet-C.
C Details of Baselines
We consider the following baselines, including state-of-the-art test-time adaptation and test-time normalization algorithms.
Sharpness-awan awarr and reliable entropy minimization method (SAR) 7 has the advantage of conducting selective entropy minimization, excluding samples with noisy gradients during online adaptation, which leads to more robust model updates. Additionally, SAR optimizes both entropy and the sharpness of the entropy surface simultaneously. ensuring the model's robustness to samples with remaining noisy gradients. Efficient forgetfrgg test-time adaptation (EATA) (21 improves the stability model updates by filtering high-entropy samples, while applying Fisher regularizer to limit the extent of changes in important parameters, thereby alleviating catastrophic forgetting after long-term model adaptation. Destroy your object Yo) S disrupts the structural class-related features of samples by chunking them, and selects appropriate samples for model adaptation by comparing the entropy change in predictions before and after chunking, thereby enabling the model to learn the correct knowledge. Test entropy minimization (TENT) [4] optimizes the model for confidence as measured by the entropy of its predictions and estimates normalization statistics and optimizes thannel-wise affine transformations to update online on each batch. Non- ii.d. Test-time adaptation (NOTE) S is mainly two-fold: Instance Aware Batch Normalization (IABN) that corrects normalization for distr--distribution samples, and Prediction ballaceed Reservoir Sampling (PBRS) that simulates i.i.d. data stream from non-i.i.d. stream in a class- balanced manner. Robust test-time Adaptation (RoTTA) [5] shares a similar approach with NOTE, which simulates an i..d. data stream by creating sampling pool and adjusting the statistics of the batch normalization
Test-time fine-tune.
(BN) layer. Visual Domain Adapter (ViDA) (6] shares knowledge by partitioning high-rank and low-rank features. For the aforementioned methods that require updating the model, we follow
23

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the online TTA setup. We assume that the source data, which is used for model pre-training, is not available for use test- test-time adaptation (TTA). We conduct online adaptation and evaluation. continuously updating the model.
Test-time normalization. TBN 12 uses the mean and variance of the current input batch samples as the statistics for the BN layer. a-BN [23 aggregates the statistics of TBN and SBN to obtain new statisties for the BN layer. IABN 33) is a method for calculating BN layer statistics in NOTE, which involves using the statistics of IN for correction. For these backward-fre methods, we also follow the online TTA setting. Additionally, we do not make any adjustments to the model parameters. Instead, we only modify the statistics of the BN layer during the inference process using different approaches.
Test-time normalization.
D Extension of Related Work
Domain-aware multi-modeling in TTA: CoLA 38 proposes a cross-device collaborative TTA paradigm, which achieves efficient TTA by sharing and aggregating domain knowledge vectors learned during adaptation across multiple devices. BECOTTA (39] aims to enhance the resistance to catastrophic forgetting and adaptation efficiency in the continual TTA process by introducing of-peeetss-s (MoE) framework. DPCore 40 aims to address continual TTA under frequent and unpredictable target domain shifts, by preventing catastrophic forgetting and negative transfer during the adaptation process. UnMix-TNS [41] addresses non-ii.d. scenarios with label imbalance by replicating K sets of BN statistics via Gaussian perturbations. However, these replicated statisties operate as an integrated whole, limiting their ability to capture diverse domain distributions in strict mixed-domain settings. These works differ significantly from ours in terms of motivation. Our work specifically targets the wild world setting with dynamic data streams- where the distribution diversity within each test batch changes arbitrarily-and the strict mixed-domaie scenario. To address these issues, we propose novel disentanglement).
framework (automatic distribution-awer aware feature
Robust test time fine-tuning in TTA: COME 42 adopts subjective-logic-base uncertainty model- ing and minimizes opinion entropy address the overconfidence and instability (model collapse) caused by entropy minimization in test-time adaptation. REM [43] improves continual TTA stability and efficiency by preventing the model-collapse issues of entropy minimization. It introduces ranked entropy minimization: progressively masking object-relevant patches and jointly using masked con- sistency loss and entropy ranking loss to align predictions across difficulty levels while preserving the intended entropy order. EATA-C 44 reduces reducible model uncertainty via a full-subnetwor consistency loss and characterizes data uncertainty through prediction disagreements. thereby miti- gating the overconfidence and miscalibration of pure entropy minimization in TTA while alleviating catastrophic forgetting. Although these methods improve stability during adaptation and prevent collapse, they still fail to achieve precise normalization in dynamic settings, preventing the model from learning effectively.
We compare against the above work that targets the same task as ours; the detailed results are shown in Table Our FIND consistently outperforms these methods by a substantial margin (10%~15%).
Table 8: Comparison with state-of-the ahe methods on CIFARIO-C, CIFAR100-C, and ImageNet-C datasets (corruption severity 5, batch size 64). Results show accuracy (%) under CrossMix scenario using ResNet-50. Best results are shown in bold.
Dataset
COME UNMIx-TNS REM CoLA FIND
CIFARIO-C
59.10
62.00
CIFARI00-C
29.76
29.98
31.55
32,52
ImageNNr-CC
16.66
16.93
18.65
18.74
The key differences between our work and prior "in-the-wild" work: We consider fully dynamic data streams and more stringent domain mixing. Besides the CrossMix scenario- scenario-where each batch strictly includes 15 domains we also construct dynamic scenarios (Random and Shuffle) where each batch may contain only single domain or varying number of domains (2-15). In addition, we provide novel analytical perspective, redefining the roles of SBN and TBN in normalization from the viewpoint of delain-related and general features. We propose a -ounnur normalization strategy for features within a batch-not addressed by previous methods. Notably,
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DDA [00] introduces an additional diffusion model for denoising samples while keeping the original model unchanged. Although DDA also evaluates the mix domain scenario its experiments, this is primarily to demonstrate the robustness of the method, rather than being the main focus of the paper. The differences between DDA and our work: DDDA operates on a per-sample basis. Even if full batch is provided as input, each sample is denoised independently by the diffusion model. As result, batch processing does not offer any additional algorithmic benefit beyond potential hardware-level parallelism. 2. DDA introduces additional diffusion models and requires multiple data forward passes, resulting in significant inference overhead. 3. Training the diffusion model requires large amounts of source data, which is inconsistent with TTA assumptions. In contrast, method offers greater scalability across different batch sizes and achieves efficient inference without relying on additional models or extra training and forward processes.
E
Details of Our Scenarios
Previous researches have predominantly focused static scenarios (whether in continual TTA non-i.i.d TTA). As illustrated in Figure the static scenario is characterized by samples within a batch originating from the same domain, with each domain persisting for extended period.
In this paper, we shift our attention to TTA in dynamic scenarios. As depicted in Figure the dynamic scenario is defined by samples within batch originating from either single domain or multiple domains, with domain changes occurring real-time rather than persisting for extended periods. This encompasses three sub-scenarios:
CrossMix: Each batch contains samples from multiple domains.
Shuffle: Batches alternate between containing samples from single domain and multiple domains.
Random:
The number of domains represented in each batch is entirely stochastic.
Teat Barch
Sarch
Static
Source Model
Adapted Model
Adapted Model
Adapted Model
Adapted Model
Gravstix
cal
Adapted
Chow
male
Dynamic Shuftls
Buackatty AX
Source Model
Adaptad Modal
Adapted
Adapted Model
Randomm
Source Model
Tait Bath R.
Adspiad Model
Yes
Adapted Model
Yeu und.
Hany
Cleady
Adapted Model
Figure 9: The visualization of scenarios mentioned in this paper, including static and dynamic (CrossMix, Shuffle and Random).
We propose three sub-scenarios that simulate real data streams in the wild world, while also encom- passing continual TTA in the traditional TTA static scenario (where, under the Random scenario, the data stream may originate from the same domain over certain period of time). Thus, these sub-scenarios provide a better evaluation of the performance of current TTA methods in real-world settings.
Hyperparameter Settings
The hyperparameters can be divided into two types: one type shared by all the baselines, and the other type consists of hyperparameters specific to each method. For the shared hyperparameters, batch size 64, learning rale = le -4 The optimizer used is SGD. The hyperparameters of each test-time fine-tuning method are set according to the TTAB benchmark [20] (the optimal hyperparameters that achieved the best performance for each method in the original paper). Following the hyperparameters specific to each test-time normalization method:
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The hyperparameters of TBN are set according to the settings in [22
The hyperparameters of IABN are set according to the settings in
The hyperparameters of a-BN are set according to the settings in 23
G
Cold-Start Mechanism and Layer Sensitivity
As shown in Figure 10a Figure Tod The sensitivity of different model layers to domain shift is correlated with both the backbone architecture and the dataset characteristics. For ResNet-50 (Figure Figure TÕc), we observed an intriguing phenomenon: shallow and deep layers exhibit lower sensitivity to domain shift, while intermediate layers show heightened sensitivity. This deviates from conventional wisdom (where shallow layers are typically domain-related and deep layers class- related). The anomaly may arise because shallow layers predominantly capture universal features (e.g.. object contours and edges) that are domain-invariant, whereas intermediate layers- transitioning from abstract to semantic representations- undero intensive feature transformation and mixing, making them more domain- domain-vulnerabb vulnerable. Furthermore, sensitivity correlates with task complexity, as evidenced by the uniformly elevated sensitivity across all layers in challenging tasks like ImageNet classification.
Figure T0e shows the sensitivity score values under different cold-start durations. We found that the cold-start duration has negligible impact on layer sensitivity quantification. Both short-term (3 batches) and long-term (100 batches) cold-start conditions consistently characterize the relative sensitivity relationships across layers, exhibiting only minor oscillations in peak values that do not compromise the final layer selection. We ultimately select the initial 10 batches as the cold-start duration.
The time overhead introduced by the cold-start phase is negligible. 1. The time complexity of the cold-start is linear with channels C and the number of BN layers N, resulting in extremely low computational cost. 2. The computation is performed in parallel with the forward pass, incurring no extra inference or training steps.
Overhead of cold-start phase:
H Analysis of Cluster Numbers of Each FABN Layer by LFD
Our analysis reveals the fundamental mechanism of LFD: it systematically organizes and clusters feature representations based on distributional similarities, thereby minimizing interference between dissimilar feature patterns within each batch. Figure II illus- trates a key architectural phenomenon: the cluster count systematically decreases with network depth in dynamic scenarios. This pattern indicates a pro- gressive convergence of feature distributions across deeper network layers, suggesting a transition from variable feature representations more stable, con- sistent patterns. In Figure each batch contains 15 domains and 10 classes. We observed interesting phenomenon: in the shallow layers (0-5), the number of clusters slightly exceeds the number of domains; in the middle layers (6-40), the number of clusters almost identical the number of domains; and in the deep layers, the number of clusters aligns closely with the number of classes. This aligns with the observations from the cold-start process: initially. the model focuses on general features such as edges and structures, which are more related to the objects themselves and less influenced by domains. As the layer depth increases, features transition from abstract to semantic, during which domains introduce interference. In the deep layers, features become directly tied to object categories, with minimal influence from domains. These find- ings provide valuable insights for optimizing the layer-wise scaling parameter a and understanding the functional roles of different network components.
8 83
Random
Suboot Number
st. S. 3
CressMix
Shuffle
BN Layer Index
Figure 11: Cluster numbers of each FABN layer under dynamic (Random, CrossMix. and Shuffle) scenarios. Each result is derived from the mean of 1,000 batches, with the col- ored bands around the lines representing the standard deviation.
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Layertadaz tides
(a) Sensitivity of each BN layer (Backbone: ResNet-50, Dataset: ImageNet-C)
(b) Sensitivity score each layer (Backbone: ResNet-50, Dataset: CIFARIO-C)
(c) Sensitivity score of each BN layer (Backbone: ResNet-50, Dataset: CIFARI00-C)
2
Scare
Loyer
(d) Sensitivity of each BN layer (Backbone: EfficientViT-MS Dataset: CIFARIO-C)
inder
(e) Sensitivity score values under different cold-start durations (Backbone: ResNet-50, Dataset: CIFARIO-C)
Figure 10: (a)-(e) demonstrate the variation trends of domain shift sensitivity across BN layers under different backbones and datasets. (d) shows the sensitivity variations across BN layers single model under various cold-start durations.
I Sensitivity analysis of y
We compress the score of each layer in FIND* to the range [0. 1] through normalization, with score proximity to indicating lower distribution shift sensitivity of the layer. As shown in Figure [2] when varies within 0, accuracy fluctuation remains below 1 % while inference efficiency improves by %-44%, demonstrating robust model performance. When 7 exceeds 0. accuracy drops by 2%-6% with unstable model behavior. Therefore, setting 7 between 0-0.1 achieves inference acceleration while preserving model performance. Meanwhile, the performance of the model is not sensitive to the y value within this interval.
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41
[Best: 40.73%
Accuraty
0.225
80
[eatt: 79.02%
Accurscy
0.35
Accuracy (96)
40
0.200
79
39
0.175
0.30
78
0.150
0.25
77
37
0.125
0.20
36
Accuracy
0.100
Accuracy
35
0.075
75
Time (s)
0.00
0.10
0.20
0.30
0.40
0.00
0.10
0.20
0.30
0,40
Y
Y
(a) CIFARIOO-G & ResNet-50
(b) CIFARIO-C EfficientViT-M5
Figure 12: (a) and (b) demonstrate the sensitivity of model inference performance (Aceuracy (%)) to variations, along with the associated changes in inference efficiency (Time (s)).
Compatibility Evaluation with Test-Time Tuning
We integrated FIND* with the test-time tuning methods discussed in paper, and we froze the layers in S-FABN that require clustering while updating the layers that do not require clustering. As shown in Table 9 compared with FIND*, test-time tuning further improves performance by approximately 2%. We obtain the following conclusions: 1. Accurate normalization is a prerequisite for successful tuning (as stated observation Section 2.2). 2. Selectively updating layers that are insensitive to domain shift yields greater gains.
Table 9: Performance of combining FIND* with test-time tuning on CIFARIO-C (corruption severity 5, batch size 64). Results show accuracy (%) under CrossMix scenario using ResNet-50. Best results are shown bold.
+ENTT
FENA
21
FIND
0.88
o=0..4
a=0
0=0.88
o=0.44
0=0..8
a=0.44
0.4
7=0.1
72.01
70.15
67.93
71.03
72.20
69.98
67.39
71.14
73.07
71.61
68.00
70.70
7=0.06
72.31
K Performance under Different Domain Scales
Table 10 shows the performance of the method proposed in this paper under different domain scales in CrossMix Scenario. Experimental results demonstrate the superior adaptability of our approach across varying levels of distributional complexity in batch data. As the feature distributions become increasingly diverse (transitioning from homogeneous to heterogeneous batch compositions), our method maintains consistent performance advantages over existing approaches. Performance analysis reveals significant improvements: compared to the baseline methods, our approach achieves a 16% improvement over RoTTA and surpasses the previous state-of-the-an method DeYO by approximately 5%. Notably, across all three evaluation datasets, our framework consistently demonstrates a 2-5% performance gain over the strongest baseline. These results validate our method's effectiveness in handling dynamically changing domain distributions within batch data.
L Performance under Different Model Structures
The generalization capabilities of our approach across different architectures are examined through ResNet-26 experiments, documented in Table [I] Under CrossMix evaluation conditions, our framework maintains its performance advantages regardless of the underlying network structure. Specifically, we achieve accuracy gains of approximately 3% over ViDA on CIFAR10-C and 4% over EATA on CIFAR100-C. These results demonstrate the aehiitecture-agnstte nature of our method and its robust adaptation capabilities across varying model configurations.
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Table 10: Comparisons with state-of-the-art methods CIFARIO-C, CIFAR100-C, and ImageNet-C (severity level= 5) under batch size 64 regarding accuracy (%). Each method was evaluated under the CrossMix scenario with various numbers of domains using ResNet-50 model architecture. Best and second-best results are shown in bold and underlined, respectively.
CIFARIO-C
CIFAR100-C
ImageNet-CC
12
12
Method
Avg-AIl
Domains
Domains Domains
Domains
Domains Domains
Domains
Domains
Domains
Source
46,59
52.54
55.84
19.23
24.25
27.15
16.21
20.07
25.20
31,90
TEST- TIME TUNE
TENT
60.79
64.69
66.59
30.33
33.07
33.44
7.41
12.69
17.24
36.25
BATA
57.67
60.89
63.79
35.52
35.05
33.34
6.97
13.24
18.47
36. 10
NOTE
58.61
61.88
64,93
28.55
31.46
33.65
12.92
17.23
22.71
36.88
SAR
59.76
63.76
65.75
31.03
33.48
33.71
7.44
12.75
18.05
36.19
RoTTA
$2.03
35.44
42.26
23.44
21.73
23.72
6.96
16.16
22.37
27.12
VIDA
57.64
60.89
63.77
27.89
31.04
32,96
6.80
12.09
18.03
34.57
De
65.23
69.22
69.89
35.35
35.71
13.59
17.85
38.69
TEST-TIME N NOMMALIZATION
TBN
57.63
60.89
63.77
27.89
31.03
12.39
17.51
a-BN
58.17
61.68
64.27
28.49
31,79
33.81
9.78
15.36
21.80
36.13
TABN
59.41
64.24
18.99
21.99
3.55
6.44
10.30
29.54
FIND
66.59
70.30
72.97
35.08
38.82
40.68
17.05
22.38
27.40
43.47
Table 11: Comparisons with state-of-the-art methods on CIFARIO-C and CIFARIOO-C respectively (severity level 5) under batch size 64 regarding accuracy (%). Each method evaluated under the CrossMix scenario with using a ResNet-26 model architecture. The best result is denoted in bold black font.
Method
CIFARIO-C CIFARI00-C
Avg.
Source (ResNet-26)
53.06
31.34
42.20
TEST- TIME FINE- TUNNE
TENT
59.01
30.37
44.69
EATA
59.34
34.24
46.79
NOTE
60.18
31.28
45.73
SAR
58.70
30.42
44.56
RoTTA
49.26
20.10
34.68
ViDA
65,80
30.52
48.16
DeYO
65.47
33.89
49.68
TEST- TIME NORMALIZATION
TBN
59.34
30.52
44.93
Q-BN
58.51
32.81
45.66
IABN
62.31
19.72
41.02
FIND (ours)
68.21
38.24
53.22
M Extension of Motivations
Figure presents our analysis model accuracy and TBN statistics across ImageNet-C corruption levels 1-, where level I represents minimal domain shift. We evaluate the distributional alignment by measuring L2 norm and cosine similarity between instance normalization (IN) statistics and TBN statistics across batch normalization layers. Our results show that increasing corruption levels correlate with both declining accuracy and decreased statistical distance between instance-level and TBN features, suggesting stronger distributional coupling within batches.
These findings, illustrated through a representative example in Figure 14 demonstrate how elevated domain shifts compromise TBN's ability to maintain distinct class-specific feature distributions. The

---

observed pattern indicates that increasing distributional shifts in domain-related features interfere with TBN's capacity characterize class-relevant features, leading to reduced discriminability across categories.
Based on these empirical observations and our theoretical analysis, identify two fundamental limitations of TBN in dynamic scenarios: 1. Coupling between different domain-relevant features in TBN and 2. Interference between domain-related and class-relevant features in TBN. These findings underscore the importance of incorporating SBN into the adaptation framework.
Brightness
Motion
Dafocus
Gaussian in
Dilanna
1250
262-
0.5t
0.
Colrra siibbety
Dislance
245
0.50
smbinnyy
L2 Dillanc
235-
240
0.94
0.50
Dilann
230
225
235
240
00,00
0..4
0.90
simtarrtyy
235
0.02
230
0.90
220
0.50
Acourady (N)
Acouracy (5)
Acouracy (56)
Accuracy (56)
Figure 13: TBN-IN distance vs. accuracy under different corruptions. The data points in the figure represent samples with corruption levels 1 through 5, where higher levels correspond to lower accuracy. We compute the average distance between per-sample IN statistics and TBN statistics in the deep layers, reflecting the dispersion of feature distributions within a batch. It reveals that the distribution of DRF interferes with the distribution CRE: as the sample corruption level increases, the feature distributions within batch become more coupled.
Figure 14: Airplane wings in different corruption. More severe corruption perturbations of the image can obscure the CRFs, causing the overall feature distribution to become more entangled and thus decreasing the model's inference accuracy.
N Performance under Static Scenario
Table 12 shows the results of the baselines and our method on ImageNet-C under the Static scenario. The data presented in the table demonstrates that both FIND) and FIND* outperform the second-best method by approximately 3%. This result indicates that our approach maintains optimal performance in both dynamic and static scenarios.
Table 12: Comparisons with state-of the-the-art methods on ImageNet-C (severity level 5) under batch size 64 regarding accuracy (%). Each method was evaluated under the static scenario using a ResNet-50 model architecture. Best and second-best results are shown in bold and underlined, respectively.
Method
Q- Q-
TBN TENT DeYO ROTTA SAR EATA ViDA FIND FIND*
ImageNet-C
29.64
27.97
28.25
29.71
19.76
28.42
27.87
27.99
31.78
32.10
Performance under Different Batch Size
The impact of varying batch sizes on adaptation performance under CrossMix conditions is illustrated in Figure 15] Our framework demonstrates remarkable stability across all evaluated batch size configurations on the three benchmark datasets, with minimal performance fluctuations. This contrasts sharply with alternative approaches, which exhibit significant sensitivity to batch size variations.
30

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Notably, on CIFARI00-C and ImageNet-C. competing methods show substantial performance degradation with reduced batch sizes, only achieving stability batch sizes exceeding 64.
Our method's batch-size invariance can be attributed to two key factors: the robust class-relevant feature representations provided by SBN, and the preservation of domain-specific characteristics regardless of batch size configurations. This architectural design enables consistent performance even in extreme scenarios when processing individual samples (batch size 1), the framework successfully captures domain-specific distributions from single-instance feature maps.
This stability across arbitrary batch sizes represents significant advantage in practical deployment scenarios where batch size flexibility is crucial.
CIFAR10-C
CIFAR100-C
ImageNat-C
Accuracy (9%
60
Accuraty (%)
20
Accuracy
SAR
TBN
20
TBN
SAB ATA
TBN
EAIA
EA1 De
Outs
10
Ours
20
DeYO
DeYD
128
128
16
Batch Size
Batch Size
Batch Size
Figure 15: Batch size accuracy. Other methods exhibit poorer performance at low batch sizes, only stabilizing as batch size increases. In contrast, our approach is insensitive to batch size variation, demonstrating greater robustness.
P Experimental Results and Analysis under Wild Scenario
Table 13: Results for d = 0.1
Table 14: Results for 5 = 0.01
Table 15: Results for 8 = 0.005
Method
10-C Avg.
Methed
100-C
Avg.
Method
10-C
Avg.
Source (ResNet 50)
57.40
(ResNet-50)
57.40
28.59
(ResNet 50)
57.40
TEST-TIME FINE-TUNE
TEST-TIME FINE-TUNE
TEST- TIME FINR-TUNE
TENT
52.48
34.58
43.53
TENT
51.77
27.16
39.47
TENT
51.99
25.97
38.98
EATA
54.99
35.60
45.30
EATA
54.47
24.39
39.43
EATA
54.42
23.42
38.92
NOTE
67.50
24.70
46.10
NOTE
67.49
24.71
46.10
NOTE
67.56
24.70
46.13
SAR
$2.19
32.99
42.59
51.48
23.34
37.41
SAR
51.45
22.34
36,90
RoTTA
49.49
22.60
36.05
RoTTA
49.27
22.33
35.80
RoTTA
49.14
21.87
35.51
VIDA
55.02
36.72
45.87
VIDA
54.47
30.59
42.53
VIDA
54.42
29.81
42.12
50.77
48.04
10.17
TEST-TIME NORMALIZATION
TEST-TIME NORMALIZATION
TEST-TIME NORMALIZATION
TBN
55.00
36.73
45.87
* TBN
54.47
30.57
42.52
TBN
54.42
29.80
42.11
c-BN
60.98
40.51
50.75
c-BN
60.54
34.51
47.53
c-BN
60.46
33,52
46.99
IABN
63.30
24.92
44.11
IABN
63.28
24.97
44.13
IABN
63.30
24.95
44.12
FIND (ours)
69.49
38.86
54.18
FIND (ours)
69.43
35.56
52.50
FIND (ours)
69.38
35.21
52.30
We extend the Random scenario by incorporating label distribution shifts to create the Wild scenario, which better approximates real-world data streams. This enhanced setup allows both distributional and label variations within batches, simulating open-world conditions. Following the methodology established in NOTE B we employ Dirichlet distributions to generate temporally correlated label sequences, with the concentration parameter (6 0) controlling shift intensity - lower values indicating more severe shifts.
Results from experiments with varying shift intensities (6 0.1, 0.01, 0.005) are presented Ta- bles 13 and 15 Our framework demonstrates remarkable stability across increasing label shift intensities, maintaining consistent performance levels. Quantitatively, our approach achieves approxi- mately 5% higher average accuracy compared to the strongest baseline, and 20% improvement over the weakest performing method.
The performance gap becomes particularly pronounced under severe label shifts, where competing methods show significant degradation. For instance, DeYo's performance deteriorates substantially, dropping below 20% accuracy CIFAR 100-C under intense label shifts. This comparative analysis demonstrates our method's exceptional resilience to distribution variations in open-worke scenarios, significantly outperforming existing approaches in handling complex, real-world data streams.
31

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Table 16: Comparisons with state-of-the-ae methods on CIFARIO-C and CIFARI00-C respectively
(severity level = 5) under batch size 64 regarding accuracy (%). Each method was evaluated under the CrossMix scenario (Round 2) with using ResNet-50 model architecture. Best and second-best results are shown in bold and underlined, respectively.
Method
CIFARIO-C CIFARI00-C
Avg.
Source (ResNet-50)
57.41
28.59
43.00
TEST-
TIME TUNNE
TENT
58.89
27.20
43.05
EATA
62.03
34.38
48.20
NOTE
66.68
24.70
45.69
SAR
57.54
27.59
42.56
RoTTA
49.11
23.58
36.34
ViDA
62.01
32.29
47.15
DeYO
67.89
17.38
42.63
TEST- TIME NORMALIZATION
TBN
62.01
32.29
47.15
a-BN
62.45
33.21
47.83
IABN
63.34
24.91
44.12
FIND (ours)
71.48
39.72
55.60
Table 17: Comparisons with state-of-the-art methods CIFARIO-C and CIFAR100-C respectively
(severity level = 5) under batch size = 64 regarding accuracy (%). Each method was evaluated
under the CrossMix scenario (Round 3) with using ResNet-50 model architecture. Best and second-best results are shown in bold and underlined, respectively.
Method
CIFARIO-C CIFAR100-C
Avg.
Source (ResNet-50)
57.39
28.59
42.99
TEST-
TIME FINE- -UNE
TENT
55,49
23.64
39.56
EATA
62.01
33.67
47.84
NOTE
67.90
24.70
46.30
SAR
54.28
24.61
39.45
RoTTA
49.21
22.11
35.66
ViDA
62.02
32.21
47.12
DeYO
65.77
12.77
39.27
TEST-TIME NORMALIZATION
TBN
62.02
32.21
47.12
a-BN
62.46
33.21
47.84
IABN
63.28
24.87
44.08
FIND (ours)
71.54
39.67
55.61
Experimental Results and Analysis on Simulated Lifelong Adaptation
While existing approaches focus on continuous adaptation to non-stationary data streams, their evaluation protocols typically utilize single-pass dataset sequences. To better approximate real- world deployment conditions, where inference cycles extend over longer periods, we propose an enhanced evaluation framework that extends test sequences through dataset replication. Specifically, we evaluate adaptation stability by creating extended sequences of CIFAR10-C and CIFAR 100-C through two-fold and three-fold replication (Round- and Round 3). Results under CrossMix
conditions presented in Tables 16 and 17
32

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Our empirical unalysis reveals distinct patterns in long-term adaptation stability. Our framework maintains consistent performance across extended sequences, showing minimal performance degra- dation between Round=2 and Round=3. In contrast, competing methods exhibit notable performance deterioration: Yo experiences accuracy drops of 2% and 5% on CIFAR IO-C and CIFARI00-C respectively. TENT shows performance degradation of 3% (CIFARIO-C) and 4% (CIFAR100) 100-C). SAR demonstrates consistent 3% accuracy decline across both datasets. Other approaches show similar degradation patterns.
R License and Asset Attribution
We use the open-source implementations TTAB 20 under the Apache-2.0 license in our experiments.
TTAB is publicly available, and we have properly credited its creators in the main text. We have respected all terms its license, and all usage compliant with its respective open-source agree- ments.
S Broader Impacts
FIND improves the robustness of deep neural networks in dynamic real-world scenarios by addressing performance degradation under distribution shifts. This can enhance the reliability and adaptability of Al systems in diverse applications, including autonomous vehicles, medical diagnostics, and remote sensing, where data is often non-stationary and heterogeneous.
These improvements may contribute to more stable and efficient AI deployments, reducing the need for frequent model retraining and lowering computational costs. Additionally, the proposed framework's 's compatibility with both convolutional and transformer architectures broadens its accessibility for various cases. We do not foresee negative societal impacts from this work.
T
Limitations
While FIND significantly enhances model robustness in dynamic scenarios, the divide-and-conquer strategy used in Layer-Wise Feature Disentanglement (LFD) introduces additional computational overhead compared to simpler normalization techniques like TBN. Although our implementation efficient and parallelized, the graph-based clustering in LFD may still become bottleneck for extremely nigh-ddmensional data or very large batch sizes. Further optimization of the clustering process and hardware-speciffc acceleration could address this issue.
U Conclusion and Future Work
In this work, we considered more practical test scenario: The test samples within the same time period are no longer independent and identical, and may come from one or more different distributions. The existing TTA methods perform poorly in this scenario. Our analysis reveals that the main reason lies in the normalization failure the BN layer. Therefore, we improved the existing test-time batch normalization methods and designed new universal BN architecture. This architecture adopts divide-amd aidee-and-con and-conquer strategy and can precisely divide and normalize complex data streams during designed various scenarios. including: Dynamic, Static,
the testing period. In the experiment, Wild and Lifelong, to test the performance, robustness, practicability and stability under continuous learning of the method. We simultaneously adopt multiple backbones. including ResNet and ViT, to test the universality of the method. Experiments have proved that the method we designed has good effects in various scenarios during the test period and has strong practicability. Meanwhile, method has achieved good results on multiple commonly used backbones by replacing the BN layer of the model, and has strong universality. Our work leaves several aspects unexplored. Specifically, we need to continue exploring the methods of online model updates so that we can also acquire effective knowledge when dealing with non-in oon-inepenndent and non nos-tiittb data streams. In addition, we also need to explore the optimal value of the FABN layer fusion parameter a to meet the specific characteristics of different layers.
33


Reviews:
[{"review_id": "TKDF1Yg4bp", "reviewer": "Reviewer_u3eW", "summary": "This paper tackles the problem of test-time adaptation in dynamic setting, where is target domain is a mixture of multiple distributions. Under this setting, standard one-size-fits-all test-time normalization techniques suffer from cross-distribution averaging. To solve this problem, this paper proposes FIND, which can captures features with similar distribution and apply different strategy to each layer. The proposed algorithm has great performance on benchmarking datasets.", "questions": "- What is the dataset used in Figure 3, and what are the four domains? Are they four kinds of corruptions? How generalizable this conclusion is? \n- Figure 4(a): I am quite confused about the conclusion here. In line 161, the author mentioned that \"SBN maintains stable performance across these variables\". Although this is true, in Figure 4(a), we can see that TBN always outperforms SBN, and the variance looks smaller (especially for the dynamic setting). I don't see how this can demonstrate SBN's robustness. Figure 4(b) makes a lot of sense, although with SBN there is no adaptation of the model so it is expected to see a horizontal line of accuracy...\n- I assume that \"Source\" means no adaptation. Why the performance is different in three difference settings? For example, in Table 2, CrossMix IN-C the accuracy is 26.05% but on Random IN-C the accuracy is 27.39%. \n- Table 3 shows that the adaptation is much more effective with the proposed graph-based connecting component strategy, compared to other clustering methods. Could you provide some explanation of why this is the case? Especially given that FIND shares many similarity with some of the clustering algorithms, e.g., HDBSCAN. \n- In Figure 7, why the proposed algorithm have similar performance under batch size = 1 and batch size = 128? If there is only one sample in the batch, how to do clustering and normalization? I am very confused.", "limitations": "Generally yes.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "# Strength\n- The solution is well-motivated. Mixture distribution is very common in real-world tasks. The author starts by observing the drop in performance, and leads to a \"divide and conquer\" normalization approach. \n- The proposed method has great performance in corruption benchmarks\n- From Figure 6, it looks like FABN outperforms TBN under a wide range of $\\gamma$ (basically TBN is the proposed method with $\\gamma=1$). \n\n# Weaknesses\n- The idea of interpolating between source and target statistics is very common in previous works, e.g., $\\alpha$-BN. Section 2.4 basically applies $\\alpha$-BN to each connected component. \n- The motivation of this paper is that TBN and relevant test-time normalization algorithms assume that the target domain is homogeneous (i.e., one-size-fits-all). However, the authors ignore the fact that there are already some test-time normalization papers consider mixture of multiple distributions. One relevant paper is [1], which fits multiple sets of running statistics for each normalization layer. However, the author didn’t mention this, or compare the proposed method to this paper. \n\n[1] Un-Mixing Test-Time Normalization Statistics: Combatting Label Temporal Correlation. ICLR 2024. \n\n# Minor\n- Equation 1: L is used for both spatial dimension (H*W) and its iterator. Though this does not affect understanding, typically one should use different notation. \n- $\\gamma$ is used both in Equation (7) and as the threshold of score in line 242. This might be a little bit confusing. \n- Line 271: detalis -> details", "was_revised": true, "final_justification": "Authors' rebuttal solves all my concerns.", "rebuttal": "## Thank you for recognizing our well-motivated solution and strong empirical results. Your great comments provide constructive guidance for the further exploration of our work. Our response to your concerns is presented as follows.\n\n\n\n>## **W1 (Difference in interpolating)**\n\nWe thank the reviewer for this insightful question, which allows us to further highlight the contributions of our method.\n\nWe would like to clarify that **the target, purpose, and core idea of our interpolating  are fundamentally different from previous methods, despite any superficial similarities in form**.\n\n- Core idea: the core of our method lies in the entire \"divide-and-conquer\" framework, where the \"divide\" step is critical. Interpolating  serves as an efficient means for \"conquering\" after precise partitioning. **Without an accurate partitioning of domain-related features, interpolating  is meaningless**. Therefore, traditional interpolation methods such as $\\alpha$-BN are ineffective in dynamic environments.\n\n- Interpolating  target: the interpolating  target of our FABN is no longer the traditional TBN (the entire batch) or IN (a single sample), but rather the TFN (multiple clusters) obtained through distribution-aware partitioning. TFN can adaptively capture the distribution diversity within a batch, which TBN and IN are unable to achieve.\n\n- Purpose of interpolating: We leverage SBN to complement the general features missing from each TFN, thus constructing a complete feature distribution (Section 2.2, Conclusion 4). The interpolation in $\\alpha$-BN or IABN is intended to reduce distribution gaps.\n\n- New theoretical insights and perspectives: We provide a novel analysis of the roles of SBN and TFN, with detailed studies of general/domain-related features in Section 2.2 and Appendix K.\n\n- Results: Our divide-and-conquer based interpolating  consistently outperforms $\\alpha$-BN and IABN in both performance and robustness across various scenarios.\n\n>## **W2 (Method comparison)**\n\nWe thank the reviewer for this good suggestion.\n\n**NOTE ([6] in our paper) and UnMix-TNS [1] are highly similar in both motivation and methodology, and we have analyzed and compared NOTE with our method in the paper.  Notably, there are substantial differences between UnMix-TNS and our approach.**  \n\n- Motivation: UnMix-TNS is designed to address **non-i.i.d** (label imbalance) scenarios (although they tested mixed domain scenarios in their experiments, this is not their main focus), while our paper specifically targets **dynamic data streams and strict mix domain settings in wild world.** In addition to the strict mix-domain scenario (where each batch contains a mixture of 15 domains), we also consider fully random and dynamic settings—where each batch may contain only a single domain or any number of domains (2–15). \n\n- Method:  Although UnMix-TNS replicates K SBNs using Gaussian perturbations, these SBNs operate as an **integrated whole** and thus cannot effectively capture multiple domain distributions in mixed-domain scenarios. In contrast, our method explicitly decomposes the computation of BN statistics into multiple clusters along the feature dimension in a layer-wise manner, thereby achieving a genuine **\"divide-and-conquer\"** approach that previous methods lack.\n\nAs shown in the following table, our approach outperforms UnMix-TNS by a significant margin **(11%-15%)** in mixed domain settings. We will include these results and cite UnMix-TNS in the revised version. We hope this clarification addresses your concerns. Thank you for your valuable feedback.\n\n| Dataset   | FIND (ours) | UnMix-TNS |\n|-----------|-------------|-----------|\n| 10-C      | 71.54%      | 60.46%    |\n| 100-C     | 40.48%      | 29.98%    |\n| IN-C      | 30.33%      | 16.93%    |\n\n[1] Un-Mixing Test-Time Normalization Statistics: Combatting Label Temporal Correlation. ICLR 2024.\n\n>## **Q1 (Details of Figure 3 in paper)**\n\n\nThe dataset used is **CIFAR100-C**, with domains corresponding to four types of corruptions: **Gaussian Noise, Zoom Blur, Snow, and Pixelate**, which represent the **real-world categories of noise, blur, weather, and digital**, respectively. **This conclusion is general and reflects the intrinsic characteristics of the models**; it also holds on the other two datasets and with the ViT architecture. We will provide additional visualizations for different datasets and architectures in the revised version.\n\n\n>## **Q2 (Explain of Figure 4(a))**  \n\nThank you for your questions, this will help us further improve the descriptions in the manuscript.\n\nIn Fig. 4(a),  **“stable” refers to SBN is unaffected by the number of domains in a batch, while TBN is influenced by it.**  \n\n- Phenomenon:  as the number of domains in the test data increases (from 1 to 15), the performance of SBNs **remains unchanged** in both static and dynamic settings, whereas the performance gap between the two TBNs **continues to widen**. This indicates that SBN is not affected by domain diversity within a batch, whereas TBN is highly sensitive to it. Therefore, SBN provides stable and reliable general features.\n\n- Additional explanation: TBN consistently outperforms SBN because SBN does not contain any domain-specific features. This does not contradict the fact that SBN is unaffected by the number of domains in a batch.\n\n\n>## **Q3 (Different source results)**\n\nExcellent question!\n\n **The data streams for the Random and Shuffle settings are longer than for CrossMix**. In CrossMix, each batch contains a mixture of 15 domains, while  the other two settings include batches from a single domain as well as mixtures of varying domain numbers (from 2 to 15). To ensure all these cases are sufficiently represented, we **extend the data stream length for Random and Shuffle to 1.5 times that of CrossMix**. Specifically, after one complete pass through the dataset, we randomly sample an additional 50% of the data for further input. Although the data stream lengths differ across settings, **the comparisons between methods are entirely fair**. We will clarify and supplement this detail in the revised version.\n\n\n>## **Q4 (Clustering difference)**\n\nThank you for this excellent question! \n\nFIND achieves **fully automatic perception and dynamic grouping without requiring any additional parameters**. Moreover, FIND possesses **the capability for fine-grained local perception**. But other clustering methods do not possess these capabilities.\n\n- Adaptation to dynamic distributions: FIND adopts a \"nearest neighbor connectivity\" principle forming connected components. This enables FIND to adaptively capture the true structure of the data distribution, making it highly robust to complex shapes and unknown numbers of clusters. In contrast, methods like K-means and HDBSCAN rely on preset cluster numbers, global density, or hyperparameters,  making them **difficult to generalize to highly dynamic distributions**, and requiring frequent parameter tuning.\n\n- Adaptation to complex distributions: By focusing on local neighbor search, FIND achieves **fine-grained clustering** and is sensitive to subtle local structures in both high-and low-density regions. Therefore, FIND can handle elongated, ring-shaped, or nested distribution structures and automatically distinguish distributions with unknown numbers or highly imbalanced sizes. Even under overlap, FIND can identify reasonable clusters based on local similarity. By comparison, K-means and HDBSCAN are mainly suitable for **spherical, balanced distributions**—while HDBSCAN can handle some complex cases, it is highly sensitive to parameters and unsuitable for real-time or large-scale scenarios. Moreover, when high-density and low-density clusters coexist, HDBSCAN is prone to misclassifying low-density clusters.\n\nWe illustrate these points with two examples:\n\n- Example 1: When domains are completely separated without any overlap, traditional clustering algorithms (e.g., HDBSCAN) and FIND can all separate them successfully.\n\n- Example 2: When domains are mostly separated but overlap at the boundaries or one domain encloses another (as shown in Fig. 3(a) in our paper), FIND can provide finer-grained perception and segmentation for the overlapping or enclosing parts. For instance, red domain samples surrounded by green domain examples can still be assigned to the correct cluster via nearest neighbor search. However, HDBSCAN and K-means only consider global density or distance, leading to hard splits at the overlap and resulting in unstable normalization.\n\n\nConclusion:  FIND achieves **fully automatic perception and dynamic grouping**. Other clustering algorithms **depend on hyperparameters or  can only partition the space globally, lacking the capability for fine-grained perception in complex scenarios**. \n\n\n>## **Q5 (Similar performances of small and large batch size)**\n\nThank you for this great observation!\n\n\n**The similar performance between bs = 1 and bs = 128 in Fig. 7(a) is a special case. Under general circumstances, increasing the batch size  improves the performance of FIND (as shown in Fig. 15 in the Appendix)**. \n\n- Reasons for special case: **The  stable capture of domain-specific features (Conclusions 2 and 4 in Section 2.2)**.  Setting bs = 1 is equivalent to having only one sample per cluster, where the TFN statistics degenerate to the feature statistics of that single sample (i.e., IN).  The domain-related feature of the single sample is not affected by other domains.  Therefore, for **low-resolution samples** (10-C), the performance of bs = 1 is similar to bs = 128.\n\n- Reasons for general case: The domain-related feature statistics are less accurate due to the small sample size (bs = 1) and will be disturbed by the style of the sample itself. Therefore, for **higher-resolution** samples (100-C, IN-C), performance remains stable when bs = 1  (still outperforms other methods compared in our paper) but is inferior to bs = 128."}, {"review_id": "kneQ6EWHGJ", "reviewer": "Reviewer_kGt6", "summary": "This paper addresses test-time adaptation in dynamic scenarios. The authors propose FIND, a divide-and-conquer test-time normalization strategy that replaces existing batch normalization layers and is adaptable to various backbones. FIND partitions features at different layers, effectively avoiding interference between samples from different distributions. Experiments demonstrate that FIND achieves superior performance in the more complicated TTA scenarios for BN models. I believe that using the first-neighbor approach provides a sound solution to decouple features from multiple domains, which may inspire new methods for the TTA community. I thus recommend weak acceptance.", "questions": "1.\tWhy is the performance of Find* omitted from Table 2?\n\n2.\tHow is accuracy measured for clustering algorithms in Table 3?", "limitations": "Please refer to the weaknesses.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths**:\n\n1. This paper addresses a challenging scenario where test data from multiple domains are mixed in the data stream, aiming to improve the robustness of TTA in the dynamic wild world.\n\n2. The structure of this paper is well-organized, introducing the method's design and underlying logic through observations, with a clear and well-articulated motivation.\n\n3. The proposed method, FIND, provides a sound and nice solution to decouple features from multiple domains, thereby achieving more precise normalization for samples from different domains. Experiments also verify the superiority of Find for calibrating the BN layer at test time.\n\n**Weaknesses**:\n\n1. Incomplete ablation study. First, it is suggested to provide the ablation and sensitivity analysis of $\\alpha$ to support the claim of mitigating the domain-specific feature perturbations. Second, it is recommended to include $\\alpha$-BN and IABN in Figure 7 for more rigorous comparisons.\n\n2. Lack of compatibility evaluation with the test-time tuning method. It is insightful to show whether the proposed method can be integrated with the test-time tuning approaches, such as Tent and ETA, to further boost the TTA performance.\n\n3. Some important related works are missing. Since FIND aims to decouple the TTA process of different domains, it is suggested to include discussions or comparisons with the domain-aware multi-modeling TTA techniques, such as DPCore [1], BeCoTTA [2], and CoLA [3].\n\n4. The introduction currently overlooks test-time adaptation methods built for truly “in-the-wild” settings. A brief overview of these approaches would anchor FIND within the broader TTA community, while underscoring that FIND tackles the stricter mixed-domain shift problem and is tailored for the BN models.\n\n[1] DPCore: Dynamic Prompt Coreset for Continual Test-Time Adaptation. ICML 2025.\n\n[2] BECoTTA: Input-dependent Online Blending of Experts for Continual Test-time Adaptation. ICML 2024.\n\n[3] Cross-Device Collaborative Test-Time Adaptation. NeurIPS 2024.", "was_revised": true, "final_justification": "The authors faithfully address my concerns by providing more ablations and comparisons with SOTA. I will maintain my score of acceptance.", "rebuttal": "## We sincerely appreciate your recognition of our motivation, novelty method and well-organized structure.  Your insightful comments are also highly valuable. Our response to your questions is elaborated below.\n\n>## **W1 (Ablation study on $\\alpha$)**\n\nWe thank the reviewer for  the  suggestions. This will help us further verify the sensitivity of our method to hyperparameters.\n\n **The ablation study on $\\alpha$ provides strong evidence supporting several conclusions in our paper**. We conducted two sets of ablation studies on $\\alpha$ with $\\gamma = 0.1$, separately for clustered and non-clustered layers. Observation: In both cases, **performance is better when the SBN ratio is higher (>0.5)**. Clustered layers are sensitive to the SBN ratio **(13% change in accuracy)**, while non-clustered layers are not **(3% change in accuracy)**. \n\n- Conclusion 1: The general knowledge (SBN) dominates during inference.  \n\n- Conclusion 2: The sensitivity of $\\alpha$ is much lower in layers that do not require clustering compared to those that do, because TFN only provides domain-specific distributions rather than the full general knowledge distribution (as discussed in Section 2.2, Conclusion 4). \n\n- Conclusion 3: The general knowledge distribution captured by SBN is more comprehensive than that of TFN/TBN (as discussed in Section 2.2).\n\n**$\\alpha =0.8$ for Non-Clustered Layers** and changes in [0, 0.2, 0.4, 0.6, 0.8, 1] for Clustered Layers. $\\alpha$ represents the weight of SBN\n| $\\alpha$ | 0    | 0.2  | 0.4  | 0.6  | 0.8  | 1    |\n|:--------:|:----:|:----:|:----:|:----:|:----:|:----:|\n| Acc/%    |57.48 |62.98 |66.81 |69.49 |70.75 |60.39 |\n\n**$\\alpha =0.8$ for Clustered Layers** and changes in [0, 0.2, 0.4, 0.6, 0.8, 1] for Non-Clustered Layers. $\\alpha$ represents the weight of SBN\n| $\\alpha$ | 0    | 0.2  | 0.4  | 0.6  | 0.8  | 1    |\n|:--------:|:----:|:----:|:----:|:----:|:----:|:----:|\n| Acc/%    |67.20 |67.47 |68.29 |69.36 |70.75 |70.80 |\n\nGood suggestions! We further evaluate the performances of  $\\alpha$-BN and IABN under different batch sizes. IABN performs poorly with both small and large batch sizes. $\\alpha$-BN also underperforms with large batch sizes, but shows improved performance when the batch size is 1, which is consistent with the principle of FIND.\n\nAcc (%) of CIFAR100-C, ResNet-50, BS changes in [1, 2,4, 8, 16, 64, 128]\n|         | 1     | 2     | 4     | 8     | 16    | 64    | 128   |\n|---------|-------|-------|-------|-------|-------|-------|-------|\n| IABN    | 25.58 | 26.23 | 26.38 | 26.04 | 26.00 | 26.03 | 25.80 |\n| $\\alpha$-BN | 35.50 | 33.70 | 33.02 | 33.46 | 33.47 | 33.22 | 33.01 |\n\nThanks again for your insightful suggestion. We will add the results in the revised version.\n\n>## **W2 (Combined with  test-time tuning)**\n\nWe appreciate this insightful suggestions, which helps to further explore the scalability of our method.\n\n **FIND is effective when combined with test-time tuning (with  2% improvement).** \n\nWe integrated FIND with the test-time tuning methods mentioned in our paper, and obtained the following conclusions: 1. Accurate normalization is a prerequisite for successful tuning (as stated in Conclusion 1 of Section 2.2). 2. Selectively updating layers that are insensitive to domain shift leads to greater gains. The table below shows results on CIFAR10-C， CrossMix scenarios:\n\n| FIND+TNET   | $\\alpha$ = 0.8 | $\\alpha$ = 0.4 | $\\alpha$ = 0      | $\\alpha$ = 1 |\n|-------------|:-----------:|:-----------:|:--------------:|:---------:|\n| $\\gamma$ = 0.1 |    72.01    |    70.15    | 67.93  |   71.03   |\n| $\\gamma$ = 0.06|    72.45    |    71.16    |   69.14        |   72.37   |\n\n| FIND+EATA   | $\\alpha$ = 0.8 |$\\alpha$ = 0.4 | $\\alpha$ = 0 | $\\alpha$ = 1 |\n|-------------|:-----------:|:-----------:|:---------:|:---------:|\n| $\\gamma$ = 0.1 |    72.20    |    69.98    |   67.39   |   71.14   |\n| $\\gamma$ = 0.06|    72.90    |    69.96    |   68.21   |   72.7    |\n\n| FIND+DeYO   | $\\alpha$ = 0.8 | $\\alpha$ = 0.4 | $\\alpha$ = 0 | $\\alpha$ = 1 |\n|-------------|:-----------:|:-----------:|:---------:|:---------:|\n| $\\gamma$ = 0.1 |    73.07    |    71.61    |   68.00   |   70.70   |\n| $\\gamma$ = 0.06|    73.17    |    72.31    |   69.97   |   72.25   |\n\nThanks again for your suggestion. We will incorporate this part in the revised version.\n\n\n>## **W3 (Compare FIND with more methods)**\n\nWe are grateful for the reviewers' suggestions. Analyzing and comparing these methods can help further highlight our contributions. \n\nOur initial selection of baselines encompassed a diverse and extensive collection of SOTA methods, with a total of 10 approaches included. To address your concerns, we have identified the following works as relevant to our discussion: COME (ICLR 2025)[1], UnMix-TNS (ICLR 2024) [2], DDA (CVPR 2023)|[3], REM (ICML 2025) [4], CoLA (NeurIPS 2024)  [5].\n\nThe results are shown in the table below. FIND consistently surpasses these methods by a large margin **(10%-15%)**. This further supports our conclusion that precise normalization plays a dominant role in effective TTA (Section 2.2, Conclusion 2).  \n\nCoLA [5] proposes a cross-device collaborative TTA paradigm, which achieves efficient TTA by sharing and aggregating domain knowledge vectors learned during adaptation across multiple devices.  BECoTTA [6] aims to enhance the resistance to catastrophic forgetting and adaptation efficiency in the CTTA process by introducing a Mixture-of-Experts (MoE) framework. DPCore [7] aims to address continual TTA under frequent and unpredictable target domain shifts, by preventing catastrophic forgetting and negative transfer during the adaptation process.  These methods differ significantly from ours in terms of motivation. Our work specifically targets the wild world setting with dynamic data streams—where the distribution diversity within each test batch changes arbitrarily—and the strict mixed-domain scenario. To address these issues, we propose a novel \"divide-and-conquer\" framework (automatic distribution-aware feature disentanglement).\n\n\nThanks again for your suggestions. we will add the descriptions and complete results of these newly given methods in the revised version. Some methods lack available code or are not compatible with our tasks or framework . We will also refer to and explain the differences in revised version. \n\nNote: The original DDA [3] paper only conducts experiments on IN-C and does not provide diffusion models for other datasets.\n\nAcc (%) of CrossMix, ResNet-50\n|           | COME [1] | UnMix-TNS [2] | DDA [3] | REM [4] | CoLA [5]  | FIND (Ours) |\n|-----------|----------|---------------|---------|---------|----------|-------------|\n| 10-C      | 60.48%   | 60.46%        | -       | 59.10%  | 62.00%     |71.54%      |\n| 100-C     | 29.76%   | 29.98%        | -       | 31.55%  | 32.52%    |40.48%      |\n| IN-C      | 16.66%   | 16.93%        | 26.10%  | 18.645% | 18.74%   |30.33%      |\n\n\n[1] COME: Test-time adaption by Conservatively Minimizing Entropy. ICLR 2025.\n\n[2] Un-Mixing Test-Time Normalization Statistics: Combatting Label Temporal Correlation. ICLR 2024.\n\n[3]  Back to the source: Diffusion-driven adaptation to test-time corruption. CVPR 2023\n\n[4] Ranked Entropy Minimization for Continual Test-Time Adaptation, ICML 2025.\n\n[5] Cross-Device Collaborative Test-Time Adaptation. NeurIPS 2024.\n\n[6] BECoTTA: Input-dependent Online Blending of Experts for Continual Test-time Adaptation. ICML 2024.\n\n[7] DPCore: Dynamic Prompt Coreset for Continual Test-Time Adaptation. ICML 2025.\n\n\n>## **W4 (Description of other work)**\n\nWe greatly appreciate this valuable suggestion, as it helps to further clarify and highlight the distinctions between our approach and existing methods.\n\n**We have analyzed related wild world approaches (e.g., SAR, NOTE) in Section 4 (Related Work) and compared them in our experiments**. In the revised version, we will also mention these works in the introduction. Compared to existing approaches, our core differences are as follows: \n\n-  Motivation: We consider **fully dynamic data streams and more stringent domain mixing**. Besides the CrossMix scenario—where each batch strictly includes 15 domains—we also construct dynamic scenarios (Random and Shuffle) where each batch may contain only a single domain or a varying number of domains (2–15). \n\n- Analysis: We provide a novel analytical perspective, redefining the roles of SBN and TBN in normalization from the viewpoint of domain-related and general features. \n\n- Method: We propose a **divide-and-conquer** normalization strategy for features within a batch—not addressed by previous methods. \n\n- Result: Our method achieves high performance and robustness across all tested scenarios.\n\n>## **Q1 (The result of FIND$*$ in Table 2)**\n\nWe thank the reviewer for this good question.\n\nWe have provided a sensitivity analysis of $\\gamma$ for Efficient-ViT in Appendix Fig. 11, and the conclusions are consistent with those for ResNet. Therefore, we did not include additional FIND* results in Table 2. We will add this content in the revised version, as shown in the table below:\n| $\\gamma$ = 0.1 | 10-C   | 100-C  | IN-C   |\n|:--------------:|:------:|:------:|:------:|\n| Cross          | 78.72% | 48.30% | 29.80% |\n| Random         | 79.61% | 49.10% | 31.17% |\n| Shuffle        | 79.60% | 48.89% | 31.24% |\n\n>## **Q2 (The measure standard in Table 3)**\n\nWe appreciate the reviewer for this question.\n\n As mentioned in line 321 in our paper,  in Tab. 3, we present the **accuracy of ImageNet-C** in the CrossMix setting after replacing the LFD module in our FIND with other clustering algorithms. For a detailed comparison of our advantages over other clustering algorithms, please refer to our response to Q4 of Reviewer u3eW. In addition to the inference accuracy on the dataset, we will provide visualizations of the clustering results produced by different clustering methods at various BN layers in the revised version."}, {"review_id": "10x9EQVJSM", "reviewer": "Reviewer_wnbc", "summary": "In this paper, authors consider test-time adaptation under a more complicated real-world scenario, where multiple distinct distributions may emerge simultaneously. This impose new challenges to previous test-time adaptation methods. Motivated by this, authors propose to  exploit the per-lay feature map similarity among test samples in the same mini-batch to construct graph structures. Afterwards, batch normalization is applied under the combination of source batch normalization (SBN) statistics and test-feature-specific-normalization (TFN) statistics, which are computed on a per graph connected component basis. This captures domain-specific feature distributions and also alleviates statistical bias in TFN estimations with the introduction of SBN statistics. In addition, to improve the computation efficiency, authors propose to dynamically determine which layer should be handled by graph partition, thus reducing unnecessary computation for layers insensitive to domain shifts. Empirical evaluation on ResNet and ViT models further proves the effectiveness of the proposed method.", "questions": "1. Section 2.4, Eq. (5) and Eq. (6). Based on my understanding, the feature aware batch normalization (FABN) is proposed to resolve the potential statistical bias in TFN estimations when the corresponding subset is small. Thus, the relative contribution of source batch normalization (SBN) should be dependent on the subset size, rather than fixed as a hyper-parameter $\\alpha$.\n2. Section 2.5, line 238. The selective feature aware batch normalization (S-FABN) relies on a cold-start phase to esimate the average score for each layer. What if the test distribution changes significantly after the cold-start phase? Will this leads to performance degradation?\n3. Sensitivity analysis of $\\alpha$, the trade-off coefficient between SBN and TFN, is missing.\n4. Section 3.6, Table 4. $\\alpha$-BN is not included in the comparison of memory and latency of different test-time adaptation methods.\n5. Section 3.7, Figure 7. The proposed method works well even under small batch size, which is quite interesting. For instance, with BS=1, the graph partition should have no effect completely, then why the proposed method still outperforms all the baseline methods?", "limitations": "Yes, limitations are provided in the appendix.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n* The test-time adaptation scenarios with multiple test distributions considered in the paper is well motivated and more closely-related to real-world settings. Authors identify the performance degradation of existing time-time adaptation methods under this setting, which naturally leads to the proposal of layer-wise feature disentanglement.\n* Authors also point out that not all the layers should be handled with similarity-based graph construction and feature-aware batch normalization. Instead, they propose to use the KL divergence to measure the shift between source and current target domains, which serves as the criterion for whether graph partition is needed for the current layer. This also leads to more efficient inference.\n\nWeaknesses:\n* Althought the selective feature aware batch normalization (S-FABN) is well motivated, the design of KL-divergence based criterion seems somehow problematic. Since graph partition is needed when there are multiple test distributions presented in a single mini-batch, then the criterion should reflect the distribution diversity among test samples, rather the difference between source and target domains.\n* Some experimental results are not thoroughly analyzed (please refer to subsequent questions for details). Besides, sensitivity analysis of $\\alpha$ and efficiency comparison against $\\alpha$-BN is missing.", "was_revised": true, "final_justification": "Authors have addressed my concerns in the rebuttal. Therefore, I will raise my rating accordingly.", "rebuttal": "## Thank you for acknowledging the motivation behind our work, the valuable analysis and insights, and the high efficiency of our methods. Your constructive feedback and suggestions provide great inspiration for our future exploration. Our response to your concerns is presented as follows.\n\n>## **W1 (The criterion of S-FABN)**\n\nThanks for  raising this important question!\n\n**We would like to clarify that the criterion in S-FABN is designed to measure intrinsic properties of the model itself and is independent of the input data**. Specifically, the criterion measures the discrepancy between source and target feature distributions at each layer, allowing us to assess the layer’s sensitivity to domain shift. A large discrepancy indicates that the layer is domain-sensitive, i.e., it focuses on domain-related features, and thus distribution-aware partitioning is required. In contrast, a small discrepancy indicates that the layer is domain-insensitive, i.e., it mainly captures generic features shared across domains, so partitioning can be skipped to improve **inference efficiency**.\n\nOur LFD (Section 2.3 in our paper) module already possesses automatic distribution diversity awareness. What we need now is a method to further improve efficiency (S-FABN). Our method is motivated by the challenge of handling data streams with various distribution diversity, for which we propose LFD—a mechanism that can automatically sense distribution diversity and perform feature partitioning. S-FABN is specifically designed to address the following issues encountered in LFD: 1. Do all BN layers in the model require LFD for distribution-aware feature partitioning? 2. Are there any layers that are insensitive to domain-related features (i.e., not affected by domain shift), such that the features in this layer are shared across both source and target domains (generic features)? If such layers exist, LFD is unnecessary for them and batch statistics can be computed directly over the entire batch, significantly improving efficiency.  **Therefore, we propose the criterion based on KL divergence in S-FABN to identify which layers focus on features that are similar between the source and target domains, thereby avoiding the additional overhead brought by LFD.**\n\nExperimental results: We evaluated on batches containing various numbers of  domains (Tab. 6 in the Appendix), as well as scenarios where the number of domains per batch varies randomly from 1 to 15 (Random and Shuffle in Tab. 1 & 2). Our LFD effectively **senses and partitions features** according to the degree of distribution diversity, achieving optimal performance.  Therefore, we do not need to continue designing indicators that can reflect distribution diversity.\n\nConclusion:  S-FABN identifies layers that are **insensitive to domain shift**, allowing us to skip LFD  for these layers and further improve efficiency.  Thank you again for raising this very valuable question. It touches on a key point of our paper.\n\n\n>## **Q1 (why $\\alpha$ is fixed)**\n\nWe thank the reviewer for this insightful question!\n\n **The setting of $\\alpha$ is almost imperceptible to the subset size.** SBN provides a comprehensive and robust distribution of generic knowledge (Section 2.2, line 164 in our paper), which is  clearer and more stable compared to TFN/TBN (Appendix K). Therefore, **SBN should be dominant in the combination**, while TBN/TFN mainly supply the  domain-related feature distribution. This can be simply formulated as:\n\n- **generic knowledge (SBN) + domain-related distribution (TFN/TBN) constructs complete distribution**.\n\n- Experimental results: We fix the $\\alpha$ of un-clustered layers to 0.8 and varying $\\alpha$ in clustered layers from [0, 0.2, 0.4, 0.6, 0.8, 1]. Under both **batch size = 64 and batch size = 512**, we consistently observe better performance when SBN dominates ($\\alpha > 0.5$). Notably, when $\\alpha = 1$, performance drops sharply, indicating that without any contribution from TFN, i.e., no domain-related distribution, the results are suboptimal.\n\n**BS = 64**, $\\alpha =0.8$ for Non-Clustered Layers (TBN+SBN) and changes in [0, 0.2, 0.4, 0.6, 0.8, 1] for Clustered Layers (TFN+SBN). $\\alpha$ represents for the weight of SBN\n| $\\alpha$ | 0    | 0.2  | 0.4  | 0.6  | 0.8  | 1    |\n|:--------:|:----:|:----:|:----:|:----:|:----:|:----:|\n| Acc/%    |57.48 |62.98 |66.81 |69.49 |70.75 |60.39 |\n\n**BS = 512**, $\\alpha =0.8$ for Non-Clustered Layers (TBN+SBN) and changes in [0, 0.2, 0.4, 0.6, 0.8, 1] for Clustered Layers (TFN+SBN). $\\alpha$ represents for the weight of SBN\n| $\\alpha$ | 0    | 0.2  | 0.4  | 0.6  | 0.8  | 1    |\n|:--------:|:----:|:----:|:----:|:----:|:----:|:----:|\n| Acc/%    | 59.28| 63.28| 66.90| 69.50| 71.15| 60.34|\n\nConclusion: **SBN needs to be dominant**, as it provides comprehensive and stable generic knowledge,  which is also **the primary reference during inference**. While TFN can offer relatively stable generic knowledge when the batch size is extremely large, in practice: \n\n- Batch size rarely exceeds 1e3. Even with a larger batch size, the statistics from TFN are still less comprehensive than those from SBN, which are computed over tens of thousands of training samples.\n\nThanks again for your excellent question! We will provide a detailed explanation of the choice of $\\alpha$ in the revised version.\n\n>## **Q2 (Is S-FABN affected by data distribution?)**\n\nThanks for raising this insightful question!\n\n **There is no performance degradation**. The Score measures the **intrinsic properties of different layers in the model** and is largely **independent of input data distribution changes**. Our tests have shown that certain layers are insensitive to domain shift—they focus mainly on generic features. For these layers, there is no need to perform distribution sensing or partitioning on the input batch; changes in the domain of input samples do not affect them, as these layers attend to the **invariant, generic features**. \n\nTest results:  Fig. 10e in  appendix demonstrates this point: we measured the average Score after **3, 10, and 100 cold-start batches**, where the distributions in each batch during cold start were **all different**. The Score distributions of each layer are **nearly identical** in all three cases. Conclusion: **The Score reflects the intrinsic characteristics of model layers and is not influenced by distribution variation**.\n\n>## **Q3 (Ablation study on $\\alpha$)**\n\nWe appreciate the reviewer’s constructive suggestion. We will add the results in the revised version.\n\nWe conducted two sets of ablation studies on $\\alpha$ with $\\gamma = 0.1$, separately for clustered and non-clustered layers. In both cases, **performance is better when the SBN ratio is higher (>0.5)**. Clustered layers are sensitive to the SBN ratio **(13% change in accuracy)**, while non-clustered layers are not **(3% change)**.  \n\n- Conclusion 1: **The generic knowledge (SBN) dominates during inference.**\n\n- Conclusion 2: The sensitivity to $\\alpha$ is much more pronounced in layers requiring clustering than in those where clustering is unnecessary. Because TFN only provides domain-specific distributions with **limited** general knowledge distributions (as discussed in Section 2.2, Conclusion 4). \n\n- Conclusion 3: The general knowledge distribution captured by SBN is more comprehensive than that of TFN/TBN (as discussed in Section 2.2 and Appendix K).\n\n$\\alpha =0.8$ for Non-Clustered Layers (TBN+SBN) and changes in [0, 0.2, 0.4, 0.6, 0.8, 1] for Clustered Layers (TFN+SBN). $\\alpha$ represents the weight of SBN\n| $\\alpha$ | 0    | 0.2  | 0.4  | 0.6  | 0.8  | 1    |\n|:--------:|:----:|:----:|:----:|:----:|:----:|:----:|\n| Acc/%    |57.48 |62.98 |66.81 |69.49 |70.75 |60.39 |\n\n$\\alpha =0.8$ for Clustered Layers (TFN+SBN) and changes in [0, 0.2, 0.4, 0.6, 0.8, 1] for Non-Clustered Layers (TBN+SBN). $\\alpha$ represents  the weight of SBN\n| $\\alpha$ | 0    | 0.2  | 0.4  | 0.6  | 0.8  | 1    |\n|:--------:|:----:|:----:|:----:|:----:|:----:|:----:|\n| Acc/%    |67.20 |67.47 |68.29 |69.36 |70.75 |70.80 |\n\n>## **Q4 (The efficiency of $\\alpha$-BN)**\n\nWe greatly appreciate your valuable suggestion, which will make our comparison more comprehensive！\n\nThe efficiency of $\\alpha$-BN is consistent with that of TBN, we have provided the efficiency of TBN in Tab. 4 in paper. $\\alpha$-BN only adds an interpolation step on top of TBN, whose computational overhead is negligible. We will supplement it in the revised version. \n\n>## **Q5 (Why our method  works well when batch size is small)**\n\nWe appreciate your insightful question！\n\nBenefiting from our FABN module, when there is only a single sample in the batch, the sample can still provide domain-related distributions without interference from other domains. Meanwhile, SBN provides a stable and comprehensive general feature distribution. As a result, our method ensures stable inference even when bs = 1.\n\n- Why is baseline methods poor: 1. These methods are based on TBN. When the batch size is small, they do not have **stable generic knowledge (whereas we do)**. 2. Without accurate normalization, continued fine-tuning can further exacerbate model collapse.\n\n-  Why is our method good:  Setting bs = 1 is equivalent to having only one sample per cluster, where the TFN statistics degenerate to the feature statistics of that single sample (i.e., IN). At the same time, we introduce SBN to provide generic knowledge. IN of  the single simple is not affected by other domains. But the domain-related feature statistics are also less accurate due to the small sample size. Therefore, for low-resolution samples (10-C), the performance of bs = 1 is similar to bs = 128 (**a special case**). For higher-resolution samples (100-C, IN-C), the performance of bs = 1 remains stable (still outperforms other methods compared in our paper) but is inferior to bs = 128 (**the general case**)."}, {"review_id": "uJkE1uvhbd", "reviewer": "Reviewer_4ioQ", "summary": "The paper proposes FIND, a novel test-time adaptation method designed for dynamic scenarios where test samples may come from multiple distributions. FIND addresses the limitations of existing normalization strategies by introducing a divide-and-conquer approach, comprising Layer-wise Feature Disentanglement (LFD) to partition features, Feature Aware Batch Normalization (FABN) to combine source and test-specific statistics, and Selective FABN (S-FABN) to enhance efficiency. Extensive experiments on benchmark datasets demonstrate FIND's superior performance, achieving significant accuracy improvements over state-of-the-art methods while maintaining computational efficiency.", "questions": "Please refer to the Weaknesses.", "limitations": "N/A", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. The paper introduces a novel divide-and-conquer normalization approach tailored for dynamic scenarios, effectively addressing the issue of interference between different distributions and leading to a 30% accuracy improvement in dynamic scenarios compared to existing methods.\n2. FIND demonstrates robust performance across various architectures and datasets, achieving superior results on both convolutional networks and transformer-based models while maintaining consistent accuracy regardless of batch size.\n3. FIND achieves significant computational efficiency with low memory usage and fast inference speed, making it highly practical for real-world deployment.\n\nWeaknesses:\n1. The experiments are conducted on a limited set of benchmark datasets (CIFAR10-C, CIFAR100-C, and ImageNet-C). While these datasets are widely used, they may not fully capture the diversity of real-world distribution shifts. Evaluating FIND on a broader range of datasets could provide a more comprehensive assessment of its robustness and effectiveness.\n2. The cold-start phase, which involves computing the average sensitivity score for each layer, may introduce additional computational overhead at the beginning of the adaptation process. This could be a drawback in scenarios where rapid adaptation is required.\n3. How does the proposed method perform on larger models with high-dimensional feature spaces? Whether the computational complexity of the layer-wise feature disentanglement and selective normalization becomes prohibitive?\n4. More related methods should be discussed or compared in the manuscript for a comprehensive analysis, including but not limited to [A-D].\n\nMinor issues:\n1. In Eqn.(1), \\sum_L  F_{i;c;L} should be \\sum_{l=0}^L F_{i;c;l}.\n2. In line 193, F_{j;c;L} is not mentioned in any equation.\n\nReferences:\n[A] Ranked Entropy Minimization for Continual Test-Time Adaptation, ICML 2025.\n[B] Uncertainty-Calibrated Test-Time Model Adaptation without Forgetting, TPAMI 2025.  \n[C] Test-Time Model Adaptation for Visual Question Answering With Debiased Self-Supervisions, TMM 2023.\n[D] COME: Test-time adaption by Conservatively Minimizing Entropy, ICLR 2025.", "was_revised": true, "final_justification": "The authors' rebuttal has addressed my concerns, and I will maintain my positive scores.\n\nResolved issues: More experiments about different datasets, TTA settings, Efficiency\n\nUnresolved issues: none", "rebuttal": "## We sincerely appreciate your recognition of the novelty, effectiveness, and robustness of our method, as well as its high efficiency and practical value. We greatly value your constructive feedback. Our response to your concerns is as follows.\n\n>## **Q1 (Use more dataset to evaluate)**\n\nWe sincerely appreciate the reviewer’s suggestion, which further demonstrates the effectiveness of our approach.\n\nWe adopted evaluation benchmarks from several classic TTA methods (e.g., TENT) as well as wild world TTA methods (e.g., SAR), namely CIFAR10-C, CIFAR100-C, and ImageNet-C. These three datasets are sufficient to effectively reflect the performance of different methods in dynamic data streams and mixed domain scenarios. **High extensibility to other datasets**: Our method is also eadily extensible to other datasets, and we provide two examples here.  We will provide the complete test results on as many datasets as possible in the revised version.\n\n- Style transfer-based dataset ImageNet-R [1]: ImageNet-R reflects **style shift**, where images are transformed from real photographs into various artistic styles (e.g., cartoons, sketches, etc.). Such shifts mainly affect low-level features such as edges and textures, resulting in milder perturbations compared to typical corruptions. Our FIND method  **achieves state-of-the-art performance**, with improvements of **3%-13%** over existing methods. \n\n- Human-made corruption dataset ImageNet-$\\overline{C}$ [2]:  Compared to ImageNet-C, ImageNet-$\\overline{C}$ includes a large variety of human-designed corruptions, such as **Blue Noise, Plasma Noise, and Caustic Refraction**. This allows for a more thorough evaluation of model robustness against structured, frequency-related, and complex synthetic corruptions. Our FIND method still **achieves the best results**, outperforming the previous SOTA by **2.5%-17%**.\n\n| Method            | Source | $\\alpha$-BN | IABN  | TBN   | TENT  | EATA  | SAR   | DeYO  | ViDA  | RoTTA | NOTE  | FIND (Ours) |\n|-------------------|---------------|-------------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------------|\n| **ImageNet-R**                | 27.94         | 31.60      | 21.63 | 31.12 | 31.36 | 31.65 | 31.22 | 32.05 | 31.12 | 30.78 | 21.20 | 34.74       |\n| **ImageNet-$\\overline{C}$**   | 33.78         | 38.01      | 23.35 | 38.63 | 38.69 | 39.00 | 37.90 | 38.42 | 38.49 | 39.62 | 24.48 | 41.91       |\n\n[1] The many faces of robustness: A critical analysis of out-of-distribution generalization. ICCV 2021.\n\n[2] On interaction between augmentations and corruptions in natural corruption robustness. NeurIPS 2021.\n\nWe will include evaluation results on these datasets in the revised version.  We would like to express our sincere gratitude once again for the valuable suggestions from the reviewer.\n\nExtended explanation：CIFAR10-C, CIFAR100-C, and ImageNet-C contain 15 types of common real-world corruptions, which can be mapped to four phenomena frequently encountered in practice: **noise (affecting the entire image at the pixel level), weather (affecting local or global areas), digital artifacts (affecting pixel blocks, color areas, or the whole image), and blur (affecting edges and details)**. These are caused by real-world factors such as signal interference, changing weather conditions, image compression, motion blur, or defocus during photography, making them highly representative of wild-world scenarios. Such corruptions impact the overall visual quality and introduce domain shift. In our paper, we follow prior works exploring wild-world settings (e.g., SAR) to evaluate our method on these three datasets. We find that these datasets are **particularly challenging** in the dynamic and CrossMix scenario, as corruptions affect the entire image in diverse ways, further intensifying covariate shift. Therefore, to best demonstrate the realism and practical significance of our scenario, we adopt these three datasets.\n\n\n>## **Q2 (Overhead of cold-start)**\n\nWe believe the question you raised is highly valuable. We will add the results in the revised version. Thanks for your good suggestions.\n\n **The time overhead introduced by the cold-start (CS) phase is negligible.** 1. The time complexity of the cold-start  is linear with channels $C$ and the number of BN layers $N$, i.e., $O(CN)$, resulting in extremely low computational cost. 2. The computation is performed in parallel with the forward pass, incurring no extra inference or training steps. The following table presents the test results with and without the cold-start phase:\n\n| Model      | With CS   | Without CS |\n|:----------:|:---------:|:----------:|\n| ResNet-50  | 0.20728 s | 0.20728 s  |\n\n>## **Q3 (Efficiency of FIND)**\n\nThanks for raising this important question.\n\n **FIND remains highly efficient even in high-dimensional models.** \n\n- Time Complexity: The main overhead comes from the first neighbor search, which is $O(B^2 n C)$, where $B$ is the batch size, $n$ is the number of clustering layers ($n \\ll N$, $N$ is the total number of BN layers), and $C$ is the number of channels. With nearest-neighbor algorithm optimization, this can be further reduced to $O(B \\log B n C)$. \n\n- Conclusion: **The time cost scales linearly with $C$ and $n$.** \n\n- Empirical Results: When the number of BN layers is increased by **2.5$\\times$ (From 53 to 135)**, the inference time increases by only **50% (From  0.16s to 0.24s)**. For further improvement, we can set $\\gamma$ to 0.2, which further increases inference efficiency **(20% improvement)** while incurring negligible performance loss (around 1%).\n\n| Efficient-ViT           | Time/s | ResNet-50           | Time/s |\n|:-----------------------:|:------:|:-------------------:|:------:|\n| All Layers 135/135      | 0.41   | All Layers 53/53    | 0.21   |\n| $\\gamma$ = 0.1  (60/135)   | 0.24   | $\\gamma$ = 0.1  (38/53)| 0.16   |\n| $\\gamma$ = 0.2  (38/135)   | 0.20   | $\\gamma$ = 0.2  (17/53)| 0.13   |\n\n>## **Q4 (Compare FIND with more methods)**\n\nThanks for this good suggestions. We will include a discussion of these methods in the revised version and conduct comparative experiments.\n\nOur initial selection of baselines encompassed a diverse and extensive collection of SOTA methods, with a total of 10 approaches included. To address your concerns, we have identified the following works as relevant to our discussion: COME (ICLR 2025)[1], UnMix-TNS (ICLR 2024) [2], DDA (CVPR 2023)|[3], REM (ICML 2025) [4], CoLA (NIPS 2024)  [5].\n\nThe results are shown in the table below. Our FIND consistently surpasses these methods by a large margin **(10%-15%)**. This further supports our conclusion that precise normalization plays a dominant role in effective TTA (Section 2.2, Conclusion 2).  \n\nNote: The original DDA paper only conducts experiments on IN-C and does not provide diffusion models for other datasets.\n\nAcc (%) of CrossMix, ResNet-50\n|           | COME [1] | UnMix-TNS [2] | DDA [3] | REM [4] | CoLA [5]  | FIND (Ours) |\n|-----------|----------|---------------|---------|---------|----------|-------------|\n| 10-C      | 60.48%   | 60.46%        |   -       | 59.10%  | 62.00%     |71.54%      |\n| 100-C     | 29.76%   | 29.98%        |  -       | 31.55%  | 32.52%    |40.48%      |\n| IN-C      | 16.66%   | 16.93%        | 26.10%  | 18.645% | 18.74%   |30.33%      |\n\nFIND is an efficient and effective method for handling dynamic and mixed data streams. Our \"divide-and-conquer\" normalization strategy is novel and enables FIND to effectively capture distribution diversity and perform feature partitioning.\nThanks again for your valuable suggestions. We will add the descriptions and complete results of these newly given methods in the revised version. Some methods are not compatible with our tasks or framework, or have not released their code. We will also refer to and explain the differences in revised version. \n\n[1] COME: Test-time adaption by Conservatively Minimizing Entropy. ICLR 2025.\n\n[2] Un-Mixing Test-Time Normalization Statistics: Combatting Label Temporal Correlation. ICLR 2024.\n\n[3]  Back to the source: Diffusion-driven adaptation to test-time corruption. CVPR 2023\n\n[4] Ranked Entropy Minimization for Continual Test-Time Adaptation, ICML 2025.\n\n[5]  Cross-Device Collaborative Test-Time Adaptation. NIPS 2024."}, {"review_id": "mDnB6Q0at4", "reviewer": "Reviewer_dD3f", "summary": "This paper proposes FIND, a method for dynamic test-time adaptation where test batches contain mixed distributions. FIND combines feature-based clustering (LFD), adaptive batch normalization (FABN), and selective application (S-FABN) to improve robustness under distribution shifts. Experiments show gains in accuracy and efficiency compared to existing TTA methods.", "questions": "1. Comparison with DDA: The proposed setting seems closely related to DDA. Could the authors provide a direct experimental comparison with DDA under the same evaluation protocol? Additionally, a more detailed discussion distinguishing the problem settings and assumptions would help clarify the novelty of this work.\n2. Generality Across Architectures: The current experiments are limited to ResNet-50. Have the authors tested the proposed method on other network architectures such as ViTs or ConvNeXt? Demonstrating consistent performance improvements across diverse model families would enhance the method’s perceived robustness and practical utility.", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "## Strengths\n1. The paper is well written, with clear explanations that make the technical content accessible. The logical flow and precise language enhance the overall readability.\n2. The visualizations, including figures and tables, are carefully designed and effectively support the narrative. They provide clear and intuitive illustrations of the proposed method and its empirical results.\n\n\n## Weaknesses\n1. The problem setting considered in this work appears closely related to DDA [1]. While DDA is cited in the introduction, the paper does not provide a direct empirical comparison against DDA, nor does it offer a thorough discussion clarifying the differences between the two settings. This omission makes it difficult to precisely assess the novelty and contributions relative to existing work.\n2. The experimental validation is limited to ResNet-50. The lack of evaluation on a broader range of network architectures raises concerns regarding the generalizability and robustness of the proposed method across different model backbones.\n\n[1] Gao J, Zhang J, Liu X, et al. Back to the source: Diffusion-driven adaptation to test-time corruption[C]//Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2023: 11786-11796.", "was_revised": true, "final_justification": "My recommendation is to Accept.\n\nI thank the authors for their detailed rebuttal. The responses have successfully addressed the main concerns and questions I raised in my initial review.\n\nResolved issues: differences between DDA and the work, generality across architectures\n\nUnresolved issues: none", "rebuttal": "## Thank you for recognizing the well-organized structure and clear logic of our paper, as well as your acknowledgment of the supportive illustrations and empirical results. Your suggestions are helpful for us to further clarify our core contributions. Our response to your concerns is presented as follows.\n\n>## **Q1 (Clarify differences between DDA and our work)**\n\nWe are extremely grateful to the reviewer for this valuable suggestion, which will help us further distinguish our work from others.\n\n**There are significant differences between our FIND  and DDA [1]. We have sufficient innovation in motivation, methods and analysis.** We will describe in detail below.\n\n**DDA focuses on shifting from model adaptation to input data adaptation, with the core motivation of avoiding frequent updates to the model itself during TTA and instead directly adapting the input data to prevent model collapse**. To this end, DDA introduces an additional diffusion model for denoising samples while keeping the original model unchanged. Although DDA also evaluates the mix domain scenario in its experiments, this is primarily to demonstrate the robustness of the method, rather than being the main focus of the paper.\n\nIn contrast, our motivation lies in **addressing dynamic data streams and strict mix domain scenarios in the wild world**, which are fundamentally different from the static settings commonly assumed in traditional TTA. Our goal is to enhance inference performance and robustness in real-world environments. To this end, we construct a variety of dynamic scenarios simulating data distributions in the wild, including 1. strict mix domain, where each input batch contains samples from multiple different domains (up to 15), and 2. dynamically changing distributions, where the distribution diversity in each batch varies randomly (with the number of domains ranging from 1 to 15). To address these challenges, we propose a novel \"divide-and-conquer“ normalization framework. Unlike traditional normalization methods that process the entire batch as a whole, our approach can automatically perceive distribution diversity within a batch and achieve layer-wise feature disentanglement.\n\nFurthermore, we examine different normalization schemes from the perspective of both general features and domain-related features, leading to several novel conclusions (see Section 2.2 and Appendix K) that are not provided by DDA.\n\nOther differences of DDA compared with us:  1. DDA operates on a per-sample basis: even if a full batch is provided as input, each sample is denoised independently by the diffusion model. As a result, batch processing does not offer any additional algorithmic benefit beyond potential hardware-level parallelism. 2. DDA introduces additional diffusion models and requires multiple data forward passes, resulting in significant inference overhead.  3. Training the diffusion model requires large amounts of source data, which is inconsistent with TTA assumptions.  In contrast, our method offers greater scalability across different batch sizes and achieves efficient inference without relying on additional models or extra training and forward processes.\n\nAs shown in the table below, our method outperforms DDA, achieves **high efficiency (requiring only 1% of DDA's time cost)**. We will provide additional explanation of the differences between DDA and our method, and include these results in the revised version. We thank the reviewer for raising this important point.\n\n|        | FIND         | DDA            |\n|:------:|:------------:|:--------------:|\n| Acc/%  | 30.33        | 26.10          |\n| Efficiency | 0.15s/1.21GB | 19.83s/12.88GB |\n\n[1]  Back to the source: Diffusion-driven adaptation to test-time corruption. CVPR 2023.\n\n>## **Q2 (Generality Across Architectures)**\n\nThank you for raising this important question!\n\n**We have provided evaluations on different architectures in the paper.** In our experiments, we provide two general architectures: CNN-based models (ResNet-50, ResNet-26) and  ViT-based models (Efficient-ViT). The results are reported in Tab. 1 and Tab. 2 of the main paper, as well as Tab. 7 in the appendix. Our method demonstrates strong generalizability and plug-and-play flexibility on different architectures. \n\nThanks again for your valuable feedback！We will emphasize these tests in the revised version."}]

Author rebuttal:

Meta-review: All reviewers have reached a consensus to accept this paper. After carefully reading the manuscript, the reviews, and the author rebuttal, I agree with this assessment. The paper addresses test-time adaptation under dynamic, mixed-distribution scenarios by proposing a novel divide-and-conquer normalization framework (FIND), which includes Layer-wise Feature Disentanglement (LFD), Feature-Aware Batch Normalization (FABN), and Selective FABN (S-FABN). The method is well-motivated, technically sound, and empirically validated across diverse architectures and datasets. The authors provided thorough responses during the rebuttal, clarifying key differences from related work, adding new ablations and comparisons, and demonstrating generalizability. I recommend acceptance and encourage the authors to further polish the paper and incorporate the reviewers' suggestions in the camera-ready version.
Decision: Accept (poster)