IMSE: Intrinsic Mixture of Spectral Experts Fine-tuning for Test-Time Adaptation
Authors: Sunghyun Baek
Jaemyung Yu
Seunghee Koh
Minsu Kim
Hyeonseong Jeon
Junmo Kim
Venue: ICLR 2026 Poster (2026)
Keywords: test time adaptation
continual learning
Primary area: transfer learning, meta learning, and lifelong learning
TL;DR: We propose a test-time adaptation method that leverages the intrinsic spectral structures of pretrained Vision Transformers, addressing underexplored challenges in both TTA and CTTA.

Abstract: Test-time adaptation (TTA) has been widely explored to prevent performance degradation when test data differ from the training distribution.
However, fully leveraging the rich representations of large pretrained models with minimal parameter updates remains underexplored.
In this paper, we propose Intrinsic Mixture of Spectral Experts (IMSE) that leverages the spectral experts inherently embedded in Vision Transformers. 
We decompose each linear layer via singular value decomposition (SVD) and adapt only the singular values, while keeping the singular vectors fixed.
We further identify a key limitation of entropy minimization in TTA: it often induces feature-collapse, causing the model to rely on domain-specific features rather than class-discriminative features.
To address this, we propose a diversity maximization loss based on expert–input alignment, which encourages diverse utilization of spectral experts during adaptation.
In the continual test-time adaptation (CTTA) scenario, beyond preserving pretrained knowledge, it is crucial to retain and reuse knowledge from previously observed domains. We introduce Domain-Aware Spectral Code Retrieval, which estimates input distributions to detect domain shifts, and retrieves adapted singular values for rapid adaptation.
Consequently, our method achieves state-of-the-art performance on various distribution-shift benchmarks under the TTA setting.
In CTTA and Gradual CTTA, it further improves accuracy by 3.4 percentage point (pp) and 2.4 pp, respectively, while requiring 385 times fewer trainable parameters. 
Our code is available in https://github.com/baek85/IMSE.

Published as a conference paper at ICLR 2026
IMSE: INTRINSIC MIXTURE OF SPECTRAL EXPERTS FINE- TUNING FOR TEST-TIME ADAPTATION
Sunghyun Baek'
Jaemyung Yu!
Seunghee Koh Junmo Kim
Minsu Kim?
Hyeonseong Jeon?
Korea Advanced Institute of Science and Technology (KAIST)
2LG Energy Solution
(baeksh, jaemyung, seunghee1211 (all1115)kkkiseeeomm kr [mskim04]) 410, cutz) @
( gensol com, junmo. kim@kaist.ac. ac.
ABSTRACT
Test-time adaptation (TTA) has been widely explored to prevent performance degradation when test data differ from the training distribution. However, fully leveraging the rich representations of large pretrained models with minimal param- eter updates remains underexplored. In this paper, we propose Intrinsic Mixture of Spectral Experts (IMSE) that leverages the spectral experts inherently embedded in Vision Transformers. We decompose each linear layer via singular value de- composition (SVD) and adapt only the singular values, while keeping the singular vectors fixed. We further identify a key limitation of entropy minimization TTA: it often induces feature-collapse, causing the model to rely on domain-specific features rather than daas-discrrmminttiee features. To address this, we propose diversity maximization loss based expert-inpe alignment, which encour- ages diverse utilization of spectral experts during adaptation. In the continual test-time adaptation (CTTA) scenario, beyond preserving pretrained knowledge, it is crucial to retain and reuse knowledge from previously observed domains. We introduce Dowain-Aware Spectral Code Retrieval, which estimates input distri- butions to detect domain shifts, and retrieves adapted singular values for rapid adaptation. Consequently, our method achieves state-of-the- thr---r performance on various distribution-shi benchmarks under the TTA setting. In CTTA and Grad- ual CTTA, further improves accuracy by 3.4 percentage point (pp) and 2.4 pp. respectively, while requiring 385 times fewer trainable parameters. Our code is available in httph:://///.m /ttp:::///hhbbb wwwptthww...oooo..eeeeeeeeeeeeee com hawon//aaa8///// IMSE IMSSE
INTRODUCTION
Real-world data often deviates from the training distribution, leading to performance degradation in deployed models. Test-time adaptation (TTA) mitigates this distribution shift by adapting a source- pretrained model to unseen target domains in online manner, without access to the source data. However, TTA is prone to forgetting task-relevant knowledge as adaptation progresses under continu- ously shifting data distributions. To address this more realistic scenario, TTA has been extended to continual test-time adaptation (CTTA). Existing approaches differ mainly in the extent of parameter updates. Some methods restrict adaptation normalization statistics affine parameters (Ioffe & Szegedy 2015 Wang et al., 2020 Niu et al. (022), ensuring stability and efficiency but limiting adaptation capacity. Others allow broader parameter updates or introduce lightweight architectural components such as prompts or adapters (Wang et al., 2022; Yu et al.) 2024 Tang et al.) 2024 Liu et al. 2024), improving flexibility at the risk of error accumulation, catastrophic forgetting, or additional inference overhead.
We identify three key limitations in existing TTA and CTTA methods. First, how to fully exploit the rich representational capacity inherent in large pre-trained models remains underexplored. Second, label-free TTA scenarios, entropy minimization often leads the model to exploit domain-cpecific
"Correspondence Junmo Kim (jummo kim @ krr)t..c.kr).

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Published as a conference paper at ICLR 2026
features rather than class disermmiiiiiii features, thereby degrading performance. Third, in CTTA settings, it is crucial not only to preserve pretrained knowledge but also to retain information from previously encountered domains. However, efficient methods for preserving such domain-specife knowledge is not yet well addressed.
To handle(or address) those limitations, propose Intrinsic Mixture of Spectral Experts (IMSE) with three components: (1) Intrinsic mixture of spectral experts: we decompose each linear layer via SVD and interpret the resulting rank-1 components spectral experts with distinct functional roles. From this perspective, linear layer can be reinterpreted as an intrinsic mixture of spectral experts, where the singular values correspond the contribution of each expert. We adapt only the singular values while keeping the orthogonal bases fixed, to utilize the pretrained feature extractors. (2) Diversity maximization loss: we maximize diversity of response patterns of spectral experts, ensuring that the model does not over-extract domain-specifer features during adaptation, even in the absence of labels. (3) Domain-awan spectral code retrieval: we explicitly preserve and reuse domain knowledge by storing adapted singular values together with domain descriptors in domain bank, thereby mitigating domain knowledge forgetting in CTTA.
We demonstrate IMSE under TTA, CTTA, and Gradual CTTA setting. Experiments with MAE (e ct al. 2022) and CLIP (Radford et al. 2021) further show its generalization ability in the TTA setting. Furthermore, it achieves superior performance over CTTA baselines with significantly fewer trainable parameters and faster runtime.
Our main contributions are summarized as follows:
We propose IMSE, TTA framework that reinterprets linear layers of pretrained models as intrinsic mixture of spectral experts. By fine-tuning only singular values, IMSE enables parameter-efficient adaptation while preserving the pretrained feature extractors.
We introduce diversity maximization loss that compensates for feature collapse caused by entropy minimization, ensuring that pretrained feature extractors are effectively utilized even in the absence of labels.
We design a domain- aware spectral code retrieval mechanism to mitigate domain knowledge forgetting, enabling rapid adaptation in continual test-time adaptation.
We proivde state-of-the-ar performance in TTA, CTTA, and Gradual CTTA settings and is further validated on diverse pretrained models, including MAE and CLIP, under the TTA setting.
2 RELATED WORK
Test-time adaptation. To preserve the glass-discriminative capability of pretrained models during adaptation in classification tasks, various methods optimize different sets of parameters and conse- quently adopt different objective functions. Early approaches based on entropy minimization avoid data augmentation and use only the predictions the current test data to define the loss. TENT (Wang
et al. 2020) fine-tunes only the modulation parameters of the Batch Normalization (Toffe & Szegedy
2015) layer to minimize prediction entropy. Building this idea, EATA (Niu et al. [022) improves
stability by filtering out unreliable high-entropy samples, while SAR (Niu et al. 2023) incorporates sharpness-aware optimization for more stable adaptation. Other works introduce pseudo-label refine- ment techniques that leverage the average of predictions obtained from multiple data augmentations and use an Exponential Moving Average (EMA) updated teacher model to further stabilize train- ing. This strategy is typically employed in approaches closer to full parameter fine-tuning, such as COTTA (Wang et al., 2022) and ViDA (Liu al. 2024). Other lines of research (Tang al. 2024, Lee et al. 2024)) keep most of the backbone intact while introducing architectural modifications, for example by inserting lightweight modules such as adapters or domain-specific tokens.
Singular Value Fine-tuning. Recent studies exploit singular-value fine-tuning for parameter- efficient fine-tuning of large models, such as SVFT (Lingam et al. 2024) and SVDiff (Han et al.) 2023), which update only the singular values of decomposed layers of a Large Language Model (LLM) and Diffusion Model, respectively. Other works, including PiSSA (Meng et al. 2024) and MiLoRA (Wang et al. 2025). leverage singular value decomposition (SVD) to improve low-rank Adaptation (LoRA) (Hu al. 2022) initialization for LLM fine-tuning.
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Initialize singular values
similarity
bank
Finetune
Linear Inyers
layers
U
V
Σ
V
Denain
Speceal code
Append
Figure I: RMSE-Retrieval with domain bank. When adapting to new domain, we select initial singular values based on domain similarity using the domain descriptor, then fine-tune the com- ponents within linear layers. The adapted spectral code S is stored in the Domain Bank, and this process repeats for subsequent domains. Note that domain descriptors are designed estimate the distribution of test data.
Our method not only fine-tunes the singular values of linear layers for test-time adaptation, but also maximizes feature diversity using singular vectors, and introduces retrieval mechanism that reuses the adapted singular values for continual test-time adaptation.
3 INTRINSIC MIXTURE OF SPECTRAL EXPERTS
We propose Intrinsic Mixture of Spectral Experts (IMSE) that adapts pretrained models to the current domain while preserving the independent base extractors intrinsically obtained during pretraining. To compensate for the reduction of feature diversity caused by entropy minimization, we introduce a diversity maximization loss that encourages diverse utilization of spectral experts. In addition, introduce Domain-Awee specific adapted singular values. This retrieval process enables stable and faster adaptation process using the most relevant spectral code. The overall framework of ASSE-Retrieval, which includes the retrieval process, is illustrated in Figure
Spectral Code Retrieval, a mechanism that preserves and reuses domain-
3.1 INTRINSIC MIXTURE SPECTRAL EXPERTS
Spectral experts and spectral code. We adapt the model by applying SVD to each linear layer, thereby adjusting the degree of contribution of diverse pretrained feature extractors to the final output.
Given a linear transformation W(!) with output dim of all) and input dim of
d in the I-th layer, 20 xn(!) diagonal
SVD factorizes a (r)) matrix W() into a left singular vector matrix UO)) E
matrix of singular values { Re x)()) and right singular vector matrix V()) R
This decomposition is formally expressed as:
500
w U EVO
10
10 OT
where each rank-1 component is defined by orthonormal basis vectors u and v, and scaled by the singular value o which is non-negative and sorted in non-increasing order.
We refer to the subset these rank-1 components u, as an i-th spectral expert and define the spectral code as the set of singular values across all L layers, represented as follows:
S (=
An input vector (!) is projected by each spectral expert through orthogonal bases u the singular vectors are mutually orthogonal, the outputs from different experts are also orthogonal,
( and (((), Since
ie., (u)) ( x( ()) ( (u)) (9) x))) for i j.
We regard the linear layer as a mixture of ( spectral experts that generate orthogonal outputs given the same input. Based the interpretation that singular values determine each spectral expert's contribution weight, we adapt the model to new domains by updating only the singular values while freezing the singular vectors. Fine-tuning singular values not only allows preserving the subspace of
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W but also leverages the rich feature extractors that pretrained models have already acquired from diverse training data.
Expert-Input alignment statistics. The output direction of each spectral expert is determined by the fixed left singular vector ( T
(1); while its response strength to an input x is given by the
scalar (3) (c) Xn. In TTA, entropy minimization induces feature collapse, where only subset of experts is dominantly activated, causing the model to focus on domain-specific rather than class- discriminative features. To quantify this collapse, we introduce expert-input alignment statistics measuring how strongly each expert responds to the test data.
Given samples with T tokens in batch, yiclding = x T input vectors, let the alignment of w x
n-th input vector x! E TR% with each right singular vector vi as a nnd | la
which isolates
the directional alignment from the magnitude. Based on this, we define two alignment-basee statistics per expert:
N
(1)
Std
1 N
(1) 22
3. )
N
Here, T. measures the mean of the i-th expert across input tokens, while Std.") quantifies the utilization diversity, indicating how differently the expert responds to different tokens. Low Std.") suggests that the expert captures domain-specific patterns shared across tokens within the batch.
Diversity Maximization Loss.
We propose a diversity maximization loss that encourages the model to generate diverse features by using expert-input alignment statistics
am = Σ
Std
LE
where Aam is set of selected layers, and ((() is the number of experts in layer 1. We choose the latter layers as the elements of Aam since the diversity pattern tends to decrease layers closer the classification head. We provide related anlaysis in Appendix [
Optimization. We optimize the spectral code using an entropy minimization objective Centmin incorporating entropy-based sample filtering as in SAR (Niu et al. 2023).
The objective aims to minimize the prediction entropy H())= = - Σ. (())) p(je), where x an input sample of the test domain, ý f(x) is the model prediction, and p(ūc) denotes the predicted probability of class c. The full entropy minimization loss is defined as Cemmin (x) = [(xx((x)) (g). where S(x) is the sample selection function that identifies reliable samples, such as low-entropy samples. The indicator function I[(-) masks out uncertain samples.
We jointly use the entropy minimization and diversity maximization objectives as follows:
LIMSE
Lentmin + Aam Lam-
(5)
We also adopt Sharpness-Awar Minimization (Foret et al. 2021 to enhance stability, following
SAR (Niu et al. 2023). Further details are provided in Appendix A
3.2 DOMAIN-AWARE SPECTRAL CODE RETRIEVAL
Fine-tuning only the singular values yields a compact spectral code that succinetly captures domain- specific knowledge. We exploit compactness of the spectral code in IMSE-Retrieval, which retrieves stored spectral codes from past domains to enable fast adaptation to new test-time domains in CTTA. To represent the input distribution, employ lightweight domain descriptor, computed by extracting patch tokens after the patch and position embedding stage and computing their channel- wise mean and variance adaptation step, the descriptor of for each input is accumulated as ((e)) using an exponential moving average (EMA). where Φ(t) = ad + (1 a )o In the following, we detail the initialization and update of the domain bank, and the retrieval process during CTTA.
{mean, variance) } across batch and token dimension. At the t-th
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Domain Bank. The domain bank is memory module that stores pairs of domain descriptors and their corresponding spectral codes, i.c., [Ø* S for each encountered domain k. It serves as a repository of Nomain-speciff knowledge from previously encountered domains during CTTA that can be retrieved to initialize model adaptation whenever a new domain is detected. Prior to continual test-time adaptation,
initialize the domain bank using information from the source domain. The original singular values Spre are stored in the domain bank together with the aggregated domain descriptors @ as [ This source entry serves as the initial anchor point for adaptation. At the beginning of continual test-time adaptation, we initialize S using Spe. Once the first domain shift is detected during adaptation, we store the adapted spectral code and the updated EMA descriptor as the second entry in the domain bank as [0b2 S2].
Spectral Code Retrieval. We detect new domains and reuse the adapted singular values guided by the current domain descriptor. To identify domain shift, we compare the current input-level de- scriptor & with the accumulated descriptor Φ1 using a symmetric Kullback-Leibler (KL) divergence (Kullback & Leibler 195I 195T)across Jacross C' channels:
D(01, 02) = + L[KLOn b2,) + (L(02,
(6)
A domain shift is detected when D(d', &(1)) exceeds a predefined threshold т. The stabilized de- scriptor (()) and its corresponding adapted spectral code ( are then stored in the domain bank to represent the corresponding domain. We retrieve the most similar previously encountered domain by comparing the current descriptor &y with the stored set {ow] where K is the number of recorded domains, and select k' arg min; D ox). The singular values associated with the matched domain k- initialize adaptation for the current input, and are further refined during subsequent updates.
This retrieval and initialization process is triggered automatically whenever new domain is detected.
4 EXPERIMENTS
4.1 SETUP
Datasets. We evaluate our method on ImageNet-C (Hendrycks & Dietterich 2019). which includes 15 corruption types categorized into Noise, Blur, Weather, and Digital. Additionally, we use ImageNet- R (Hendrycks et al. 2021a) (renditions) and ImageNet-A (Hendrycks al., 2021b) (adversarial examples) to test robustness against different distribution shift types. Implementation details are provided in the Appendix A
Single domain test-time adaptation. We use the full validation set (50,000 images) from ImageNet- C, where each corruption type is evaluated independently. Unless otherwise specified, we use a standard VIT model (Dosovitskiy et al. 2021) fine-tuned on ImageNet- 1k (Krizhevsky et al. 2012) as the default backbone. To assess the generalizability of our method under different pretraining strategies, we Vision Transformers pretrained via MAE (He et al.) 2022) and CLIP (Radford et al. 2021). For the CLIP-pretrained variant, we utilize the fine-tuning model from (Cherti et al. 2023). which is finetuned on ImageNet-12k and subsequently on ImageNet- Ik. Beyond standard corruptions, we assess adaptation performance under different distribution shift types using ImageNet-R and ImageNet-A, which contain artistic rendering images and naturally occurring adversarial samples, respectively. These datasets present fundamentally different challenges compared to ImageNet-C.
Continual test-time adaptation. Following ViDA (Liu et al. 2024). we use 5,000 images from the ImageNet-C validation set provided by RobustBench (Croce et al.] 2021). The model continuously adapts to the incoming test data stream without access to domain boundary information.
Gradual continual test-time adaptation. To assess whether IMSE can detect and adapt to subtle distribution changes, we construct a gradual-shift evaluation scenario using ImageNet-C. Following the corruption order used in our main CTTA experiments (e.g., Gaussian Noise - Shot Noise + Impulse Noise + Defocus Blur - in which the severity level of each corruption smoothly varies as: 1 ++ 2 + 3 + 4 + 5 > 4 + + 2 1. Repeating this process for all 15 corruption types results in 135 sequential test domains.
JPEG Compression), we generate a continuous sequence
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Table I: Test-time adaptation on ImageNet-C (50k). (C)) over 15 corruptions at severity level 5 using ViT-Base models with different pretraining strategies. Results with * are reproduced by us.
Protrain
Methol
Noise
Blur
Weather
Digital
Avg.(1)
Gouss.
Shot
Imsul.
Defoc
Glass
Motion
Zoom
Snow
Frost
Fog
Brit.
Cont::
Elastic
Pixel.
JPEG
34.2
65.5
51.0
16.4
29.9
34.5
28.5
49.1
33.3
45.1
12.2
CoTTA
40.3
31.8
39.6
35.5
33.1
46.9
37.3
2.9
46.4
59.1
71.7
55.5
46.4
59.4
59.0
44.4
DDA
52.5
54.0
52.1
33.8
40.6
33.3
30.2
29.7
35.0
5.0
48.6
2.7
50.0
600
58.8
39.1
MEMO
58.1
58.5
51A
41.2
57.1
52.4
64.1
80.3
44.6
52.8
72.2
72.1
59.1
AdCCoitaasi
54.4
55.8
55.8
52.5
42.2
58.7
54.3
64.6
60.1
76.8
53.7
61.7
71.9
69.6
59.9
Supervised
CFA
56.9
58.0
58.1
$4.4
48.9
59.9
56.6
56.4
64.1
67.7
79.0
58.8
64.3
71.7
70.2
62.4
TENT
$7.6
58.9
$8.9
$7.6
54.3
61.0
$7.5
65.7
54.1
09.1
78.7
62.4
62.5
72.5
70.6
62.8
DePT-G
71.8
63.6
58.0
59.0
58.0
54.7
61.2
57.9
66.1
64.4
78.7
62.4
62.9
72.5
70.5
63.6
EATA
51.8
55.3
55.6
58.0
59.1
63.4
61.5
67.7
66.2
73.2
77.9
68.0
68.4
73.1
70.3
6/.88
DPAL
39.8
61.7
61.0
59.1
60.5
64.9
63.8
70.2
68.9
72.6
79.7
62.6
70.9
75.6
73.1
67.0
IMSE
62.5
69.0
Source
56.8 56.8
57.5
46.9
35.6
53.1
44.8
62.2
62.6
65.7
77.7
32.6
46.0
67.0
67.6
55.5
TENT"
60.2
61.4
61.8
59.1
56.7
63.5
59.0
59.0
64.1
3.3
79.2
67.6
60.9
72.9
70.6
60.0
MAE
57.4
55.8
66.1
72.4
63.8
DPAL"
61.6
63.2
63.4
59.4
59.7
64.6
61.3
63.0
70.4
63.7
'79.0
6019
69:1
74.9
72.6
65.9
IMSE
61.9
63.8
63.4
61.3
61.2
66.7
65.6
71.2
68.4
72.9
80.2
68.4
70.8
75.7
73.4
68,3
Source
TENT"
55.4
57.6
57.6
50.7
$1.9
59.5
54.2
64.6
57.5
N8.5
80.1
63.0
6.8
72.3
70.0
58.0
CLIP
SAR'
54,9
57,0
57.1
50.5
53.4
59.7
55.3
64.5
60.6
67.7
78.2
62.3
63.1
71,6
69.4
61.7
DPALL"
55.0
57.3
57.0
51.4
54.0
60.0
50.9
65.9
62.7
N9.
79.7
62.8
64.8
72.8
70.7
62.3
IMSE
55.5
57.7
57.6
55.3
58.2
65.5
65.4
69.1
65.7
71.8
79.9
64.6
70.3
74.1
71.4
65.5
4.2 BASELINES
Single Domain TTA.
We adopt the baselines used in DPAL (Tang et al. 2024), including T3A (Iwa-
sawa & Matsuo 202I).
CoTTA (Wang al. 2022). DDA (Gao et al. 2023). MEMO (Zhang et
2022), AdaContrast (Chen et al.) 2022). CFA (Kojima et al.) (022). TENT (Wang et al. 2020
DePT-G (Gao et al. 2022). SAR (Niu et al. 2023 and EATA NNuu et al. 2022).
Continual TTA and Gradual Continual TTA. We primarily compare with TENT (Wagg et al. 2020), COTTA (Wang et al. 2022), and ViDA (Liu et al. 2024), the most widely adopted baselines with public implementations for continual TTA ImageNet-C. For fair comparison, we adopt standard ViT normalization (mean [0.5, 0.5, 0.5], std = [0.5, 0.5, 0.5]) in our main experiments, noting that some methods like ViDA don't use normalization in their official implementations.
4.3 EXPERIMENTS ON VARIOUS TTA SETTINGS
We analyze the effectiveness of IMSE through single-domain test-time adaptation experiments on the ImageNet-C dataset. In Table I our method shows state-of-the-an performance across all three pretraining strategies. The performance gap becomes more emphasized with MAE and CLIP pretraining. IMSE outperforms DPAL by 3.4 percentage points (pp) and 2.8 pp. respectively. These experimental results indicate that adjusting only the singular values is effective regardless of the pretraining method.
We further evaluate the robustness of our method under different types of distribution shift by using ImageNet-R and A. In Table our method demonstrates strong adaptation performance on both datasets. Specifically, our method outperforms DPAL (Tang et al. 2024) by 5.0 pp on ImageNet-R and by 4.9 pp ImageNet-A. Additionally, effectiveness of IMSE under more challenging domain shifts (IaGgNNet33DCC, OfficeHome, and DomainNet) is reported Appendix G
4.4 CONTINUAL TEST-TIME ADAPTATION
We compare the performance of the IMSE-Retrieval and baselines in the continuously changing CTTA scenario. As shown in Table 4 IMSE-Retrieal shows the best performance. Our method consistently outperforms other baselines across every corruption domain, yielding an average improvement 6.7 percentage points (pp) over ViDA. In particular, during the transition from noise to blur corruptions, IMSE- Retrieval surpasses ViDA by 7.2 pp on Defocus Blur and by a substantial margin of 15.2 pp on Glass Blur. Furthermore, except for the Brightness corruption, method outperforms ViDA by

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Published as a conference paper at ICLR 2026
Table 2: Test-time adaptation on ImageNet- R/A. Accuracy (%)(f) on two different datasets using supervised pretrained ViT-Base model.
Table Gradual CTTA on ImageNet-C. Re- sults with are reproduced by us.
Method
Avg Acc. (%)
Method
ImageNet-R
ImageNet-A
Source
67.3
Source
57.2
31.1
TENT*
70.7
TENT
61.3
44.5
CoTTA"
69.5
SAR
62.0
45.3
DPAL
64.8
49.9
ViDA
72.5
IMSE
69.8
54.8
IMSE-Retrieval 74.9
Table 4: Continual test-time adaptation on ImageNet--C (5k). Accuracy(%)(1) over 15 corruptions severity level 5 using supervised ViT-Base model. Results with are reproduced by us.
Noise
Blur
Weather
Digital
ImageNet. (5k)
Gauss.
Shot
Impal.
Defoc
Glass
Motion
Zoom
Snow
Frest
Tog
Brit.
Contr.
Elastic
Pixel.
JPEG
Avg.(1)
Source
46.8
46.7
46.7
44.1
31.1
48.6
44.5
54.3
50.4
54.9
75.3
31.3
45.2
65.8
66.1
50.1
TENT"
48.0
50.2
51.2
45.5
34,0
51.4
46.9
57.3
54,6
569
76.3
39.5
46.4
66.7
52.8
CoTTA"
47.0
47.1
47.3
44.7
31.6
49.0
45.2
54.8
$1.0
55.5
75.9
32.0
45.9
66.1
66.7
50.7
VIDA
50.5
56.3
56.5
50.8
42.6
56.5
52.2
61.6
58.3
63.0
77.1
58.2
49.8
67.1
68.0
57.7
IMSE Retrieval
57.3
60.4
39.7
58.0
57.8
60.7
60.8
68.2
66.3
68.5
78.2
59.9
67.1
74.1
69.6
64.4
considerable margin across all subsequent domains. Remarkably, these gains achieved without any pseudo-labe label refinement via data augmentation or EMA teacher models, which are essential components in CoTTA and ViDA.
4.5
GRADUAL CONTINUAL TEST-TIME ADAPTATION
Table 3 reports the average accuracy under the gradual-shift setting. IMSE-Retrieval achieves the highest performance of 74.9% outperforming CTTA baselines such as TENT, CoTTA, and ViDA. We additionally investigate the influence of the domain domain-change threshold т. A margin of one step around each transition point is allowed when measuring detection quality to account for the smooth nature of the shifts. When the threshold is increased to more tolerant value from 0.02 to 0.04, the Fl score of domain-change detection decreases from 0.77 to 0.28, while the overall adaptation performance increases from 74.9% 75.6%. This trade-off indicates that highly sensitive domain-chame detection not always advantageous, and that choosing a moderate threshold helps achieve strong performance with compact Domain Bank under Gradual CTTA setting.
5 ANALYSIS
Effect of Singular Value Selection Strategy. To further understand the contribution of different spectral components TTA, we selectively fine-tune subsets of singular values. While our main approach updates all singular values in each linear layer, this experiment investigates the performance impact tuning only the top-R% or bottom-R$s singular values, keeping the rest fixed. As shown in Figure 2a tuning the top 50-90% of singular values achieves comparable performance than updating all singular values. contrast, tuning only the bottom- RR% consistently leads to notable performance degradation. For example, when R is 80, updating the top 80% yields the best accuracy of 69.1%. %, while tuning the bottom 80% results in lower performance of 68.4%. As R decreases, the difference between the top and bottom components becomes more pronounced. When only 20% of the singular values are tunable, the top components still maintain reasonable performance 67.7%. whereas the bottom components drop sharply to 64.7%. These results demonstrate that spectral experts associated with high-magnitude singular values are more informative and play dominant role adaptation under distribution shift.
even slightly better
The Role of Diversity Maximization Loss. In this section, we examine how feature diversity in the ViT's last-block output correlates with adaptation performance. Figure 26 shows feature diversity, measured the mean of the dimension wise standard deviations of token representations within batch samples. Figure 2c shows the corresponding adaptation performance under Gaussian noise corruption at severity level 5.
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55
Ruernge Accurts
22.60
2.53
53
Top Bottom RXs
BKTMI 0925
ROSt
BITHIN loss
Joss
Accurscy
Scom
200
400
600
800
250
400
600
830
R,00)
lieration
lteration
Threshold T0lgscoo scale)
(a)
(b)
(c)
(d)
Figure 2: (a) Comparison of top-/t% vs. bottom- singular value selection. (b) Feature diversity
across various training methods. (c) Adaptation performance across various training methods, (d) Im- pact of the threshold t on domain shift detection and adaptation performance. CE and TTA losses denote Lee and Cemmin respectively.
Table 5: Test-time adaptation on ImageNet-C under non-i..d. setting, Average accuracy (%)
across 15 corruption domains for different concentration factors a.
Method
1=100 (Mild)
a=0.5 (Moderate)
Q=0.1 (Severe)
a=0.05 (More severe)
IMSE w/o Lam
67.79
67.78
67.64
67.33
IMSE
68.92
68.88
68.62
68.41
Improvement +1.13
+1.10
+0.98
+1.08
We assess the effect of the caarsitymmximizzation loss combined with entropy minimization, as defined in Equation (5). which encourages diverse utilization of spectral experts in later blocks during adaptation. As shown in Figure 2b] maximizing the proposed objective function effectively prevents the collapse of feature diversity and simultaneously boosts adaptation accuracy to 61.9%, while maintaining diversity trend close to that of the supervised setting. Further analysis of the diversity of aligmment across different transformer block depths is provided in Appendix D
Specifically, Supervised adaptation with cross-entropy loss (C.z) shows steady increase in diver- sity and achieves higher adaptation performance, suggesting the model learned glass-discrmminatiee features for the current domain. In contrast, the model is adapted in an unsupervised manner using entropy minimization (Cenmin), ), the diversity of the last block gradually decreases, and the accuracy drops to 60. 20. This diversity collapse under unsupervised training arises because entropy mini- mization loss enforces high confidence even for uncertain samples, prompting the model to exploit -omain--pecific patterns dominant across the incoming test data. As a result, the sentation captures comain-related rather than class dissrmiicriiiiaevve information, yielding sub-optimal performance.
repre-
Robustness of Diversity Maximization in Non-i..d Settings We further assess whether diversity maximization could unintentionally suppress class-discriminative information under extreme label imbalance. Following DELTA (Zhao et al. (2023), we adopt the Dirichlet non-i.i.d. setting, where the concentration factor a controls the degree of label imbalance within batch. We vary a from 1.0 to 0.05, where smaller indicates a more severe imbalance. As shown in Table incorporating Lam consistently improves adaptation accuracy by approximately 1.1 pp across levels of non-i.i.d. shifts. Notably, under the most severe class imbalance (a 0.05), using the diversity maximization loss boosts performance from 67.33% to 68. 68%41% This stable improvement confirms that diversity maximization effectively complements entropy minimization, maintaining robust representations even when the input distribution is extremely skewed.
Domain Shift Detection Quality. To understand the relationship between domain shift detection quality and adaptation performance, we measure the hyperparameter sensitivity of the domain shift detection threshold т, which controls the sensitivity of domain shift detection. Figure 2d reports classification accuracy and Fl score for domain shift detection quality at various 7 values. Figure 2d shows that higher Fl score generally leads to higher classification performance. Overall, our method maintains competitive accuracy despite reduced domain-shiff detection quality and achieves better performance compared to other methods. To further explain this behavior, we analyze two extremes as follows. When 7 is too low, minor fluctuations trigger frequent shift detections, increasing the number of entries in the domain bank. However, because method reuses previously stored spectral
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Table 6: Comparison of performance and ellicieney across different CTTA methods. Results with are reproduced by us.
Table 7: Effect of domain deseriptor under Continual test-time adaptation on ImageNet-C.
Method
Acc (8XX1)
Params.(L)
Runtime (see batch)(L)
Method
Avg Acc. (%)(1)
TENT'
Source
50.1
CoTTA"
50.7
86.4M
2.52
IMSE
62.2
VIDA"
57.7
14.2M
3.49
IMSE-Retrieval
64.4
36.8K
0.99
IMSE-Retrieval (Mean)
63.1
IMSE- IMSE-Retrivval (Var)
63,2
64.4
Table 8: Test-time adaptation ablation study on loss components using ImageNet- C. inddcaatss the component is used.
Table 9: Continual test-time adaptation abla- tion study on components using ImageNet-C. v indicates the component is used.
Lesmin
Las
Avg. Acc, (%0()
Lemmin
Lan
Domain Bank
Avg. Acc. (%))1)
67.8
59.4
32.7
69.1
62.8
64.4
codes, these redundant entries less performance degradation. When high, the change of test domain is undetected, leading to suboptimal adaptation and forgetting of previously encountered domains, resulting
performance drop. These findings emphasize that accurate domain shift detection is crucial not merely for maximizing classification accuracy, but for maintaining an efficient and meaningful domain bank in CTTA.
Efficiency of IMSE-Retrieval. To evaluate efficiency, we measure runtime on a single A6000 GPU with a batch size of 64 and analyze IMSE-Retrieval across three aspects: trainable parameters, runtime, and additional storage, as shown in Table First, IMSE-Retrieval achieves the highest performance (64.4%) while requiring only 36.8K trainable parameters. which corresponds to 0.05% of the parameters updated by CoTTA and about 0.26% relative to ViDA. Second, the measured runtime shows that IMSE-Retrieval is 3.5 times faster than ViDA and 2.5 times faster than CОTTA. This efficiency is primarily related to the low computational cost of SVD. The SVD of all linear layers is performed only once offline preprocessing step before adaptation, taking approximately 5.0 seconds. During adaptation, reconstructing weights via seconds per batch, which is marginal relative the 0.99 seconds required for the full adaptation pass (only about 7% of the total adaptation time). Although IMSE-Retrieval is slower than TENT, our approach achieves much higher accuracy. Third, the storage required for the Domain Bank is approximately 0.33 MB per domain, which is negligible relative to the ViT-Base backbone size (330.23 MB). These results demonstrate that Retrrievl not only provides strong adaptation performance for CTTA but also maintains high efficiency across all measured aspects.
UVV adds an overhead of 0.07
ABLATION STUDY
Effect of Domain Descríptors. Using both mean and variance to compute distributional similarity via KI. divergence is theoretically well-founded, as these first- and second-order statistics jointly capture the essential characteristics and IMSE-Retrieval (Var) denote the variants of our method that retrieve spectral codes based on mean and variance statistics, respectively. Retrieval with variance performs slightly better than (Mean), and the superior performance of statistics, confirms their complementary roles.
distribution. As shown in Table IMSE-Retrieval (Mean)
which combines both
Component Ablation Studies. We conduct two complementary ablation studies that separately analyze (1) the role of entropy minimization and diversity maximization under TTA setting, and (2) the impact of the diversity maximization and Domain Bank under CTTA setting, when entropy minimization is fixed. We estimate the individual contributions of entropy minimization and diversity

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Table 10: Effect of target modules of IMSE. v indicates the component is used.
Accuracy (9%)
Atin.qkv
Attn.proj
MLPiel
MLP13
Accuracy (%)
51.0
66.2
66.8
V
65.8
Asn Blog scale)
67.2
V
68.6
Figure 3: Hyperparameter sensitivity of Adm-
68.9
69.0
maximization. As shown in Table 8 Lestmin provides the essential adaptation signal, while aam prevents representation collapse during adaptation. This observation indicates that the two losses play complementary roles TTA.
Next, we fix Cenimin and further ablate the remaining two components: the diversity maximization loss and the Domain Bank-base bassd retrieval mechanism. As shown in Table when combined with entropy minimization, incorporating diversity maximization and the Domain Bank individually improves performance by 3.8 pp and 4.2 pp. respectively, demonstrating that each component is effective the CTTA scenario. Incorporating all three components yields the highest performance, indicating that they play complementary roles in CTTA.
Finetuning different layers. To understand which ViT modules benefit most from fine-tuning singular values, perform ablation study in the TTA setting. As shown in Table IO adapting the second MLP module (MLP.fc2) slightly outperforms the attention projection module (Attn.proj). Adapting both yields further gain, indicating their complementary relationship. The best performance is achieved when all linear layers are adapted. For efficiency, adapting only the attention projection and MLP output layers provides favorable trade-off.
Hyperparameter sensitivity Adm We conduct an ablation study on the weight the diversity maximization loss in the TTA setting. Using supervised ViT-Base model, we change the weight over [1.3, 3, 10, 20, 30, 50, 100, 200] and measure the average accuracy across the 15 common corruptions of ImageNet-C. As shown in Figure 3 we obtain the best accuracy of 69.0% when the weight is set 50, and higher weights reduce accuracy. Notably, the method remains robust even as the scale of Aam varies widely from 1 to 200, and weight of 200 still achieves around 68% accuracy.
CONCLUSION
In this paper, we propose IMSE, a parameter-efficient test-time adaptation (TTA) framework that adapts singular values via singular value decomposition while mitigating feature diversity collapse through diversity maximization loss. For continual test-time adaptation (CTTA), we further introduce Rett-eetrieval, which enables rapid adaptation by reusing previously adapted singular values based on domain similarity. Extensive experiments on ImageNet-C/R/A demonstrate that IMSE consistently improves performance across diverse pretraining strategies, including supervised, MAE, and CLIP pretraining. Furthermore, IMSE-Retrieval achieves state-of-the-art results in both CTTA and Gradual CTTA settings with up to 385 times fewer trainable parameters. We hope these results provide a strong foundation for future work on efficient and robust adaptation in continuously evolving real-world environments.
Limitations. While our method requires far fewer trainable parameters than existing approaches, introduces some additional memory usage due to storing decomposed singular vectors alongside the original weights. In addition, the domain bank stores both the domain descriptors and the domain- specific adapted singular values, which requires extra storage in CTTA.
Broader impact. Our method enables efficient, robust adaptation of vision models under distribu- tion shift, making it broadly applicable real-world scenarios where test distribution differs from training distribution. However, care is needed when deploying adaptive systems without control over domain changes failure detection.
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REPRODUCIBILITY STATEMENT
All experiments are conducted on publicly available datasets (c.g., ImageNet-C) without private data. Implementation builds the publicly released DPAL and ViDA codebases, and all modifications necessary to reproduce our method are described in the manuscript. Section 4. and Appendix [A] include model architectures, hyper- parameesr,,etrss optimization settings, and processno steps.
ACKNOWLEDGMENTS
This research was supported by LG Energy Solution Co., Ltd.
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ViT-Large Published as a conference paper at ICLR 2026
A IMPLEMENTATION DETAILS
Single-domain test-time adaptation (TTA). We use batch size of 64 for all experiments. We employ Adam as an optimizer with Sharpness-Aware Minimization (SAM) (Foret et al. 2021). We apply learning rate of 3e-3 for ImageNet-C (Hendrycks & Dietterich 2019) (Hendryeks al. 2021a) and ImageNet-R, and 4e-3 for ImageNet-A (Hendrycks et al.) 202 Results of Supervised ViT-Base are taken from the DPAL (Tang et al.] (024).. We exclude the final three transformer blocks of ViT from training, following the protocol established by SAR and DPAL.
Table 11: Learning rates for each method across different pretrained models.
Method
MAE
CLIP
TENT
le-3
le-3
3e-4
SAR
le-3
3e-3
le-3
DPAL
4e-3
3e-3
4e-3
IMSE
Ic-3
3e-3
4e-3
CTТА and Gradual CTTA. We use the same batch size of 64 and adopt Adam as optimizer with SAM. We implement all baseline methods using their default configurations, following ViDA (Liu et al. 2024). In our method, we exclude the final three transformer blocks of ViT from training. We the learning rate of IMSE-Retrieval 7e-3 in CTTA, and 3e-3 in Gradual CTTA. The EMA coefficient used for updating the domain descriptor, a, is set to 0.8. We use a domain-change threshold of 0.05 in CTTA and 0.02 in Gradual CTTA.
Entropy-baseed sample filtering. We follow SAR (Niu et al. 2023 entropy filtering strategy in both scenarios, using the threshold r = 0.4 log(# of classes) to exclude unreliable samples during adaptation.
Diversity Maximization Loss. To preserve the model's s class dinsriiicriiinnaoion ability, we introduce the diversity maximization loss Lam, which promotes diverse response patterns across spectral experts of each layer. We set the loss weight to Adm 50 and apply Zam to the set Adm. which consists of all linear layers in the last three Transformer blocks.
B EXTENSION TO VIT-LARGE
In addition the results Section 4.3 we further evaluate our method on a larger architecture, ViT- Large, to examine its scalability and generalization. ViT-Large provides a significantly greater capacity for representation and is expected to leverage richer pretrained knowledge more effectively during the adaptation process. In Table 12 IMSE shows oftte-of-theartt performance compared to baseline methods. Our method outperforms SAR, the second best performing approach, by approximately 4. pp. It demonstrates the substantial benefits of our spectral expert adaptation when applied to larger model architectures. These findings align with the core philosophy of our work-that our spectral expert adaptation method scales effectively with model capacity, enabling better utilization of the rich knowledge contained in more powerful pretrained models.
C ADDITIONAL ABLATION ON MODULE COMBINATION
We extend the ablation study in Section of the main paper to a broader set of module combinations. We decompose the gkv projection in the attention module into three separate linear layers for q. k, and In Table 13 Attn.q, Attn.k, and Attn.v denote the individually separated components. As shown in Table 13 attention value (Attn.v), attention projection (Attm.proj). and second layer of MLP block (MLP.fc2) contribute substantially adaptation performance. Notably, find that explicitly separating the q. k, and projections leads to further performance improvements, achieving a 0.2 pp gain compared using the combined qkv projection.
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Table 12: Test-time adaptation ImageNet-C (50k). Accuracy (1) over 15 corruptions severity level 5 using supervised pretrained ViT-Large model. Results with are reproduced by us.
Noise
Blur
Weather
Digital
ImageNet-C (50k)
Impul.
Defoc.
Zoom
Snow
Fog
Contr.
Avg.(1)
Source
62.5
62.0
63.3
52.9
45.3
60.7
55.2
66.0
62.4
62.6
79.9
40.1
56.2
74.3
72.8
61.1
TENT
65.2
66.0
66.1
60.8
54,4
64.1
60.4
63.7
804
58.0
75.9
73.6
65.5
SAR
67.4
68.3
69.3
55.8
59.6
66.1
64.2
68.8
68.1
70.5
81.6
59.0
69.7
78.0
75.8
68.1
68.4
62.5
67.9
81.5
75.7
IMSE
70.1
71.0
71.0
68.1
68.5
71.8
71.7
75.8
74.0
76.3
82.7
68.5
76.0
80.4
78.3
73.6
Table 13: Ablation study on target modules. The best is bolded and the second best is underlined.
Attn.q
Attn.
Attn.v
Attn.proj
MLP.fol
MLP.f22
Acc (t)
51.0
59.6
61.8
66.6
67.4
68.4
V
68.6
V
69.0
V 69.2
D DIVERSITY ANALYSIS ACROSS TRANSFORMER BLOCKS
We analyze how the diversity of alignment statistics varies across network depth. Specifically, we measure the diversity at the second layer of the MLP block (MLP.fc2) within the 3rd, 6th, and 9th Transformer blocks. Figure 4 compares three settings: entropy-minimization loss (Centmin), our full objective (CIMSE), and cross entropy loss (Ccr).
The results show that when only Lenmin is applied, the diversity of expert-input alignments decreases more severely in deeper layers and appears noisier in the early layers. We assume that early layers are relatively less affected by the entropy-ming cetropy-miiimzzation loss and focus on extracting domain-related fea- tures rather than utilizing them. Based on these observations, we compute the diversity-mant maximization loss on the deeper Transformer blocks to better preserve feature diversity during adaptation.
E DOMAIN DESCRIPTOR SIMILARITY ANALYSIS
To better understand the behavior of domain descriptors across different test domains, measure the pairwise distance between descriptors. In F domains belonging to the noise category (e.g., Gaussian noise, Impulse noise, Shot noise) exhibit highly similar descriptors due their shared low-level statistical characteristics. In contrast, the Contrast corruption shows significantly larger distances from all other domains in the descriptor space. This indicates that it possesses unique distributional properties.
F THE USAGE OF LARGE LANGUAGE MODELS
We utilize large language models (LLMS) as auxiliary tools during our experiments. We employ LLMs for debugging and writing repetitive code, and they were used for basic grammar correction during writing our manuscript. The research ideas, experimental design, and all scientific conclusions are our own work.
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0.0165
0.0173
0.0175
0.0160
Olversio
0.0172
Diversity
0.0155
0.0171
LE
CE loss
0.0150
0.0170
MISE
0.0145
0.0169
0.0165
250
500
750
250
500
750
250
500
750
Iteration
Iteration
Iteration
(a)
(b)
(c)
Figure 4: (a) Diversity of alignment patterns 3rd Transformer Block. (b) Diversity of alignment patterns in 6th Transformer Block. (c) Diversity of alignment patterns in 9th Transformer Block.
Coussias bolse
502
6:2
0.20
21:04
15:12
10:50
8:44
0:53
1.4b
13.44
2.81
20.30 54
1.24
2:35
1.35
Impulae noise
2.00
0:02
0.00
23.00
13.00
10:40
8.37
0.82
1-40
15:24
2.02
25.
12
1.22
2:12
1.31
Defocus Mar
Flass Mar
16
10
12.00
1m
8.66
5.60
6.00
0.07
2:53
3.80
2.17
6.74
1.54
0:52
1.61
Zoom Mar
1.4
8:37
6.37
3.26
5.07
0.00
1:20
21
3.20
1,07
3.44
0.70
0.22
0.75
Feost
1:45
1.54
1.49
2.26
0.12
10
8.12
6.07
0.14
0:18
0.12
2
1.55
Brigh
0.00
0.50
2.37
1.07
2.43
2.02
0.10
0.20
Centraet
5.79
1.44
10.25
3.50
2,43
4.75
Elastoc
3.24
1.22
3.24
0.73
0.14
5.13
7.04
6.30
0.56
Phrelate
3.15
2:3
6.62
0.22
1.03
4.73
0.00
JP84
1.31
1:11
1:41
0:25
IG
241
8:6
Sloot boler
Gleaa Defomea Alor
Medims Alur
Stmeer
Frot
Fndd
Brightnant
Comtraat
Elrtii
Panlate
JPEG
Gasssias
Impridor
Figure
Domain distance matrix. Pairwise distance matrix among 15 domain descriptors.
16

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Published as a conference paper at ICLR 2026
Table 14: Test-time adaptation on ImageNet-3DCC (50k). Accuracy(%) over 11 corruptions at severity level 5 using supervised pretraining ViT-Base. Results with are reproduced by us.
quartization
Ger
fng
light
rear Foczs
sy motion
motion
Avg
Source 20.3
53.1
64.7
47.3
39,4
52.8
57.3
59.1
56.3
70,3
43.2
47.4
50.7
TENT 1.2
64.1
68.2
52.1
7.5
56.1
60.7
65.6
70.3
76.2
$6.4
51.22
53.3
SAR'
13.8
64.7
68.7
54.3
41.4
57.1
51.4
66.3
70.8
76.4
57.8
02.5
57.9
DPAL"
13.1
64.2
68.3
53.7
43.4
57.0
61.2
6538
70.0
75.8
36.6
61.7
57.6
IMSE
15.5
65.0
70.3
55.2
44.5
88.1
62.3
67.3
71.6
77.1
58.9
63.9
89.1
Table 15: Test-time adaptation on OfficeHome.. Accuracy(%)))) over 12 source-target domain pairs and average performance. Results with * are reproduced by us.
Method
R-1A
R-+C
R-P
A-R
A-C
A-P
C-R
C-AA
C-P
P-R
P-AA
P-+C
Avg.(t)
Source
79.68
56.05
88.35
87.46
58.55
82.90
84,66
78.37
84.29
87.74
75.32
55.69
76.58
TENT"
79.68
56.08
88.91
88.01
59.61
83.10
85.42
79.68
85.01
87,90
75.48
55.71
77.05
SAR"
79.72
56.72
88.37
87.62
61.42
83.03
85.40
79.48
84.61
87.81
76.02
56.26
77.20
DPAL"
79.93
55.57
86.52
87.14
59.17
82.61
85.33
79.02
84.09
86.68
75.85
55.25
76.43
IMSE
81.04
56.35
88,91
88.13
60.36
83.44
85.74
79.39
84.88
88.04
76.14
56.28
77.39
G ADDITIONAL RESULTS
Challenging benchmarks. We further evaluate IMSE under more challenging domain-shift bench- mark, ImageNet-3 -CCC. Compared to standard 2D common corruptions (Hendrycks & Dietterich 2019). ImageNet-3DCG (Kar et al., 2022) more challenging its corruptions are generated us- ing 3D scene geometry, resulting in more realistic and real-world-plausiee distribution shifts. All experiments are conducted in a test-time adaptation setting using a supervised pretrained ViT-Base model. As shown in Table 14 IMSE achieves consistently strong performance across all corruptions, demonstrating its effectiveness under challenging domain-shie shift benchmarks.
Domain Adaptation Benchmarks. We additionally evaluate our method the domain adaptation benchmarks, Office-Home (Venkateswara et al.) (017) and DomainNet (Peng et al., 2019) under test-time adaptation setting (using supervised pretrained ViT-Base). In experiments, 126 categories from DomainNet, selecting Real, Clipart, Painting, and Sketch as the evaluation domains following MME (Saito al., 2019). For OfficeHome, we use all 65 categories and include Real World, Art, Clipart, and Product as domains. Domain adaptation benchmarks differ from corruption- based benchmarks because they require additional supervised training and exhibit different class distributions across domains. Despite these differences, IMSE achieves consistently strong performance on both benchmarks in Table [5] Table T6. This demonstrates that IMSE is effective not only corruption-basee based TTA benchmarks but also on domain adaptation benchmarks.
H LONG-TERM CONTINUAL TEST-TIME ADAPTATION
We evaluate the long-term stability and scalability of IMSE-Retrieval To simulate long-tern continual test-time adaptation setting where the same domain reappears multiple times, we split each ImageNet- C corruption (all at severity 5) into 10 datasets of different 5,000 images. This setup reflects realistic deployment scenarios where the same domain recurs multiple times with different samples. As shown in Table 17, the proposed method maintains strong and stable performance across all rounds and consistently outperforms prior approaches. These results demonstrate that IMSE-Retriew robust under repeated re-occurrence of the same domain.
17

---

Published as a conference paper at ICLR 2026
Table 16: Test-time adaptation on DomainNet. Accuracy($6)) (t) over 12 source-target domain pairs and average performance. Results with * reproduced by
Method
R-C
R-+P
R-S
C-R
C-P
C-+
P-R
P-C
P-+
S-R
S-C
S-P
Avg.(1)
Source
66.84
76.14
59.44
80.46
69.85
65.93
86.72
69.04
59.95
82.19
72.95
73.62
71.93
TENT
68.25
76.45
60.36
81.91
72.32
67.01
87.60
69.97
59.21
82.76
73.05
73.11
72.67
SAR"
69.64
77.78
64.23
81.91
72.83
67.73
86.72
70.77
59.41
82.77
73.53
73.41
73.39
DPAL
68.14
77.34
60.86
81.78
72.79
66.07
84.93
70.16
58.86
81.61
72.54
70.11
72.12
IMSE
69.33
77.78
62.40
82.45
73.23
67.57
87.85
70.42
59.72
83.10
73.73
73.55
73.43
Table 17: Continual test-time adaptation on ImageNet-C under the domain-recurring setting.
Average accuracy (%) for each round (R1-R10) and the average over all rounds. Results with * reproduced by us.
Method R1
R2
R3
R4
R5
R6
R7
R8
R9
R10
Avg.(t)
Source"
49.2
50.2
50.4
50.0
49.8
50.4
50.7
49.8
50.4
50.0
50.1
TENT"
53.3
56.9
57.8
57.8
57.5
58.7
59.2
57.9
57.9
58.1
57.5
CoTTA*
49.7
52.1
53.1
53.1
53.2
54.0
54.6
53.5
54.0
54.0
53.1
ViDA
53.7
57.2
59.3
58.7
59.1
59.5
59.4
59.7
59.6
59.8
58.6
IMSE-Retrieval
63.7
65.1
65.8
65.2
64.8
65.9
65.0
65.4
65.1
65.3
65.1
18


Reviews:
[{"review_id": "zzuRwqZh4L", "reviewer": "Reviewer_23Fr", "summary": "The paper introduces IMSE (Intrinsic Mixture of Spectral Experts), a new framework for continual test-time adaptation (CTTA). IMSE decomposes each linear layer in Vision Transformers using singular value decomposition (SVD), interpreting the orthogonal basis matrices as a mixture of spectral experts and the diagonal matrix of singular values as spectral weights. During adaptation, IMSE fine-tunes only these spectral weights while keeping the orthogonal bases fixed, enabling highly parameter-efficient adaptation.\n\nTo guide unsupervised adaptation, the authors propose a combined loss function that integrates entropy minimization with a diversity maximization term to prevent feature collapse. IMSE achieves state-of-the-art performance on ImageNet-C, -R, and -A benchmarks, outperforming strong TTA baselines such as TENT, SAR, and DPAL while requiring significantly fewer trainable parameters.\n\nFor continual TTA, the paper further introduces a Domain Bank that stores domain-specific spectral codes and descriptors, enabling retrieval and reuse of prior adaptations to mitigate catastrophic forgetting. Comprehensive ablation studies demonstrate the contribution of each proposed component.", "questions": "Could the authors quantify the computational cost of performing full SVDs across all linear layers in large-scale ViTs (e.g., CLIP or MAE)? Have they considered using truncated or randomized SVD to reduce preprocessing overhead, and if so, how would this affect adaptation performance?", "limitations": "", "rating": 8, "confidence": 3, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "Originality: IMSE offers a novel interpretation of test-time adaptation through the lens of spectral experts, extending SVD-based parameter-efficient fine-tuning (e.g., LoRA, SVDiff) to the unsupervised TTA setting. The idea of freezing orthogonal bases and adapting only singular values is conceptually simple yet highly effective.\n\nEfficiency and Practicality: By updating only singular values, IMSE achieves orders-of-magnitude parameter reduction (~2000× fewer trainable parameters) while maintaining or exceeding SOTA performance.\n\nContinual Adaptation Innovation: The introduction of the Domain Bank provides a simple but powerful mechanism for mitigating catastrophic forgetting across sequential domains.\n\nComprehensive Ablation Analysis: The paper includes well-designed ablation studies that isolate the impact of each component.", "weaknesses": "Domain Bank scalability:\nUsing simple KL divergence over mean–variance descriptors might struggle to discriminate fine-grained domain shifts, potentially leading to incorrect retrievals.\n\nNo direct measure of forgetting:\nAlthough the Domain Bank is designed to mitigate catastrophic forgetting, the paper does not include quantitative evidence, e.g. Backward Transfer (BWT), to verify that performance on previously adapted domains remains stable after subsequent adaptations.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "o8GraPplnp", "reviewer": "Reviewer_4qVn", "summary": "This paper proposes Intrinsic Mixture of Spectral Experts, a novel framework for test-time adaptation. IMSE updates only the singular values while keeping the singular vectors fixed, thus enabling parameter-efficient adaptation. To prevent the entropy minimization objective from collapsing feature diversity, the authors introduce a diversity maximization loss based on spectral vector–input alignment. For CTTA, they propose a Domain-Aware Spectral Code Retrieval mechanism, which stores domain-specific singular values and retrieves them according to domain similarity to mitigate forgetting. Experiments on ImageNet-C  and CLIP  backbones show that IMSE achieves state-of-the-art results while using fewer trainable parameters.", "questions": "See above.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The paper correctly identifies two practical problems in TTA: the overfitting tendency of entropy minimization and catastrophic forgetting in CTTA.\n2. The idea of reinterpreting linear layers as mixtures of rank-1 “spectral experts” is interesting. It provides a compact and interpretable way to perform fine-grained adaptation.\n3. Updating only singular values makes IMSE computationally efficient and easily applicable to existing pretrained models such as ViT or CLIP.\n4. The reported improvements on ImageNet-C and the low parameter count are convincing, and the experiments are well organized.", "weaknesses": "1. How robust is the retrieval process when encountering a completely new domain that differs substantially from all stored domains?\n2. Updating only singular values implicitly constrains parameter updates to a diagonal submanifold of the low-rank space. Does this constraint reduce optimization expressivity when confronted with severe domain shifts?\n3. How much extra computational cost is introduced by SVD?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "mlgFDm5gFu", "reviewer": "Reviewer_wHid", "summary": "This paper addresses the test-time adaptation (TTA) problem by leveraging the knowledge in pretrained networks. Specifically, it decomposes each linear layer via singular value decomposition (SVD) and adapts only the singular values. For continual test-time adaptation (CTTA), the method estimates input distributions to detect domain shifts and retrieves previously adapted singular values for rapid adaptation. Extensive experiments demonstrate that the proposed approach achieves state-of-the-art performance.", "questions": "Please see the above weaknesses. If you can conduct additional experiments to further evaluate your method, I would be willing to raise my score.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "1. Using $\\text{Std}_{i}^{(l)}$ to measure whether each expert captures domain-specific patterns is an interesting design.\n\n2. Detecting new domains by comparing the current input-level descriptor $ϕ$ with the accumulated descriptor $\\phi_{(t)}$ is an effective way.\n\n3. This paper analyzes, in an unsupervised manner, that entropy minimization tends to capture domain-related rather than class-discriminative information.", "weaknesses": "1.  In lines 161–163, since $\\mathbf{v}_i^{(l)}$ fixed, it is unclear how it can define each spectral expert’s response. Could the authors provide a more detailed explanation of this point.\n\n2. The paper conducts experiments only on three OOD datasets. Could authors also evaluated the method on classical domain adaptation benchmarks such as Office-Home[1] or DomainNet[2]?\n\n3. The paper introduces two loss components, entropy minimization $L_{entmin}$ and diversity maximization $L_{dm}$, but lacks an ablation study isolating their individual contributions. Could the author show the effect of using only entropy minimization, only diversity maximization, and their combination to better understand each term’s impact on adaptation performance.\n\n4. The paper does not include experiments on time analysis (e.g., runtime efficiency) or memory analysis (e.g., computational cost and storage of spectral codes). Could authors provide such experiments to better demonstrate the efficiency of the proposed method?\n\n[1] Venkateswara, Hemanth, et al. \"Deep hashing network for unsupervised domain adaptation.\" Proceedings of the IEEE conference on computer vision and pattern recognition. 2017.\n\n[2] Peng, Xingchao, et al. \"Moment matching for multi-source domain adaptation.\" Proceedings of the IEEE/CVF international conference on computer vision. 2019.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "nCNzgO4rW6", "reviewer": "Reviewer_Q6jF", "summary": "The paper introduces IMSE (Intrinsic Mixture of Supervised Experts), a test-time adaptation method that decomposes linear layers in a pretrained model using singular value decomposition (SVD), treating each rank-1 component as a spectral expert. During adaptation, only the singular values are updated while the bases remain fixed, allowing parameter-efficient updates. The method combines entropy minimization with confidence-based filtering, a diversity maximization loss to promote balanced expert activation, and a domain descriptor mechanism for detecting distribution shifts and retrieving previously adapted spectral parameters from a memory bank.", "questions": "1. he framework assumes that adapting only the singular values of pretrained linear layers is sufficient for capturing domain shifts. Could the authors provide theoretical or empirical evidence supporting this assumption, especially for shifts that may require new basis directions?\n2. The method combines entropy minimization, diversity regularization, and domain memory. Have the authors performed detailed ablations to assess the individual and joint impact of each component? For example, how does performance change when the diversity loss is removed?\n3. The KL-divergence-based domain descriptor mechanism is used to trigger new adaptations and retrieve stored parameters. How robust is this approach under gradual or noisy distribution shifts? What mechanisms are in place to prevent over-segmentation or memory bloat when many small shifts occur?\\\n4. The diversity regularization loss penalizes widespread activation of individual spectral experts. Could this unintentionally suppress task-relevant features that happen to be common in a new domain? How does the method balance between promoting diversity and retaining important features?\n5. Could the authors discuss whether the IMSE framework or its components (e.g., diversity loss, spectral adaptation) can be extended to multi-source domain generalization or continual learning settings where test-time updates are not allowed?\n6. While the method is evaluated on common TTA benchmarks, it would be helpful to include results on tasks involving more gradual or subtle domain shifts, or with more fine-grained domain boundaries. Could the authors include such evaluations in a revision?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "The use of spectral decomposition to form a mixture-of-experts representation is an interesting approach to test-time adaptation.", "weaknesses": "1. The assumption that spectral experts can generalize across domains by only adapting singular values lacks theoretical justification and is not thoroughly evaluated in challenging domain-shift scenarios.\n2. The interplay between the different components (e.g., diversity loss, entropy minimization, and domain memory) is complex, but the paper lacks sufficient ablation studies to isolate their individual contributions.\n3. The scalability and stability of the domain memory mechanism under long-term continual adaptation are not fully explored, leaving questions about its robustness in practice.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)