NEO — No-Optimization Test-Time Adaptation through Latent Re-Centering
Authors: Alexander Murphy
Michal Danilowski
Soumyajit Chatterjee
Abhirup Ghosh
Venue: ICLR 2026 Poster (2026)
Keywords: test-time adaptation
domain adaptation
on-device
Primary area: transfer learning, meta learning, and lifelong learning
TL;DR: We introduce an optimization-free and hyperparameter-free TTA method, which achieves state-of-the-art results in limited adaptation data settings, at no additional computational cost compared to not adapting.

Abstract: Test-Time Adaptation (TTA) methods are often computationally expensive, require a large amount of data for effective adaptation, or are brittle to hyperparameters. Based on a theoretical foundation of the geometry of the latent space, we are able to significantly improve the alignment between source and distribution-shifted samples by re-centering target data embeddings at the origin. This insight motivates NEO – a hyperparameter-free fully TTA method, that adds no significant compute compared to vanilla inference. NEO is able to improve the classification accuracy of ViT-Base on ImageNet-C from 55.6\% to 59.2\% after adapting on just one batch of 64 samples. When adapting on 512 samples NEO beats all 7 TTA methods we compare against on ImageNet-C, ImageNet-R and ImageNet-S and beats 6/7 on CIFAR-10-C, while using the least amount of compute. NEO performs well on model calibration metrics and additionally is able to adapt from 1 class to improve accuracy on 999 other classes in ImageNet-C. On Raspberry Pi and Jetson Orin Nano devices, NEO reduces inference time by 63\% and memory usage by 9\% compared to baselines. Our results based on 3 ViT architectures and 4 datasets show that NEO can be used efficiently and effectively for TTA.

Published as a conference paper at ICLR 2026
NEO NO-OPTIMIZATION TEST-TIME ADAPTATION THROUGH LATENT RE-CENTERING
Alexander Murphy' Michal Danilowski' Soumyajit Chatterjee
Abhirup Ghosh
University of Birmingham
Braae Software Research
UUniversity of Cambridge
ABSTRACT
Test-Time Adaptation (TTA) methods are often computationally expensive, re- quire large amount of data for effective adaptation, or are brittle to hyperparam- eters. Based on a theoretical foundation of the geometry of the latent space, we are able to significantly improve the alignment between source and distribution- shifted samples by re-centering target data embeddings at the origin. This insight motivates NEO hyperparameter--aeeeee free fully TTA method, that adds no significant compute compared to vanilla inference. NEO is able to improve the classification accuracy of ViT-Base on ImageNet-C from 55.6% 59.2% after adapting on just one batch of 64 samples. When adapting on 512 samples NEO beats all 7 TTA methods we compare against on ImageNet-C. ImageNet-R and ImageNet-S and beats 6/7 on CIFAR-IO-C, while using the least amount of compute. NEO per- forms well on model calibration metrics and additionally is able to adapt from 1 class to improve accuracy on 999 other classes in ImageNet-C. On Raspberry Pi and Jetson Orin Nano devices, NEO reduces inference time by 63% and memory usage by 9% compared to baselines. Our results based on 3 ViT architectures and 4 datasets show that NEO can be used efficiently and effectively for TTA.
INTRODUCTION
A central challenge machine learning is maintaining performance under distribution shifts be- tween training and deployment. For instance, an image classifier may excel on curated training
data but degrade on real-world inputs with snow, fog, or motion blur. Test-Time Adaptation (TTA)
methods (Li et al. 2018 Wang et al.) 2224 Liang al., 2020 [Wan et al.) 2021 Niu et al.) (023)
address this by leveraging unlabeled test samples without requiring access to training data, making them particularly suited to the modern setting of large pre-trained models.
updates that signif- icantly increase memory consumption (Wang al. 2022 Ma et al., 2025), inference latency (Niu ett al. [2024] 2023), and sensitivity to hyperparameter choices (Wang et al. (021). Others impose architectural assumptions (e.g., the presence of batch normalization layers) (Wang al. 2021 Niu
Existing TTA methods face several limitations, such as backpropagation-basee
et al. 2023 Song et al.) 2023) or require large number of target samples to achieve stable adapta- tion (Iwasawa & Matsuo| 202I). Moreover, as adaptation and inference are performed continually on data arrival, TTA methods with high computational demands incur significant latency and mem- ory overhead on both edge and server deployments.
We propose NEO, an optimization and hyperparameter-ffee fully (not using source data) TTA method with no significant additional latency or memory overhead. Moreover, NEO is more accurate and better calibrated than baseline TTA methods, which up to several times the compute, as shown in Figure 2b It is robust with the capability to adapt with just a single sample and with unbalanced classes for considerable accuracy improvements shown in Figure
We observe that due to the distribution shift at input, including data-independent stochastic shifts, the activations from the penultimate layer, embeddings, shift structurally. Our key idea is to ap- proximate this shift by tracking the displacement of the global centroid of the embeddings and then re-centering test-time features accordingly. In practice, this means that given corrupted sample
"Correspondence 1eexanermorphhy784@gm com

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# Classifier head
self.classifiee nn, mm.Lineariconffg..a hww.riigghhieeniiieeeeee config. labels)
NEO classifier head
self.classitier NEOlcontig hidden_size,
Figure 1: Elegant adoption: NEO can be added by replacing the nn Linear with our custom layer.
NEO
59
Accuracy (%)
58-
Source sample (x)
NEO Cont.
56
Target semple (R)
55
h(2) &
((F)
40
60
100
R(x)
Runtime (s)
Latent speca
(b) NEO improves accuracy using little latency or memory
(a) High-level overview of NEO
Figure 2: (a) Given a domain shifted sample, æ, we encode it to h())) and shift it using a single shared vector A. The shifted representation closer the embedding of the corresponding clean sample (unknown), h(z), resulting in more accurate predictions. (b) Runtime (x axis), accuracy (y axis), and memory usage (point radius) of TTA methods for ViT-Base on 15 corruption from ImageNet-C evaluated on 512 samples per corruption. NEO outperforms all methods in terms of runtime, accuracy, and memory.
with embedding h(z), NEO corrects it by subtracting single shared vector A, bringing the rep- resentation closer to the embedding of its clean counterpart h(x: (although unknown) and thereby restoring accuracy
illustrate the re-centering in Figure 2a While estimating such distribu- tion shift is challenging in pre-trained models, often trained on unknown data sources, we leverage structural properties of neural collapse (Papyan al. 2020) develop practical and principled method, without relying on source data.
NEO is elegant and simple adopt, requiring only single line change standard Vision Trans- former implementation, by replacing nn Linear with our custom NEO layer as shown in Figure incurs negligible computational and memory overhead as stores only a single vector to correct the shift. Furthermore, with just handful of samples, it consistently improves accuracy over state- of-the-art TTA methods that demand orders magnitude more compute and memory. Finally, we also extend NEO with continual variant, using just one easily interpretable hyperparameter, that maintains robustness under evolving test distributions, making it particularly suitable for real-world, constrcccd deployments.
1. We propose NEO, a lightweight TTA method, that re-centers embeddings using global centroid estimate. We evaluate NEO on datasets and 3 different ViT architectures, showing consistent improvement in accuracy and model calibration. Moreover, NEO beats all 7 TTA methods that we compare against, when adapting on 512 samples from ImageNet-C.
2. We perform a thorough investigation on the effect that an input distribution shift has on the latent space, finding significant shared shift across samples and classes. We connect this shift with neural collapse to provide a principled explanation for why global re-centering is sufficient for adaptation.
3. We show that NEO is both efficient and versatile: it can adapt with as little as single sample or class, extend naturally to continual adaptation across evolving corruptions, and maintain low latency and memory usage both edge devices and cloud servers. Combined with being hyperparameter-fiee free, this makes NEC practical for diverse real-world deployment scenarios.
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2 PROBLEM STATEMENT AND SETUP
Consider pre-trained classification model { Rm + Re, composed of encoder h R - Rd and linear classification head _2 + C such that f = 0 h. The model is trained on source dataset D (X, Y), where X E R x contains labeled training samples. We aim adapt f to domain-shifted target dataset D (X; Y), where X R contains n' target input samples, and Y R xC contains the associated labels. We focus on covariate shift that changes X and leaves the conditional distribution of the labels on input data unchanged.
A fully TTA algorithm A adapts the model f by accessing just the target samples X without access to source data or target labels, such that fudapt = A(f. X). The goal of A is to optimize an evaluation metric {fadapt, X, Y), such accuracy. The evaluation metric may access the target labels, but A does not. We focus on two metrics: accuracy and expected calibration error (ECE) (Pakdaman Naeini et al. 2015). ECE quantifies the mismatch between predicted confidence and true accuracy which is important for evaluating model trustworthiness (see more in Appendix B.4).
TTA is useful in practical systems requiring adaptation in-the-wild data distributions. For ample, consider an on-car camera-based traffic signal recognizer that feeds into the car dashboard. Here, the application requires the model to be on-car for robustness against network failures. The model also needs to be adapted to remain accurate on images captured by the local camera. To meet real-time inference requirements and limited on-car compute resources, the adaptation needs to be time and resource-efficient, which forms the constraints we focus on in this paper.
RELATED WORKS AND BACKGROUND
host of existing TTA methods minimize classification entropy through updating affine parameters of batch normalization (BN) layers, including TENT (Wang al. 202T), SAR (Niu et al. 2023),
and EATA (Niu et al. 2022). This line of work has been complemented by pseudo-labe based
clustering (Liang et 2020), non-i.id. adaptation (Gong 2022). and continual adaptation
Wang et al. 2022).
Despite their effectiveness, the above methods are computationally intensive as they rely on opti- mization through backpropagation (Danilowski et al.] (202).. There are three primary approaches of efficient TTA methods: firstly, reducing the memory footprint by selecting important layers to adapt (Ma et al. 2025). secondly, using custom model architectures (Song eet al.] 2023 Hong et al.) [023 Jia et al. 2024 and finally, avoiding The final approach is the most efficient, and there are two broad ways to achieve it: i) optimization through only forward passes using iterative optimizers (Niu et al. 2024 Dong et al. 2025 and vi) adapt analytically without optimization.
Table 1: Comparisons selected baselines. FTTA: Fully
TTA without using source data. HF: hyperparameter free, OF: optimization free, BI: Batch size independence, BF: backpropagation free, FP: # of forward propagations.
FTTA
HF
OF
BI
BF
# FP
T3A
/
V
SAR
/
X
X
2
LAME
X
TENT
X
CoTTA
V
X
X
X
35
FOAN Surgeon NEO-Cont. (ours)
X
X
2
backpropagation altogether.
X
X
X
X
1
NEO (ours)
For example, adjusting BN statistics (Schneider et al. 2020 Nado et al., 2020; Su et al., 2024)
classifier adaptation via prototypes or outputs (Wang et al. 2024 Iwasawa & Matsuo 2021
Boudiaf et al. 2022). NEO belongs to the latter, most efficient category, avoiding optimizers wholly.
An analytical solution to TTA is hard, due to the stochastic nature of the input noise and the com- plexity of modern neural architectures. Prior optimization-Fi methods require large batch sizes along with large dataset compute robust statistics, which essential for their algorithms. Some
FOA 32 samples compute statistics from the source data.
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Cumulative Frequency (%)
100
80
Vector compared with h(w)
Cos.
L.2 Diff.
h(²))
-0.44
4.33
h(2)
Ac
0.51
3.65
h(m)
AG
Ac
0.64
5.47
40
Contrest
h(2)
AG
-
1.00
0.00
Flastic Transfam
Axelate
h(T)) PG
0.49
3.64
20
Compressin
50
100
150
200
250
Latent dimensions
(b) Different shifts improve cosine similarity and L2 norm (a) Few high magnitude dimensions form the shift difference between corrupted and source data
Figure 3: (a) Cumulative frequency of highest magnitude dimension in ft(²) - h(ã) over 50000 samples (showing 250 out 768 dimensions). small number of dimensions account for the largest magnitude of the difference between source and corrupted embeddings. (b) Cosine similarities and difference of L2 norms between souree embeddings and (adjusted) corrupted embeddings (i.e. first row contains average of cos(h(æ)). h(ā)) and average of [[]A(æ))] [l)())]l)) Embeddings are taken from ImageNet-C severity level Gaussian Noise, on VīT-Base model (pre-trained on ImageNet). Values are averaged over 50000 samples.
existing TTA methods, components which center embeddings the center of source data, but rely on available source data to do so (Niu et al. 2024). We find a surprising structure in the change in the latent geometry. which we connect through the neural collapse phenomenon (Papyan al., 2020), to make NEO fully independent of training data. Neural collapse emerges in the terminal phase of training and formalizes the geometric structure of the classifier weights and embeddings (see more in Appendix (A2)). While this has been explored for domain generalization (Chen et al., 2024) and detecting ouitt--disribution samples (Harun al. 2025), as per our knowledge, this has not been investigated in the context of TTA methods.
4 CHARACTERIZING INPUT DATA DISTRIBUTION SHIFT
In this section, we observe that input data distribution shifts introduce structural change in the latent space.
4.1 LATENT SHIFT AFFECTS FEW DIMENSIONS THE MOST
We find that the most significant change between the source h((:)) and corrupted embeddings, ((+)), occurs in just a few embedding dimensions. We calculate the dimension with the largest change in magnitude for each sample when comparing source and corrupted data. Figure 3 (left), show that for corruptions such as contrast, less than 20 out of 768 dimensions have the largest difference for 95% of samples. For all corruptions, 80% of data has less than 50 dimensions as their highest magnitude change, signifying the possible existence of a globally shared shift across samples and classes. Motivated by this we formalize the structural change in latent space and create the foundation for NEO.
4.2 CHARACTERIZING PER-SAMPLE LATENT SHIFT VECTORS
Let X, C X be the collection of samples from class c. The (global) centroid of the latent represen- tations for samples from X is Ma and the class- wise centroid of the samples from class c, X, is pe- Let PG and j.c denote the same quantities for corrupt samples, X and X.-
Let us define the global centroid shift as AG = LG Ma and class centroid shift as A. = u pe Ac. while accounting for the global centroid shift. Using the global and class centroid shifts, we can define h()) = h(x) + A + A. + 5, where ó is a sample-specifer residual component and
is from class
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In Figure 3a we show the cosine similarity between source data and cornupted data, that is aligned globally. class-wise and sample-wise. The largest increase in cosine similarity is caused by the global alignment, signifying the importance of globally aligning the corrupted latent space. Class- wise alignment increases cosine-similarity again, but only marginally when compared to the increase caused by global alignment. We also show the difference in norms between source and aligned corrupted embeddings. We can see that global alignment greatly reduces the difference in norms. Surprisingly, class-wise alignment increases the difference in norms significantly. This shows that even though cosine similarity may be increased by class-wise alignment, it does not guarantee that norms are similar to those of source embeddings.
Note that none of the alignments we tested above are computable in the fully TTA setting, as no source data or target labels are available. Thus, we also show the cosine similarity and difference of norms for a computable alignment in the last row, which centers corrupted data at the origin. The centering increases cosine-similarity nearly as much as the global shift does while delivering the smallest difference in norms to the source embeddings this centering is the foundation for NEO.
4.3 ALIGNMENT AND ACCURACY
There strong link between linear classification, the cosine similarity between the classifier weights and the embeddings, and the L2 norm of the embeddings. To further analyze this con- nection, we draw on the theory of neural collapse (Papyan et al. 2020; Sūkeník et al. 2023).
Proposition 4.1. Consider a network f with a linear classifier. Assume the model is trained to neural collapse with cross-entropy loss, weight regularization and uniformly distributed classes. Then given We the classifier weight vector corresponding to class we have
y = arg max wr)((a)) + be - y = arg max | (a)ool) h(x)).
Proposition 4.1 (proof in Appendix A.3 shows that under neural collapse assumptions with cross- entropy loss, the assigned class is solely determined by the cosine similarity of embeddings and classifier weights. If we have large cosine similarity between h(x) and h(ă), then the similarity between the classifier weights and h(z) will be similar to that of the classifier weights and h(x). Note that [ does not influence the assigned class, as is a constant factor for all classes, but does influence the logit distribution. Thus the difference in norms between h(x)) and h()) will influence the confidence of predictions.
4.4 CENTERING AT THE ORIGIN IS GLOBAL ALIGNMENT
In Figure 3b we show that centering the corrupted embeddings the origin, significantly improves cosine similarity and difference of norms, compared with source embedding. This not given though; neural network's ' embeddings could be centered at any point that is not the origin.
Proposition 4.2. Consider network exhibiting neural collapse and trained with cross-entropy loss and regularization. Under the assumption of the unconstrained features model (Mixon et al. 2022) (Ireating h(x)) as a freely optimizable variable) and balanced classes, we have DG PAG PG üo
Proof. We define Ao AG Mc. as the difference between the mean embeddings of clean and corrupted data. It's been shown that under cross- cross-entropy loss μG = 02 (Hong & Ling 2024 Zhu
et al. 202I). From this follows that Ac jAG MG PG-
Proposition 4.2 shows that under neural collapse assumptions, the global alignment is equivalent to centering at the origin. This underpins our empirical findings shown in Figure 3b) where we show that shifting h()) by Ag and by ÅG result nearly identical cosine similarities and L2 differences when comparing with h())). Using the theoretical foundation we developed, we now propose NEO.
We also provide the results for MSE loss in Appendix A.1
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4.5 NEO
Having established that h(@)) jác: has desirable properties when fed into the linear classifier, we present NEO, which works on this exact principle. The global mean of corrupted embeddings is updated with each new batch of data, weighting all samples it sees equally, under the assumption that all test-time samples come from the same distribution. This global mean of corrupted embedding then used to center the embeddings at the origin.
For line 4 in the pseudo-code, the Avg operator is used to turn the matrix of embedding vectors returned by the encoder function into sin- gle embedding vector averaged across b sam- ples in the batch. The feature extractor and classifier are slightly modified from the previ- ous sections, as they are able to process batches of data. It is easy computational requirements are added by NEO.
Algorithm NEO
Require:
Dataset X, feature extractor h, classi- fier 0
1: Pg -- 0g. i 4- 0
2: for each batch B E R in X do
that significant
3:
i+i+1
4:
NG + (i 1)/2 Pig + 1/2 Avg(h(B))
The only operations involving vectors matri-
5:
y= 0(h(B) PG15)
ces are averaging, addition, scalar multiplica- tion and single expansion of vector into matrix.
6: end for
NEO robust in various ways. Various existing TTA methods try to approximate shifted class centers (Iwasawa & Matsuo (021), which results in few samples per class-center, and unreliable estimates. NEO approximates just one global shift and able to use every sample to estimate this shift, making it very robust estimate. Moreover, methods that rely 2020) can cause reduction in accuracy when pseudo-labels are inaccurate (Wang et al. 2022) NEO does not rely on labels, thus adding another layer of robustness. Furthermore, the weights of h stay unchanged, preventing catastrophic forgetting, that may occur other methods (Niu et al. 2022). Lastly, NEO does not depend the size of batches, just the amount of data it sees throughout adaptation, taking any samples into account equally and independently, making it reliable in settings where large batches unavailable.
(Liang et al.)
Since NEO weights all samples equally, it may be unsuitable for scenarios where the distribution shift changes. Thus we propose NEo-Continual, which uses the same equation to realign the test-time features to the source features, but uses an exponential moving average, controlled by a hyper- parameter a, keep track of the test-time feature simplex mean, making it suitable for continual adaptation problems. We simply replace the update rule from NEO with:
NaG < (1 11-0) at) -āG + Avg(h(B)).
5 EXPERIMENTS
In this section, we first introduce baseline TTA methods, datasets, models and devices, we use in our experiments. We then perform multiple experiments to show the effectiveness of our proposed method and also why and how it works. Even though our motivation has made theoretical assump- tions such as the existence of neural collapse, we do not require this for our experiments and use regular, publicly available models and datasets.
Baseline TTA Methods. We compare our method with popular adaptation methods: T3A (Iwa- sawa & Matsuo, 2021), SAR (Niu et al., 2023), LAME (Boudiaf al. (022). TENT (Wang al.) 2021), COTTA (Wang et al., 2022). FOA (Niu et al. 2024) and Surgeon (Ma et al., 2025). The hyperparameters used are taken directly from their original paper, or slightly adjusted when default hyperparameters cause catastrophic forgetting our experiment setup. We use a batch size of 64 for all experiments, except those investigating adaptation sample size, class distribution and resource utilization.
Datasets. We evaluate on ImageNet-C (50 samples x 1000 classes x 15 corruption types)
Heendrycks & Dietterich, 2019), CIFAR-10-C (1000 samples 10 classes x 15 corruption types)

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Table 2: Accuracy (%) with 95% confidence intervals across different corruption types and adap- tation methods with ViT-Base on ImageNet-C. Accuracy is calculated on the 512 samples used to adapt. The highest accuracy per corruption type is in bold, and the second-highess is underlined.
Corruption
Adapt
T3A
SAR
LAME
TENT
CoTTA
FOA
Surgeon
NEO
Noise
Goussian
57.0 (0.5)
56.7 (1.7)
(1.7)
56.7
(1.6
(1.6
57.2 (0.6)
58.7 (0.6)
57.7 (0.5)
Shot
36.9 (0.5)
57.0
$7.3 (0.9)
57.5 (1.0)
57.1 (L.)
58.6 (0.4)
58.8 (0.5)
57.6 (0.5)
Impulse
(0.4)
57.0 (1.0)
(1.1)
56.7 (0.9)
(7.6
$7.7(1.1)
57.7 (0.4)
58,9 (0.6)
58. (0.4)
Blur
Defocus
(0.5)
(1.2)
47.5 (1.2)
(L.)
(1.2)
48.2 (1.2)
49.2 (0.4)
49.1 (0.8)
49.8
Glass
35.3 (0.5)
35,9 (0.9)
36.3 (0.9)
(1.0
36.8 (0.8)
36.0 (1.0)
36.8 (0.5)
36.8 (0.7)
37.9 (0.4)
Motion
53.3 (0.4)
(1.1) (1.1)
(1.0 (1.0)
53.3 (1.1)
54.4 (0.44
54.8 (0.6)
55.0 (0.4)
Zoom
44.8 (0.5)
45.3 (1.4)
46.3
44.7
(1.4
(1.4)
47.1 (0.5)
45.7 (0.6)
47.5 (0.5)
Weather
Snow
(..5)
62.7 (1.7)
(1.5)
(L.6
(1.6
(L.4)
64.3 (0.4)
62.2 (0.7)
64.6
Frost
62.6 (0.5)
(1.5) (1.5)
(1.5
(1.4)
(1.4)
63.9 (0.4)
61.7 (0.6)
65.0 (0.5)
Fog
65.8 (0.4)
62.9 (1.2)
(1.1)
(1.0
(1.3
64.8 (1.0)
70.7 (0.4)
63.0 (0.6)
71.2 (0.4)
Brightness
77.9 (0.4)
78.1 (1.1)
(1.1)
78.1
78.2(1.2)
77.9 (0.8)
78.2 (0.4)
78.1 (0.5)
78.3 (0.4)
Digital
Contrast
27.5 (0.4)
(1.3)
(L.4)
36.9 (1.0)
(1.0)
54.5 (0.5)
31.751.)
58.2
Elastic
(0.4)
45.8 (0.9)
45.7 (0.9)
(0.7)
46.7 (0.8)
46.3 (1.2)
49.6 (0.4)
46.2 (0.7)
49.8 (0.4)
Pixclate
(0.4)
(1.1) (1.2)
(L.1
(1.1)
67.8 (1.1)
67.2 (0.4)
67.6 (0.7)
68.2 (0.4)
JPEG
67.9 (0.4)
67.3 (1.5)
67.3 (1.5)
66.9
(1.5)
67.8 (1.7)
68.6 68.6
68.9 (0.7)
69.1 (0.4)
ImageNet-C
55.6 (0.4)
55.9 (1.2) (1.3)
(1.2
(1.2)
55.9 (1.2)
58.4 (0.4)
56.1 (0.7)
59.2 (0.4)
CIFAR-10-C
80.4 (2.8)
80.1 (2.6)
80.6 (2.8)
(2.9)
81.3 (3.2)
80.6 (2.0)
80.9 (2.8)
82.7 (1.7)
82.4 (2.2)
ImageNet-R
59.2 (1.1)
58.7 (1.2)
59.3 (1.1)
(1.1)
(1.I)
59.2 (1.2)
60.2 (1.4)
60.2 (1.6)
60.3 (1.0)
ImageNet-S
45.4 (1.4)
(1.4)
(1.4)
(1.3
45.7 (1.4)
45.2 (1.6)
46.3 (1.7)
47.0 (1.7)
47.2 (1.4)
Hendrycks & Dietterich 2019), ImageNet-Rendition (30,000 samples, 200 classes)
(Hendrycks
et al. 2021 and ImageNet- (50 samples x 1000 classes) (Wang et al. 2019).
Models. In our experiments we use three different sizes of Vision Transformer (ViT) Dosovit- skiy et al. 2021): ViT-S, ViT-Base and ViT-L, which have 22, 86, and 307 million parameters and embedding dimensions 384, 768 and 1024 respectively. We use versions finetuned on ImageNet (Dngg al. 2009) or CIFAR-10 (Krizhevsky & Hinton 2009).
Metrics. We evaluate accuracy in ways. Firstly, the accuracy achieved samples used dur- ing the adaptation process. Secondly, the accuracy achieved on data not used for adaptation, after finishing the adaptation process. The type of accuracy used is stated in experiment descriptions. We use expected calibration error (ECE) (Pakdaman Naeini et al. 2015) to evaluate the trustworthiness of the model (i.e. does 90% confidence translate 90% accuracy), where lower ECE is better.
Devices. In our experiments, we evaluate Raspberry Pi 4B (8GB) and NVIDIA Jetson Orin Nano (8GB), comparing TTA methods in terms of memory consumption and execution time, We also evaluate cloud server with AMD Instinct MI300X (192GB VRAM).
For more details on implementation, including code, see Appendix
5.1 RESULTS
NEO improves accuracy across corruption types. Table 2 shows accuracy results over 15 cor- ruption types in ImageNet-C for NEO compared to 7 baselines. Under corruptions NEO has the highest accuracy and the second highest in the remaining 3, only beaten by Surgeon, which uses considerably more runtime and memory. On average NEO increases performance by 3.6% and in the contrast corruption NEO can nearly double accuracy compared to using adaptation. It is also notable that NEO does not reduce accuracy under any corruption type. has been shown that TTA is often sensitive to hyperparameters and can suffer from catastrophic forgetting, thus delivering near zero accuracy (Niu et al.) 2023) (Kojima et al. 2023). NEO is hyperparameter-Fi and thus extremely robust compared other TTA methods.

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VIT-B
0.3
Aocuracy Increase
ECE Change
ECE Score
-0.00 00.04
MT-S
-0.06
VIT-L
No Adapt
T34
SAR
LAME
TEAT
Co
FoA
Surpeon
NEO
C-10-C
(a) NEO accuracy
(b) NEO ECE
(c) ViT-S ImageNNet-C ECE
Figure 4: (a) Accuracy increase (%) and (b) ECE change compared to no-adaptation for ViT-S, VIT- and ViT-L on ImageNet-C. CIFAR- 10-C, ImageNer-Skete -keetch and SeaagNettRRedittee Accuracy is taken for the whole dataset and no confidence intervals signify a 95% confidence interval of less than 0.05 for accuracy and less than 0.005 for ECE. (c) ECE scores for VIT-S on ImageNet-C averaged over the whole dataset, 15 corruptions and multiple runs.
2.5
C-TTX
50-
59
Aceracy Increase
NEO
Surgeos
58-
Accuracy
-8
REO Cord.
57-
56
55
0.5
S10000
0.0
Number Samples
Number
VmT
VaseBase
Var
(a) NEO adaptation size
(b) NEO adaptation classes
(c) Continual Adaptation
Figure 5: (a) Accuracy (%) for ViT-B on ImageNet-C under varying number of samples to adapt with. (b) Accuracy (%) for ViT-B ImageNet-C under varying number of classes to adapt with (50 samples used to adapt in total). Accuracy is calculated on samples not used for adaptation except for 50,000 samples. (c) Accuracy increase (%) for continual adaptation, adapting on 15 randomly
ordered corruptions from ImageNet-C with 512 samples from each.
NEO improves accuracy and ECE across models and datasets. In Figure 4 we show that NEO consistently improves accuracy across ImageNet-C. CIFAR-IO-C, ImageNet-Sketeh and ImageNet- Rendition, with an over 4% accuracy increase Sketch. Across all VIT sizes NEO improves ac- curacy, with a trend of ViT-B consistently gaining less accuracy than ViT-S and VIT-L. When com- paring with adaptation, there is improvement match in ECE for 9/12 settings evaluated. On ImageNet-C with ViT-S NEO achieves lower ECE than all compared TTA methods. This shows that NEO can be used not only efficiently improve model performance, but also trustworthiness, by producing well-calibrated predictions.
NEO can adapt with just 1 sample class. In some settings, samples to adapt with may be very limited, and not all classes may appear during adaptation. In Figure (5a] we show that adapting with improve accuracy by 1.5% on ImageNet-C. Adapting with just batch
just I sample is enough (64 samples) is so effective that further samples improve accuracy only marginally. Figure shows that adapting with data from just class improves accuracy by over 3% the remaining 999 classes in ImageNet-CC Adapting with 50 classes does not improve accuracy noticeably. Being able to adapt with few samples and classes shows that NEO is extremely robust and efficient.
NEO is effective for continual adaptation. We show the accuracy of the continual version of in Figure 5c. where we present average accuracies while adapting on randomly ordered sequences of 15 corruptions from ImageNet-C. We use 512 samples from each corruption and the model not informed when a corruption type is changed. NEO--Cnninual is more accurate than CoTTA and is only outperformed by Surgeon. Both of these methods use far more resources than Pro-Continual.
Understanding Ωg across corruptions. To understand the behavior of ΩG across corruption types, we adapted using single domain and tested the remaining 14 in ImageNet-C as shown
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Causaiaa
Gaussion
Shot
Impilto
Impidse
Defocus
Applled Comuutiin
Glans
Applled Coruption
Motion
Zoom
Zoom
Show
Frosi
Frust
Fog
Beghtnees
Brightnss
Contrast
Pivelate
Pieelaee
JPEG
JPEG
Gauation
Shat
Imgulin
Dalocn
Srow Front
Fog
Conteusl
Elesti
Plotiato
JPED
Gauation
Gua
Impuise
Daloco
Zoon
Srow
Frout
Elasti
Pluntato
JPED
0.0
Source Corruption
Source Corruption
(a) Accuracy change between corruptions
(b) Cosine similaritics between corruptions
Figure (a) Accuracy change using μe calculated from "Source Corruption" and adapting to samples from "Applied Corruption" (b) Cosine similarity between üa calculated from "Source
Corruption" and "Applied Corruption".
Peak Memory (MB)
2600
Elapsed Time
250
6400
6000
5700
No Adapt.
T34
SAR
LAME
TENT
POA
Surgeon
NED Cont
NEO
No Adapt
So
T34
SAR
LAME
TENT
FOA
Surgeon
NCO Cont.
NEO
Pcak Memory for Jetson
Elapsed Time for Jetson
Figure 7: Peak memory and elapsed time for adapting Vit-Base ImageNet-C (1000 samples
Gaussian Noise) with Nvidia Jetson Orin Nano.
in Figure 6a and ii) measured cosine similarity of üG between domains shown in Figure 6b We discover that Na has high accuracies and cosine similarities between certain corruptions such as noises or blurs. This has practical relevance it can save resources needed to adapt to every do- main observed.
NEO is as efficient as no adaptation. While Figure[bsshove 2blshows that NEO adds no additional compute in larger cloud environment, in Figure[we we show efficieccy results when running the methods an edge device, Nvidia Jetson Orin Nano. NEO is the only method that does not increase the time used for inference, as well the peak memory usage. Results Raspberry Pi follow similar patterns and are in Appendix C.4
CONCLUSIONS
In this paper, present novel yet simple TTA algorithm, NEO grounded our insights the geometry of latent space and the theory of neural collapse. is extremely efficient on both server and edge devices and is robust to scarcity and bias in the adaptation dataset. Our simple implementation will help practitioners to adopt this method. We believe that our paper makes important contributions two directions: the understanding of how embedding space is structured for neural networks and efficient test-time adaptation. We believe our work will trigger further development in both avenues.
Limitations. While NEO by design is not restricted to any specific model architecture, in line with the current technology trend, we evaluate vision transformer architectures, and leave other archi- tecture choices for the future. Our insights are inherently limited to understanding the activations from the penultimate layer and leave the investigations for other layers for future scope.

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Published as a conference paper at ICLR 2026
7 ACKNOWLEDGMENTS
Abhirup Ghosh and Alex Murphy acknowledge Royal Society Research Funding RGS R2 (422383 for supporting this research. We acknowledge Dr. Wendy Yanez Pazmino, for supporting us with edge device environments.
ETHICS STATEMENT
While NEO overall an effective and efficient TTA method, there are ethical caveats, such as TTA being applied settings that illegal or immoral. Improved TTA performance could misused to do harm in such situations. Of course, there are a range of positive impacts as well, such as reduced energy consumption and increased performance for applications such as health and safety. Our code is publicly available to allow others to use NEO in the safest and most transparent way possible.
REPRODUCIBILITY STATEMENT
To aid with reproduction and transparency, we make our code publicly available here We provide more details reproduction, such as hyperparameters and evaluation metrics, in Appendix
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A MORE THEORETICAL RESULTS
Here we present NEO for MSE, an explanation of neural collapse and the proof for Proposition 4.1
A.1 NEO FOR MSE
For models trained under MSE loss instead of cross-entropy loss, we need to adjust NEO.
Proposition A.1. Consider a network f exhibitiin neural collapse and trained with MSE loss. Then, Âg ja and the bias of the classifier b = lc. Under the assumption of the unconstrained features model (iixnn al. 2022) (treating h(x:) as a freely optimizable variable), we have
1
W(h(a) (pa) C = -l==W(()) +
Proof. Under the assumption of neural collapse, Papyan et al. (2020) have proven, using result from Webb & Lowe (1990), that the ideal weights and bias of the classifier under mean square error loss and balanced classes are the following:
W = aM
lc aM ug.
Thus, for the MSE case we subtract the shifted simplex mean and set the bias to (1/C)
(((()) - (ia) + c (M(()) + pa pa - (a) + c lc W (h(()) + +b.
The podd for NEO under MSE loss:
Algorithm NEO-MSE
Require: Dataset S, feature extractor h, classifier weights W
1: AG t- Og. i <- 0
2: for each batch B E RRxxm in S do
3: i -+++1
4: jAG + (i- 1)/i jag + 1/i mean (h( B))
5: y= (h(BB) pc1.)) + 1c1,,
6: end for
A.2 NEURAL COLLAPSE
Recent work analyzing the behavior of the last layer in neural networks, has discovered phe- nomenon known as neural collapse (Papyan et al. 2020)). It occurs when continuing to train a neural network after it has achieved near zero loss, also known as the terminal phase of training. It's property of the last layer of the feature extractor, but recent work has also been expanding neural collapse to more layers in a neural network (Sūkeník et al., (023).
In addition to na and μ. which we defined in the problem statement, we also define the within-class covariance to be Ew Avgi, ((h - (h,,. - p.)' ). where hic is the embedding of sample
x from class Papyan et al. (000)) identify the following four properties of neural collapse:
(NC1) Variability collapse: The variation of features within the same class goes zero.
Ew - 0
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(NC2) Convergence to simplex equiangular tight frame (ETF); The class means of the features form the vertices of an ETF simplex, with equal length and angles between them. Essentially, all class means equal distance and at equal angle from each other.
lIue - Mall2 -Ilee - 14 - Ve,d d
C
(Pe Me) - C-1 dcd C-1 Ve,
(NC3) Convergence self-duality: The class means and classifier weights converge to each other upon rescaling.
W
MT
+0
W
|
(NC4) Simplification to nearest class-center: At inference, the classifier solely decides which class to predict, by taking the class mean with the lowest euclidean distance.
arg max(me; h(x))) be arg min l[h(z) pel12
where ja: (pe pc)/ llce Hall2. M Ue PG.c I,.... Cl E R W contains the classifier weights and de,e is the Kronecker delta symbol (Papyan et al. 2020).
A.3 ALIGNMENT AND ACCURACY
Recall that Proposition sttsttss::
Proposition. Consider a network I with a llsttllaer linear classifier, Assume the model is trained to neural collapse with pross-entrony loss, regularization and evenly distributed classes. Then letting we denote the classifier weight vector corresponding to class c, we have:
arg max war)(a)) + be
y = arg max (r.
h(x=))
The proof for Proposition 4.1 follows.
Proof. Under neural collapse with cross-entropy loss, regularization and evenly distributed classes, the bias b equals the zero vector (Hong & Ling 2024). Then by combining
w. h(x))
y = arg max (())) + be = arg max wx)(w) and cos(w,, h(x))) [w. [(x))
conclude that
arg max wch(xx) bo = y arg max | (x))lll)(())o)s(( h(x))
B REPRODUCTION DETAILS
In this section we present details of our experiments to aid with reproduction. Additionally, please find the code used for our experiments here: our code is based on the repository used by FOA (Niu et al. 2024). The implementation for Surgeon
A large part of
based on the original paper repository (Ma 2025).
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B.1 TTA METHODS
In our experiments we compare with T3A (Iwasawa & Matsuo 2021), SAR NNu al. 2023). LAME (Boudiaf et al. ) TENT al. 2024) and Surgeon (a al. 2025). We use the default hyperparameters specified in the papers, unless the default hyperparameters cause catastrophic forgetting (accuracy goes to zero), in which case we modify the method to use hyperparameters that do not cause catastrophic forgetting (as most papers do not have results for all models or datasets that we use).
Wang et 20211, COTTA WWng et al. 2022). FOA (Nuu
For Surgeon we set the learning rate of Adam to 10-5, For TENT we use a learning rate 0.00025 for all datasets, reduced for on-device resource consumption (due to memory limitations) and sample/class size experiments (only applicable to NEO).
keep a batch size of 64 throughout most experiments. The batch size is only
B.2 DATASETS
We evaluate on ImageNet-C (50 samples 1000 classes x 15 corruption types) (Hendrycks &
Dietterich 2019
CIFAR-1O-C (1000 samples x 10 classes x 15 corruption types) (Hendrycks & Dietterich 2019 ImageNet-Rendition (30,000 samples, 200 classes) (Hendrycks al. [022 and
Snaecher-Sketch (50 samples x 1000 classes) (Wang et al. 2019).
CIFAR-10-C available here:
ImageNet-C is avail- ImageNet-RRndiinee is available here:
able here:
-t ImageNet-Sketch is available here:
For CIFAR-1O-C we only the 15 basic corruption types and not the 4 additional types.
B.3 MODELS
three different sizes of Vision Transformer (ViT) (Dosovisskiy et al., 2021]: VìT-S, ViT-Base and ViT-L, which have 22, 86, and 307 million parameters and embedding dimensions of 384, 768 and 1024 respectively. We use versions finetuned on ImageNet (Deng al. 2009] or CIFAR-I0 (Krizhessky & Hinton 2009).
In experiments
For models used on ImageNet we obtained model weights from timm (Wightman 2019) We used Sasmallpatcch6_2221 ; bait_base cassse_pachh622211 2242 and sit_large_pacch aatch16_2224 224'. For models fine- tuned on CIFAR-10, we used publicly available weights from huggingface: 'MF21377 1977vit- small-patch16-225 faaifflo-2--innttumeee finetuned-Cifarl0", 'nateraw/vit-bare base- pateepptchhec 1--chh6-24-cifrr and 'tzhao3/vit-L. 1IFAR10', They use the same ViT architecture as our ImageNet ViTs, but are finetuned on CIFAR- 10.
B.4 METRICS
We evaluate accuracy in two ways, depending on the type of experiments.
The first way is that we use the accuracy achieved on samples used during the adaptation process. This means that the model starts out unadapted (resulting in potentially low accuracy) and adapt over time (increasing accuracy).
The second way is that we use the accuracy achieved on data not used for adaptation, after finishing the adaptation process. This means we split the dataset into an adaptation set and validation set. We then calculate accuracy on the validation set, only after adaptation is finished.
We evaluate model calibration using ECE (Pakdaman Nacini et al. 2015), which quantifies how well model's assigned probabilities align with the actual correctness. ECE is computed by grouping predictions into bins (in our case 15) based on the confidence of the prediction. The difference between observed accuracy and average confidence is calculated and then weighted average is taken. A low ECE signifies good calibration while a high one implics bad calibration that is over- confident on wrong predictions under-confident correct predictions.
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Table 3: Accuracy (%) with standard deviations across different corruption types and adaptation methods with ResNet-50 on ImageNet-C. The highest accuracy per corruption type is in bold, and the second scchne- is underlined. 512 samples used for adaptation and level corruptions.
Corruption
No Adapt
SAR
TENT
CoTTA
NEO
NEO-BN
Noise
Gaussian
20.96 (0.64)
14.00 (1.09)
14.00 (1.09)
13,80 (1.48)
23.05 (0.32)
13.87 (1.75)
Shot
21.94 (1.12)
16.34 (1.48)
16.67 (1.20)
16.54 (1.33)
24.35 (1.43)
16.73 (1.37)
Impulse
21.94 (0.09)
13.87 (0.70)
13.87 (0.16)
13.80 (0.09)
23.89 (1.29)
13.80 (0.40)
Blur
Defocus
14.71 (1.34)
11.65 (0.96)
12.11 (0.57)
11.59 (0.33)
16.93 (1.15)
11.85 (1.52)
Glass
8.33 (1.06)
13.61 (0.51)
13.35 (0.40)
13.15 (0.37)
9.24 (1.33)
13.48 (0.70)
Motion
16.93 (0.66)
23.50 (1.04)
24.15 (1.45)
23.76 (1.90)
19.47 (1.06)
23,11 (1.36)
Zoom
19.40 (0.40)
35.42 (0.56)
35.61 (0.37)
35.48 (0.24)
21.03 (1.18)
34.96 (0.32)
Weather
Snow
23.76 (1.36)
40.69 (2.23)
40.82 (2.19)
40.43 (2.38)
(1.00)
39.45 (2.51)
Frost
33.01 (1.31)
41.28 (2.31)
41.41 (2.32)
41.47 (2.02)
35.61 (0,51)
40.82 (0.97)
Fog
29.62 (0.24)
56.90 (0.93)
57.36 (1.30)
57.03 (0.89)
33.01 (0.89)
56.12 (1.78)
Brightness
64.65 (1.12)
66.67 (0.75)
66.73 (0.66)
67.06 (0.72)
64.71 (1.33)
65.49 (0.72)
Digital
Contrast
9.24 (1.13)
24.87 (0.88)
24.67 (0.49)
24.87 (0.64)
10.61 (1.22)
24.67 (1.15)
Elastic
12.24 (0.80)
42.25 (1.85)
42.25 (1.71)
42.38 (1.52)
15.30 (1.06)
41.41 (1.39)
Pixelate
12.50 (0.48)
38.02 (1.06)
38.61 (L.43)
38.54 (0.79)
14.00 (0.09)
37.17 (1.36)
JPEG
45.90 (0.32)
40.69 (2.58)
40.49 (2.44)
40.49 (2.30)
46.94 (0.40)
39.84 (2.53)
ImageNet-C
23.68
31.98
32.14
32.03
25.66
31.52
B.5
RESOURCE EFFICIENCY
The following component versions were used for experiments on resource usage:
The Raspherry PI 4B (8GB RAM) used the following software versions: Debian 12 ("book- worm", kernel: 6.6.51 -.).--- Python 3.1 1.2, torch 2.8.0, torchvision 0.23.0.
NVIDIA Jetson Orin Nano (8GB) used the following software versions: Ubuntu 20.04.6 LTS (kernel: 5. 1.10.192,,,,ra, Python 3.8.10, CUDA 11.4, torch 2. 1...000004331538mmmee
torchvision 0.16.0.
AMD Instinct MI300X (192GB VRAM) and INTEL(R) XEON(R) PLATINUM 8568Y+ used the following software versions: Ubuntu 24.04.1 LTS, Python 3.12.3, rocm- libs version 6.4.1.60401-83 24.04, torch 26.0+rocm642gii7766888 torchvision
C ADDITIONAL RESULTS
C.1 RESULTS ON CNNs
In Table 3 can see that on ResNet-50, NEO still is able to deliver considerable improvements over using no adaptation. We compare vanilla NEO, as well as NEC-BN, which updates batch normal- ization parameters, as is common in many other TTA methods (but not applicable to transformers). What notable, is that in case where using no adaptation is the second most effective, NEO most effective method. All other methods, deliver reduction in accuracy, suggesting that NEO is suitable for adaptation in settings where no other method able to improve.
C.2 ABLATION STUDIES
In Table 4a we can see that NEO is batch size independent, and there no significant difference in final accuracy when changing the batch size. This confirms our theoretical analysis of NEO. When
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Published as a conference paper at ICLR 2026
Table 4: Ablation Studies
Batch Size
Accuracy (%)
Alpha
Accuracy (%)
56.91
0.00
53.27
4
57.04
0.01
53.40
8
56.99
0.01
53.59
16
57.02
0.05
54.39
32
56.97
0.10
55.14
64
56.98
0.50
56.64
(a) Average accuracy across all corruptions for vary- ing batch sizes. ViT-Base on ImageNet-C, using all level 5 corruptions, when adapting with NRO. Adapt- ing on 512 samples and evaluating remaining ones.
(b) Average accuracy across all corruptions for lev- els of a. ViT-Base on ImageNet-C. using all level 5 corruptions, when adapting with NROO-Continoous Adapting on 512 samples and evaluating on remain- ing ones.
Table Neural Collapse (NC) statistics across different ViT architectures. Measured on ImageNet.
Metrics used from (Wu & Papyan 2024)
Model
NC1
NC2
NC3
NC4
ViT-Small
0.6070
1.2207
1.1969
0.8518
ViT-Base
0.5110
1.0092
0.9501
0.9238
ViT-Large
0,4640
1.2548
1.2069
0.9067
using NEO-Continuous, we can see in Table 4b| adapting on 512 samples per corruption, higher outperforms the lower ones. This is because of the effectiveness of NEO in low sample settings, not needing many samples get the full benefits of adaptation. A lower adaptation will only slowly update the model and thus provide less overall accuracy.
C.3 NEURAL COLLAPSE STATISTICS
In Table we can see the NC statistics for NC1 (Variability Collapse), NC2 (Convergence to simplex ETF), NC3 (Convergence to self-duality) and NC4 (Simplification nearest class-center). We can see a clear decrease in NC1 as model size increases. NC2 and NC3 follow a similar trend to each other, where ViT-Base performs best. Similarly, NC4 is highest for ViT-Base, closely followed by ViT-Large. Overall, we can see that ViT-Base shows the highest neural collapse.
C.4 RESOURCE CONSUMPTION ON RASPBERRY Pi
Peak Memory (MB)
6000
Elapsed Time (s)
800
4000
500
2000
300
1000
200
No Adapt
T3A
SAR
LAME
TENT
FOA
NEO
NEO Cont.
No Adapt
T3A
SAR
LAME
TENT
FOA
NEO
NEO Cont.
(a) Peak Memory for Raspherry Pi
(b) Elapsed Time for Raspberry Pi
Figure 8: Peak memory and elapsed time for adapting on Vit-Base on ImageNet-C. Raspberry Pi
128 samples- Gaussian Noise 5 Batch Size = 8.
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NEC is the most efficient TTA method for both memory usage and inference time. Due to the large memory requirements of CoTTA and Surgeon we could not show results for them on Raspberry Pi.
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C.5 IMAGENET-C BREAKDOWN BY CORRUPTION TYPE
Table 6: Accuracy (%) with 95% confidence intervals across different corruption types and adap- tation methods with ViT-Small ImageNet-C. Accuracy is calculated the 512 samples used to adapt. The highest accuracy per corruption type is in bold, and the second-highest is underlined.
Corruption
No Adapt
T3A
SAR
LAME
TENT
COTTA
FOA
Surgeon
NEO
Noise
Gaussian
(0.6)
31.8 (1.4)
(1.)
34.7 (1.5)
(1.4
33.7 (0.8)
35.3 (2.2)
(0.7)
Shot
32.1
32.1
34.7 (0.9)
(0.8
(0.9)
31.7 (0.7)
(1.7 (3.7
34.7 (0.6)
Impulse
33.0
32.7 (0.9)
35.5 (1.2)
34.5 (2.8
(1.3)
(0.5)
(2.6)
35.5 (0.5)
Blur
Defocus
(0.5)
31.3 (1.2)
30.7(1.2) (1.3)
32.1 (1.5)
31.99 (0.8)
37.1 (0.6)
32.0 (1.4)
35.9 (0.5)
Glass
(0.6)
(0.7)
24.9 (0.7)
(0.7
(0.8)
23.7 (0.8)
25.1 (0.5)
24.3 (1.0)
(0.6)
Motion
(0.6)
(1.2)
(1.2 (1.)
40,4 (L.)
(0.5)
40.8 (1.9)
44.4
Zoom
32.5 (0.6)
32.3 (1.2)
(1.2)
(1.)
(1.I)
(1.0)
35.2 (0.5)
32.9 (2.2)
36.4 (0.6)
Weather
Snow
(0.6)
44.4 (0.9)
(1.0)
(0.8
(0.9
(0.9)
47.2 (0.6)
43.7 (3.4)
48.5 (0.5)
Frost
(0.7)
44.2 (1.4)
44.9 (1.4)
(1.4
(1.5)
43.8 (1.3)
46.4 (0.6)
44.6 (1.6)
47.6 (0.8)
Fog
46.3 (0.6)
(0.9)
46.3 (1.1)
(0.8)
(L.)
(0.6)
46.3 (1.6)
Brightness
70.4
70.8 (0.8)
71.3 (0.9)
(0.9
71.4 (0.9)
70.3 (1.3)
(0.7)
71.5 (2.5)
71.9 (0.5)
Digital
Contrast
(0.5)
16.0 (0.8)
17.9 (2.2)
(..7
(0.9)
(0.9)
21.5 (0.5)
15.9 (1.8)
19.7 (0.4)
Elastic
36.9 (0.6)
36.9 (1.2)
36.4 (1.8)
(1.2)
37.0 (1.2)
424 (0.6)
38.3 (3.1)
43.8 (0.5)
Pixelate
55.6 (1.0)
56.5 (1.0)
(1.2
(1.0
(1.2)
56.3
(2.8)
(0.6)
JPBG
55.2 (0.5)
55.4 (0.9)
(1.0)
(0.8)
(1.0)
(1.1
$7.9 (0.7)
54.3 (2.3)
57.8
ImageNet-C
39.6 (0.6)
39.7 (1.1)
40.7 (1.3)
(9.00
40.8 (1.1)
39.7 (1.1)
42.4 (0.6)
40.2 (2.2)
43.2 (0.6)
Table 7: Accuracy (%) with 95% confidence intervals across different corruption types and adap- tation methods with ViT-Large on ImageNet-C. Accuracy is calculated on the 512 samples used to adapt. The highest accuracy per corruption type is in bold, and the second-highest is underlined.
Corruption
No Adapt
T3A
SAR
LAME
TENT
CoTTA
FOA
Surgeon
NEO
Noise
Gaussian
63.1 (0.7)
63.4 (1.6)
(3.5
(3.0(
(3.6
63.4 (1.5)
63.1 (0.6)
65.6 (1.5)
64.5 (0.7)
Shot
61.6 (0.6)
(1.1)
(1.1)
60.7 (1.0)
(1.0)
61.6 (1.3)
62.2 (0.7)
64.6 (2.9)
Impulse
63.7 (0.6)
64.3
64.0 (1.4
(1.4
64.4 (1.1)
64.0 (0.6)
64.1 (1.6)
65.0 (0.6)
Blur
Defocus
52.7 (0:7)
53.1 (1.2)
53.2
53.9 (1.6
52.8 (0.9)
56.8 (0.5)
53.5 (2.1)
56.2 (0.7)
Glass
44.8 (0.6)
44.8 (1.0)
44.9 (1.1)
(1.1
45.7 (0.9)
(1.1)
46.0 (0.7)
45.5 (2.3)
46.4 (0.5)
Motion
60.5 (0.6)
(1.4)
60.7 (1.3)
(1.3
(1.4)
(1.3)
61.8 (0.6)
60.5 (3.1)
(0.6)
Zoom
(0.7)
(1.7)
55.2
55.8 (1.6
55.5 (1.6)
56.8 (0.6)
54.9 (1.5)
57.0 (0.7)
Weather
Snow
66.3 (0.8)
65.8 (2.0)
(2.0)
65.1 (2.0)
66.2 (1.9)
66.2 (1.5)
66.6 (0.6)
66.1 (3.2)
68.1 (0.7)
Frost
62.3
62.3 (1.1)
(1.1)
(1.7
62.7 (1.1)
62.9 (1.1)
63.9 (0.6)
62.2 (2.8)
64.4 (0.7)
Fog
(0.5)
61.9 (1.4)
62.4 (1.2)
(1.2
62.2 (1.0)
62.2 (1.5)
64.7 (0.5)
62.1 (2.2)
67.2 (0.6)
Brightness
80.2 (0.5)
80.5
80.3 (0.9)
(1.2)
80.6
80.1 (1.0)
80.1 (0.6)
79.7 (2.6)
80.6
Digital
Contrast
39.7 (0.5)
39.2 (1.2)
(1.6)
(1.2
40.3
(1.2)
46.0 (0.6)
41.1 (1.5)
42.9 (0.6)
Elastic
(0.6)
55.7 (1.0)
(1.2)
(1.0)
56.1 (1.1)
55.5 (0.9)
$9.0 (0.5)
54.7 (3.1)
59.3 (0.6)
Pixelate
(0.6)
74.8 (1.3)
(1.3)
76.2 (1.2)
74.7 (1.2)
(2.0) (0.4)
(0.5)
JPEG
72.7 (0.5)
(L.1
(1.4
72.9
(1.2
(0.6)
71.1 (3.0)
74.1 (0.5)
ImageNet-C
61.1 (0.6)
(1.3
60.6
(1.6
61.1
62.6
61.3 (2.5)
63.1 (0.6)
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C.6 ACCURACY RESULTS ON FULL DATASETS
All results are averaged over seeds 1234, 2020, 9999. Not all TTA methods are available for all experiments.
57.5
Average Accuracy
No Adapt
47.5
SAR
LAME
45.0
CollA
42.5
Surgeon
40.0
NEO
37.5
128
512
2048
32768
Number Samples
Figure 9: VIT-S ImageNet-C
62
60
Average Accuracy
58
T3A
LAME
TENT
52
FOA
Surgeon
50
NEO
NEO Cont.
128
512
2048
8192
32768
Number of Samples
Figure 10: ViT-B ImageNet-C
Average Accuracy
No Adapt
66
SAR
64
TENT
CoTTA
Surgcon
60
NEO
128
512
2048
32768
Number Samples
Figure 11: VIT-L ImageNet-C
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90
Average Accuracy
88
No Adapt
SAR
LAME
CoTTA
FOA
NEO Cont.
64
128
256
512
1024
2048
4096
8192
Number of Samples
Figure 12: ViT-S CIFAR-IO-C
87
Average Accuracy
86
T3A
LAME
TENT
FDA
NEO
8192
Number Samples
Figure 13: ViT-B CIFAR-IO-C
91
90
Average Accuracy
89
No Adapt
88
SAR
87
86
CoTTA
Surgcon
NEO
NEO Cont.
128
1024
2048
8192
Number Samples
Figure 14: VIT-L CIFAR-10-C
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56
54
Average Accuracy
52
50
No Adapt
43
T3A
46
LAME
44-
NEO
NED Cont.
128
512
2048
B1.92
32768
Number of Samples
Figure 15: ViT-S ImageNet-R
66
Average Accuracy
No Adapt
60
SAR
LAME
NEO
Number of Samples
Figure 16: ViT-B ImageNet-R
71
Average Accuracy
69
68
67
Adapt
66
T3A
SAR
65
TENT
64
NED Cont.
63
128
8192
32768
Number Samples
Figure 17: VIT-L ImageNet-R
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42
Average Accuracy
36
No Adapt
T3A
LAME
TENT
30-
NEO Cont.
28
128
512
2048
8192
32768
N Number of Samples
Figure 18: ViT-S ImageNet-S
Average Accuracy
46
No Adapt
A3A
LAME
NEO
NEO Cont.
42
128
512
2048
8192
32768
Number of Samples
Figure 19: ViT-B ImageNet-S
58
Average Accuracy
54
No Adapt
T3A
LAME
52
TENT
NEO
51
NEO Cont:
128
512
2048
8192
32768
Number of Samples
Figure 20: ViT-L ImageNet-S
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C.7 ECE RESULTS ON FULL DATASETS
Calculated over seeds 1234, 2020 and 9999.
ECE Score
0.2
0.1
0.0
No Adapt
T3A
SAR
LAME
TENT
COTTA
FOA
Surgeon
NEO
Figure 21: ViT-B ImageNet-C
0.3
ECE Score
0.2
0.1
0.0
No Adapt
T3A
SAR
LAME
TENT
COTTA
FOA
NEO
Figure 22: ViT-L ImageNet-C
0.15
ECE Score
0.10
0.05
0.00
No Adapt
T3A
SAR
LAME
TENT
COTTA
FOA
NEO
Figure 23: VIT.S CIFAR-10-C
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0.2
ECE Score
0.1
0.0
No Adapt
T3A
SAR
LAME
TENT
FOA
NEO
Figure 24: ViT-B CIFAR-IO-C
ECE Score
0.10
0.05
0.00
No Adapt
T3A
SAR
LAME
TENT
COTTA
FOA
Surgeon
NEO
Figure 25: VIT-L 1IFAR-10-C
0.6
ECE Score
0.4
0.2
0.0
No Adapt
T3A
SAR
LAME
TENT
NEO
Figure 26: VIT-S ImageNet-R
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ECE Score
0.2
0.1
0.0
No Adapt
T3A
SAR
LAME
TENT
NEO
Figure 27: ViT-B ImageNet-R
0.3
ECE Score
0.2
0.1
0.0
No Adapt
T3A
SAR
LAME
TENT
NEO
Figure 28: VIT-L ImageNet-R
0.8
ECE Score
0.6
0.4
0.2
0.0
No Adapt
T3A
SAR
LAME
TENT
NEO
Figure 29: VIT-S ImageNet-S
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0.3
ECE Score
0.2
0.1
0.0
No Adapt
T3A
SAR
LAME
TENT
NEO
Figure 30: ViT-B ImageNet-S
0.3
ECE Score
0.2
0.1
0.0
No Adapt
T3A
SAR
LAME
TENT
NEO
Figure 31: VIT-I ImageNet-S
C.8 CONTINUAL ADAPTATION ON IMAGENET-C 512 SAMPLES OVER CORRUPTION INDEX
These figures show adaptation over time (starting adaptation at index and ending at 15). Cor- ruptions are randomly ordered over different repetitions, resulting results that do not depend on specific sequence of corruptions.
Average Accuracy
No Adapt
36
CoTTA
34
Surgeon
NEO Cont.
32
Corruption Sequence Index
Figure 32: VIT-S ImageNet-C
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62
Average Accuracy
56
54
NEO
50
CaTTA
Surgcon
NEO Cont.
Corruption Sequence Index
Figure 33: ViT-B ImageNet-C
66
Average Accuracy
Adapt
50
NEO
Surgeon
NEO Cont.
Corruption Sequence Index
Figure 34: VIT-L ImageNet-C
D DISCLOSURE OF AI USAGE
LLMs were used to help search for relevant works, writing parts of the code (e.g., plots, bash scripts) and proof-reading.
28


Reviews:
[{"review_id": "NxaFo7afAJ", "reviewer": "Reviewer_HPPs", "summary": "This paper proposes NEO, a hyperparameter-free test-time adaptation (TTA) method that addresses distribution shifts by re-centering corrupted embeddings at the origin. The core contribution is leveraging neural collapse theory to justify a simple yet effective approach: computing the global centroid of target embeddings and subtracting it to align features with source data. NEO requires no backpropagation, adds minimal computational overhead (storing only a single vector), and demonstrates competitive or superior accuracy compared to seven baseline TTA methods on ImageNet-C, CIFAR-10-C, ImageNet-R, and ImageNet-S using Vision Transformer architectures. The method achieves 59.2% accuracy on ImageNet-C with ViT-Base (vs. 55.6% without adaptation), operates efficiently on edge devices, and maintains robustness even when adapting with as few as one sample or one class.", "questions": "1. Can you measure NC1-NC4 metrics on your ViT models? Specifically: $\\Sigma_W \\approx 0$, equiangular class means, self-duality, $\\mu_G \\approx 0_d$? How robust is NEO when these fail?\n\n2. Have you tested NEO on CNNs (ResNet-50, EfficientNet)? Would you expect similar effectiveness if neural collapse differs?\n\n3. How does performance degrade with class imbalance? At what ratio does $\\mu_G = 0_d$ break down?\n\n5. Is NEO's advantage over FOA from (a) no source data or (b) better adaptation? Can you ablate with source statistics?\n\n6. How to set $\\alpha$ in NEO-Continual? Show sensitivity analysis across $\\alpha \\in [0.01, 0.9]$.\n\n7. Why does ViT-Base underperform ViT-S/L (Figure 4a)?\n\n9. Can pre-computed corruption taxonomy enable zero-shot adaptation (Figure 6)?\n\n10. Quantify exact FLOPs overhead for NEO vs. vanilla inference.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "**Originality:** Novel connection between neural collapse theory and TTA. Propositions 4.1-4.2 provide theoretical justification showing $\\mu_G = 0_d$ under neural collapse, making $\\Delta_G = \\tilde{\\mu}_G$. The empirical finding that shifts affect <50 of 768 dimensions for 80% of samples motivates the global alignment strategy effectively.\n\n**Quality:** Comprehensive evaluation across three ViT architectures, four datasets, seven baselines. Strong robustness demonstrated: single-sample adaptation, continual learning, edge deployment (Raspberry Pi, Jetson). Figure 3b validates theory with 0.49 cosine similarity to source. Cross-corruption analysis (Figure 6) provides practical deployment insights.\n\n**Clarity:** Well-structured progression from empirical observations â†’ theoretical justification â†’ algorithm. Figure 1 illustrates single-line implementation elegantly. Algorithm 1 is concise and clear.\n\n**Significance:** Addresses critical TTA limitations (cost, memory, hyperparameters) with strong practical value. Achieving highest accuracy (59.2% vs. 58.4% FOA) while being 63% faster demonstrates real-world applicability.", "weaknesses": "**Unverified Theoretical Assumptions:** Theory relies on neural collapse, but no empirical validation that ViT models exhibit NC1-NC4 properties (within-class collapse, equiangular tight frame, $\\mu_G \\approx 0_d$). Proposition 4.2's unconstrained features and balanced class assumptions are strong yet unverified. Need: (a) measure NC metrics on evaluation models, or (b) ablations showing robustness when assumptions fail. Class imbalance in real deployments contradicts balanced class requirement.\n\n**Architecture Specificity:** Claims architecture-agnostic but only evaluates ViTs. CNNs (different inductive biases) may not exhibit same latent properties. Given TENT/SAR target CNNs, this gap is critical. Need: test on at least one CNN (ResNet-50) or explicitly restrict claims to Transformers.\n\n**Missing Failure Analysis:** NEO loses to Surgeon on 3/15 corruptions (Gaussian/Shot/Impulse) and FOA on brightness, with no explanation. Theory assumes global shifts, but what about class-specific components? Figure 3b shows class-wise $\\Delta_c$ gains marginal improvement (0.64 vs. 0.51), suggesting untapped potential.\n\n**Weak FOA Comparison:** FOA is most similar (backprop-free, 2 forward passes, efficiency-focused). Paper doesn't explain conceptual differences or why NEO wins (59.2% vs. 58.4%). Is the gain from no-source-data or better adaptation? Need ablation: give NEO source statistics like FOA to isolate re-centering contribution.\n\n**Continual Hyperparameter Contradiction:** NEO-Continual uses EMA parameter $\\alpha$, contradicting \"hyperparameter-free\" claim. No guidance on setting $\\alpha$, no sensitivity analysis despite continual adaptation being a key contribution. Need: sensitivity across $\\alpha \\in [0.01, 0.9]$ or explicit limitation acknowledgment.\n\n**ViT-Base Anomaly Unexplained:** Figure 4a shows ViT-Base gains less than ViT-S/L consistently, contradicting theory that dimensionality shouldn't matter. This pattern deserves investigation.", "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": "1xlAenq4jQ", "reviewer": "Reviewer_rtzZ", "summary": "The paper introduces NEO, a hyperparameter-free and optimization-free Test-Time Adaptation (TTA) method that operates by re-centering latent embeddings at the origin. It leverages theoretical insights from neural collapse to justify that centering corrupted test embeddings improves alignment with the clean feature space. NEO requires only forward passes, negligible compute, and no access to source data. Experiments across four datasets (ImageNet-C/R/S, CIFAR-10-C) and three ViT architectures show consistent improvements over prior TTA methods under its own evaluation setting.", "questions": "I am also somewhat confused about the Peak Memory comparison on the Jetson device, as the relative differences between methods seem inconsistent with results typically observed on standard GPUs (e.g., A100).\n\nAdditionally, the influence of batch size has not been thoroughly analyzed, particularly for the continual version of NEO.\n\nIt would be helpful to clarify whether the method can maintain strong performance under non-i.i.d. settings (e.g., imbalanced label distributions) and whether it also generalizes effectively to CNN-based architectures.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "The studied forward-only test-time adaptation problem is practical and interesting.\n\nNEO’s one-line implementation (replacing nn.Linear with a custom layer) is elegant and simple to use. It adds no backprop, parameters, or optimization loops.\n\nEvaluations on low-power devices (Jetson Orin) highlight NEO’s edge-readiness—rarely studied in TTA works.", "weaknesses": "The reported results of the baselines appear questionable. While I understand that the authors may have used different evaluation settings, this explanation is not convincing, as the reported performance is significantly lower than in the original papers. Since this work does not aim to introduce a new evaluation protocol, it should follow the established settings used in prior works such as FOA to ensure fair comparison. As a result, I remain doubtful about the reported results, which undermines confidence in the claimed effectiveness of the proposed method.\n\n\nThe theoretical analysis relies on idealized assumptions—such as balanced classes, cross-entropy training, and zero-centered clean features—which may not fully hold in real-world scenarios. It also remains unclear how well these assumptions apply to models whose features are not zero-centered.", "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": "A3JxI7Yobm", "reviewer": "Reviewer_4bB3", "summary": "The paper proposes NEO, a simple test-time adaptation method that performs feature re-centering by subtracting the mean of test embeddings. The method is motivated by the Neural Collapse theory and aims to handle distribution shifts without optimization or access to source data. Experiments are conducted mainly on ImageNet-C and related benchmarks.", "questions": "1. Could the authors leverage the neural collapse assumption to explain why existing entropy minimization–based test-time adaptation (TTA) methods are prone to feature or classifier collapse during adaptation?\n2. Could the authors further discuss, from a theoretical perspective, whether the neural collapse assumption still holds—and whether NEO remains effective—in realistic scenarios such as those with class imbalance?", "limitations": "", "rating": 2, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1. The method is simple and easy to implement.\n2. The paper provides a clear and intuitive geometric explanation based on Neural Collapse.\n3. Experimental results show that the approach achieves comparable accuracy to some optimization-based TTA methods while requiring less computation.", "weaknesses": "1. Lack of methodological novelty. The core idea of this paper’s method is highly similar to the Back-to-Shift mechanism in FOA[1], particularly under the special case where the source feature mean equals zero. Similar effects have already been explored in that setting. The authors are encouraged to further clarify the distinctions between NEO and existing work, and to elaborate on the method’s genuine theoretical or practical contributions.\n2. The effectiveness of NEO strongly depends on the assumption that the source-domain embedding mean is zero. If this assumption does not hold (e.g., when models use different normalization mechanisms such as BatchNorm or GroupNorm), the performance of the method may degrade significantly. To verify the generality of this assumption, it is recommended to include additional experiments using models with BatchNorm, GroupNorm, and other normalization layers, and to compare NEO’s robustness across these settings.\n3. Insufficient validation of batch-size independence. Despite the claim that the method is batch-size agnostic, the experiments only apply test-time adaptation to a limited number of samples (e.g., a single small batch), and the adapted model is reused for all remaining evaluations—raising questions about true batch-size independence. To substantiate this claim, the authors should perform full test-time adaptation on all test samples using different batch sizes (e.g., 1, 8, 64, 512), where the entire adaptation process is repeated independently for each batch size, and then compare the resulting performance to assess true batch-size independence.\n4. Lack of evaluation under label shift scenarios. When class prior distributions differ between the source and target domains, simply subtracting the current batch mean may introduce bias and fail to properly correct distribution shifts. It is recommended to include experiments under label shift settings, as used in studies such as SAR[2], rather than evaluating adaptation only on samples from selected classes.\n5. The experiments that adapt using only one batch or one class are compared solely with the “no adaptation” baseline, without including other TTA methods. This limited comparison is insufficient to demonstrate whether NEO still outperforms existing methods under few-sample or class-restricted adaptation scenarios.\n6. Insufficient comparison in continual adaptation experiments. In the continual adaptation section, the paper compares NEO with only a few existing methods. It is recommended to include common anti-forgetting TTA methods such as EATA[A], ViDA[B] and KFF[C] to more comprehensively demonstrate NEO’s performance in long-term adaptation scenarios.\n7. The method is evaluated using only 512 adaptation samples, which may favor NEO. Optimization-based TTA methods typically employ conservative strategies (e.g., small learning rates) to prevent overfitting. When adaptation data is limited, a slightly higher learning rate may substantially improve their performance. Therefore, this setup may underestimate the performance of other methods.\n8. Incomplete disclosure of hyperparameter settings. For some baseline methods—especially those using the same model architecture but with undisclosed configurations—the paper does not provide complete hyperparameter details. To ensure reproducibility and fair comparison, the appendix should include the full hyperparameter settings for each method and model.\n\n[1] Test-Time Model Adaptation with Only Forward Passes. ICML 2024.\n\n[2] Towards stable test-time adaptation in dynamic wild world. ICLR 2023.\n\n[A] Efficient test-time model adaptation without forgetting. ICML 2022.\n\n[B] ViDA: Homeostatic Visual Domain Adapter for Continual Test Time Adaptation. ICLR 2024.\n\n[C] Class-aware Domain Knowledge Fusion and Fission for Continual Test-Time Adaptation. NIPS 2025.", "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)