Adaptive Debiasing Tsallis Entropy for Test-Time Adaptation
Authors: Xiangyu Wu
Dongming Jiang
Feng Yu
Yueying Tian
Jiaqi Tang
Qing-Guo Chen
Yang Yang
Jianfeng Lu
Venue: ICLR 2026 Poster (2026)
Keywords: Test-Time Adaptation
Entropy Minimization
Representation Learning
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

Abstract: Mainstream Test-Time Adaptation (TTA) methods for adapting vision-language models, e.g., CLIP, typically rely on Shannon Entropy (SE) at test time to measure prediction uncertainty and inconsistency. However, since CLIP has a built-in bias from pretraining on highly imbalanced web-crawled data, SE inevitably results in producing biased estimates of uncertainty entropy. To address this issue, we notably find and demonstrate that Tsallis Entropy (TE), a generalized form of SE, is naturally suited for characterizing biased distributions by introducing a non-extensive parameter q, with the performance of SE serving as a lower bound for TE. Building upon this, we generalize TE into Adaptive Debiasing Tsallis Entropy (ADTE) for TTA, customizing a class-specific parameter q^l derived by normalizing the estimated label bias from continuously incoming test instances, for each category. This adaptive approach allows ADTE, even without hyperparameter tuning required by TE, to accurately select high-confidence views and seamlessly integrate with label adjustment strategy to enhance adaptation. Besides, our investigation reveals that both TE and ADTE can serve as direct, advanced alternatives to SE in TTA, without any other modifications. Experimental results show that ADTE outperforms state-of-the-art methods on ImageNet and its five variants, and achieves the highest average performance on 10 cross-domain benchmarks, regardless of the model architecture or text prompts used. Our code is available at https://anonymous.4open.science/r/TTA-Entropy.

Published as a conference paper at ICLR 2026
ADAPTIVE DEBIASING TSALLIS ENTROPY FOR TEST- TIME ADAPTATION
Xiangyu Wu"
Dongming Jiang* Feng Yu"
Yueying Tian
Jiaqi Tang
Qing-Guo Chen Yang Yang" Jianfeng Lu
Nanjing University of Science and Technology + University of Texas at Dallas Alibaba Cloud v University of Sussex Hong Kong University of Science and Technology
ABSTRACT
Mainstream Test-Time Adaptation (TTA) methods for adapting vision-language models, e.g., CLIP, typically rely on Shamnon Entropy (SE) test time to mea- sure prediction uncertainty and inconsistency. However, since CLIP has a built-in bias from pretraining on highly imbalanced web-crawled data, SE inevitably re- sults in producing biased estimates of uncertainty entropy. To address this issue, we notably find and demonstrate that Tsallis Entropy (TE), generalized form of SE, is naturally suited for characterizing biased distributions by introducing a non-extensive parameter q, with the performance of SE serving as a lower bound for TE. Building upon this, we generalize TE into Adaptive Debiasing Tsallis Entropy (ADTE) for TTA, customizing a class-specific parameter q' derived by normalizing the estimated label bias from continuously incoming test instances, for each category. This adaptive approach allows ADTE to accurately select high- confidence views and seamlessly integrate with label adjustment strategy to en- hance adaptation, without introducing distribution-specific hyperparameter tun- ing. Besides, our investigation reveals that both TE and ADTE serve direct, advanced alternatives to SE in TTA, without any other modifications. Experimen- tal results show that ADTE outperforms state-of-the-ar methods on ImageNet and its five variants, and achieves the highest average performance on 10 cross-domain benchmarks, regardless of the model architecture text prompts used. Our code is available at https:/ //githttbb..///// com/ (amm//jixx33/AAA
INTRODUCTION
Vision-L.anuuage Models (VLMs) (Radford al., 2021; Wu et al., 2022: Zeng et al., 2024; Wu al., 2025d; Li et al., 2025; Jiang 2025; Yu et al., 2025; Zeng et al., 2025b), pretrained on large-scale datasets (Sharma et al., 2018; Schuhmann et al., 2022), exhibit remarkable generalization abilities across various downstream tasks. Despite this, they are susceptible to performance degradation when confronted with considerable discrepancies between training and testing domains. To mitigate this, technology known Test- Test-Time Adaptation (TTA) (Shu et al., 2022; Zhu et al., 2024; Zhou al., 2025; Wu et al., 2025c), enables models to adapt instantaneously to diverse instance distributions during testing, in contrast to earlier prompt learning techniques (Zhou et al., 2022; Hu et al., 2023; Xing et al., 2024; Wu et al., 2024; Huang et al., 2024) that require complex training procedures.
Among these representative TTA works, TPT (Shu et al., 2022) and its enhancement, DifTTT (Feng et al., 2023), learn instance-level prompts by selecting high-confidence augmented views for each test instance. Zero (Farina et al., 2024) simplifies the TTA process, demonstrating that the prediction of the marginal probability distribution remains approximately invariant under entropy minimiza- tion. ML-TTA (Wu et al., 2025c), equipped with Bound Entropy Minimization (BEM), enables the adaptation of multi-label instances. The central idea is to select lower entropy views as the high- confidence views, aiming to reduce uncertainty among these views, a readily demonstrable theory.
"qqual contribution. Corresponding author.

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Published as a conference paper at ICLR 2026
Augneused Views
266
lug.
P
mina(
ming (1
ming (aum)
Ensemble
Emsmmble
Ensemble
60
402
600
1EC0
Daso apso (0.76)
X
Golden retriever (0.80)
Golden retrieven(0.80)
Figure 1: (a) VLM bias, showing higher confidence and accuracy for head classes and lower confidence and accuracy for tail classes. (b) The standard Shannon Entropy (SE)-based method is widely used in TTA. (c) and (d) Our proposed method, which uses Tsallis Entropy (TE) and Adaptive Debiasing Tsallis Entropy (ADTE) for selecting high-confidence views.
However, VLMS (e.g., CLIP), as discussed in research (Allingham et al., 2023; Parashar et al., 2024; Zhu et al., 2023; 2024; Wu et al., 2025a; Ke et al., 2025), are pretrained on imbalanced web-scale datasets, inevitably possessing inherent prediction bias. This bias causes the model to consistently exhibit 1ow /hohhihh confidence in the tail /head categories, leading to lower///r sowerhhis / hhigrer accu- racy, as shown in Figure (a). For this reason, during the TTA process, the predicted probability for a category 1, denoted p. may significantly differ from its true unbiased probability (i.e., Ip p > 0). Methods based on Shannon Entropy (SE), defined as H = Σ, P log P. are im- pacted because their entropy calculations rely on these potentially biased probabilities p. Moreover, from its definition, SE fails to account for varying degrees of bias in probabilities across different classes (i.e., head, midele, and tail classes). Instead, SE applies uniform computation for- mula (-p log p) across all probabilities, as shown in Figure 1 (b). As result, in TTA methods that rely on SE, the entropy values estimated for each augmented view are themselves biased. This bias, in turn, affects the selection of high-confidence views from a set of augmented views.
Our first key observation that Tsallis Entropy (TE) (Tsallis, 1988; 1998), a generalization of SE, is well-suited for characterizing uncertainty in the presence of biased distributions. By introducing an additional parameter q', TE can characterize likelihoods exhibiting statistical dependence and effectively mitigate the impact of bias. First, we demonstrate that TE is a limiting case of SE when q + 1. On the other hand, when q < 1, TE tends to select more confident views (characterized by higher Terk in Definition 1), implying that the performance of SE can be regarded bound for that of TE. In other words, there must exist an appropriate parameter K such that models using TE outperform those using SE in the selection of high-confidence views. Subsequently, demonstrate that when < 1, TE can effectively alleviate the impact of inherent bias for VLMs.
lower
However, there are two major difficulties in applying TE in TTA practice: (i) manually tuning the optimal value of in standard TE is impractical for various test distributions; and (fi) the optimal parameter ğ for each category may also differ, since each category is affected by bias differently, as discussed earlier. Therefore, we generalize TE into Adaptive Debiasing Tsallis Entropy (ADTE) for TTA, customizing a class spesssie q¹ for category 1, shown in Figure (d). These parameters are derived via min min-max normalization of the estimated label biases from continuously incoming test instances. Significantly, both TE and ADTE can serve as direct, advanced alternatives to SE and integrate seamlessly with the logit adjustment strategy to enhance adaptation performance. Experi- ments show that, irrespective of the model architecture or text prompts employed, ADTE surpasses the SOTAs on ImageNet and its five variants, achieving the highest average performance across 10 cross-domain benchmarks.
2 RELATED WORKS
Test-Time Adaptation (TTA). TTA methods (Shu et al., 2022; Karmanov et al., 2024; Zhu et al., 2024; Wu et al., 2025c; Zhou et al., 2025) dynamically adjust pre-trained models using unlabeled test data during inference, e.g. detection (Ouyang et al., 2024; Zhao, 2024; Edstedt et al., 2024; Zhao et al., 2026) tasks. TTA has been explored in various settings, including "fully" TTA (Wang et al., 2021; Zhao et al., 2023a), "online" TTA (Lee & Chang, 2024; Lee et al., 2024a), and "con- tinuous" TTA (Liu et al., 2024; Song et al., 2023). TPT (Shu et al., 2022) is one of the first works
7 is called non-extensive parameter in the literature (Tsallis, 1988; 1998).
2

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to apply prompt tuning for adapting VLMs to previously unseen distributions. Zero (Farina al., 2024) demonstrates that minimizing entropy does not alter the dominant class prediction, providing theoretical basis for this approach. Other works have introduced new techniques: Frolic (Zhu et al., 2024) uses label-free prompt distribution learning and bias correction, MI-TTA (Wu et al,, 2025c) employs bound entropy minimization objective in multi-label scenarios, and BCA (Zhou et al., 2025) leverages Bayesian principles to refine predictions as new data arrives.
Entropy-basee Uncertainty Minimization in Adaptation. Entropy Minimization (EM) (Grand- valet & Bengio, 2004; Berthelot et al., 2019; Gilo et al., 2024; Yang et al., 2024; Wan et al., 2024; Wu et al., 2025b; Dai et al., 2025: Zeng et al., 2025a) is a common strategy for reducing prediction uncertainty and promoting clearer decision boundaries. Early work (Grandvalet & Bengio, 2004)
used minimum entropy regularization to leverage unlabeled data, while MME (Saito et al., 2019)
and Tent (Wang et al., 2021) showed its effectiveness for adapting to varied test distributions. Re- cently, Tsallis Entropy (TE) has emerged as an alternative with tunable parameter & controlling the sharpness of the entropy landscape. In domain adaptation and self-training (Lu et al., 2023; Liu et al., 2021; Lee et al.; Zhao et al., 2023b), TE has been optimized to improve pseudo-label reliabil- ity and robustness to noise in supervised or source-free settings, focusing on feature representation learning. While EM minimizes standard Shannon entropy, TE offers a more flexible formulation that may extend to online test-time adaptation.
Logit Adjustment (LA). LA (Menon et al., 2021; Li et al., 2022; Zhao et al., 2024; Xu et al., 2024; Jia et al., 2024; Miao et al., 2024) is primarily used for long-tailed recognition and dlas-imbalaance learning. It adjusts a model's logits to compensate for biases caused by imbalanced training data. GCL (Li et al., 2022) adds Gaussian perturbation to logits, giving larger perturbations t il classes to enhance their gradient contribution. LoTNext (Xu et al., 2024) introduces graph-based and long-tailed loss adjustments to improve spatial and temporal prediction. HTC (Jia et al., 2024) ad- dresses the long-tail issue with candidate label set disambiguation, class distribution estimation, and classifier weight estimation. COCL (Miao et al., 2024) combines debiased large-margin learning and outlier-class-awe logit calibration to effectively mitigate biases. We employ the logit adjustment to estimate the class-specific parameter q' for each category in Tsallis Entropy.
3 PRELIMINARIES
Consider the CLIP (Radford et al., 2021) model pretrained on Drain = {(xerrain y.rain) | xxtain
Atrain Itriin E yttainn & Minie
Ji=l and downstream test set Diest = {(x!"") y!!at) | x(111 E M y
yoest Mic
fiml which may follow an arbitrary distribution. We illustrate the standard Test- Test-Time Adap- tation (TTA) process with Zero (Farina et al., 2024), which consists of Random view augmentation, Confident views selection, and Confident views ensemble.
Random View Augmentation. Given a test instance xest from Diest and a set A of N random augmentation functions, xest is augmented N times create set of diverse views, which denoted as X == {x/[0a Xx/=" = Ax( )
Confident Views Selection. In information theory, Shannon Entropy (SE. (Shannon, 1948)) is com- monly used to quantify uncertainty?. For each view, uncertainty is measured by SE, defined as:
H (P xx))))
Σ P(y==1x 1=1
log P l x)
where 1 E yesr denotes a class label, and L is the number of classes in the test set. The core of Zero (Farina et al., 2024) lies in minimizing the marginal entropy over the prediction distributions corresponding to the selected high-confidence augmented views (i.e., views with lower entropy) by ratio т, which reduces the model's 's uncertainty and prediction inconsistency across these views. However, due to the inherent prediction bias of models like CLIP, the estimated SE values for head or tail categories themselves biased. This bias in SE estimation, in turn, affects the selection of high-confidence views.
2 Thermodynamic entropy, an earlier concept, is typically expressed via Boltzmann Gibbs-Shannoe entropy Hgas -h >. P: log,s, Ps, where & is the Boltzmann constant. Hgcs is mathematically identical to Shannon Entropy, hut generally less familiar to the machine leamning community
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Confident Views Ensemble. Unlike TPT (Shu al., 2022), which uses high-confidence views to update the model's prompts during TTA, Zero (Farina et al., 2024) simplifies the TTA process. argues that the updated model''s prediction remains invariant under entropy minimization, which allows the final prediction to be obtained by directly aggregating the high-confidence views. The model then immediately adapts to the next test instance. Due to its simplicity and effectiveness, SE, has become a standard metric for high-confidence view selection in recent TTA methods.
4 METHOD
4.1 TSALLIS ENTROPY
When multiple probability distributions are involved, Shannon entropy Hoz quantifies total uncer- tainty under the extensivity assumption, meaning that the entropy of independent parts simply adds, Le., H5a (fA, = (A) (B). In the real world, such with biased model predic- tions, this additive property does not hold. To capture such non- -oneexttnssvvity TE generalizes SE by introducing parameter q that characterizes the degree of non-additivity, defined as:
1 H. (P((1x)))) = --
Σ P(y =1 P 1
where g ER the additional hyperparameter. Using TE, the total entropy can be calculated as H. (f (f B)) = H (A) H.. + (1 (L) [B), where the additional term (1 H (A)H B) used characterize influence between components. We first demonstrate that TE possesses the following crucial properties, which make SE the lower bound in performance for TE. In other words, there exists an appropriate parameter q for which models based on TE are capable of selecting more accurate and confident views compared to those relying on SE.
Top-K Cumulate latiiiiii ive Rel Reliability:
Definition 1. VLMs like CLIP classify images by computing similarity scores between an image and "a photo of {classes)" For an augmented view x the similarity with a class 2 x where zi denotes the textual embedding representing class l. We denote the Top-K Cumulative Reliability Terk as the sum of the K highest similarity scores. Mathematically, given by:
(x test)
Σ 24 x)x
1ETK
where TK is the set of indices corresponding the K highest similarity scores. Actually, CLIP rypically achieves an extremely high Top-K (e.g., K=5 or K=10) accuracy, indicating that although CLIP may not always predict the exact label, it is proficient at generating candidate set that contains the correct label.
Shannon-Tsall llss 9-1 Equivalence:
Shannon Entropy
Tallis Entrapy u=0.1
Property 1. As g + 1, TE becomes equivalent to SE:
0.8
Tralis Entrapy e=0.5
lim (P lest) H (P( | ))
(4)
Entropy
Balls Entropy
Tealls Entropy c-1.1
9-1
Entropy c=2
See the Appendix B.1 for the detailed proof. Property demonstrates that TE is a generalization trated in Figure for a case with two classes. This property confirms that TE is consistent with the well-cstablished SE theory and can be used to analyze more intricate non- extensive probability distributions by adjusting q.
0.4
ballis Entropy caa
SE, as illus-
0.0
0.0
0.2
0.4
0.6
0.8
1.0
Probsbility the first class
Figure 2: Comparison hetween SE. and TE.
Higher Terk under TE as X and Comparison with SE:
Property 2. Through experimental analysis, we find that as the parameter q decreases, the set of high-confulence views selected by TE tends to have higher average Terk value (for K > 1). For two different parameter values 91 and q2 with qı < 92, and their corresponding selected view sets Xy. and Nz, of equal size, we observe:
Σ
(x]
>
Σ
Terx (x2).
(5)
K2 XIEX
12 X2E
4

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Furthermore, there exists a particular q" and corresponding view set Xge, TE outperforms SE in this regard, with the view selected by SE denoted as x
Terx(x1) XIEX
Σ
Tcrk (X2).
(6)
X
JASSE
X2
See the Appendix B.2 for the detailed experimental analysis. Property 2 indicates that, in contrast to SE, TE tends to select views with higher Terg. and the corresponding ground truth has a higher similarity level. The core objective of TTA is to select the most confident and accurate views.
4.2 CORRECTING BIASED ENTROPY EFFECT WITH TE
With the theoretical properties of TE established, we now investigate how its additional parameter q can mitigate the biased entropy effect observed with SE in VLMs. For tail category, the biased prediction and unbiased prediction P are both close to O, with P > p (based on empirical results; this is likely due to the CLIP model being very uncertain about a il predictions, as shown in Figure (a)). This results in a biased entropy value, where (-p pog p) ( (-p pog p) > 0.
To analyze the effect of TE, rewrite Equation examine the entropy value of each category:
H (P) Σ El= P9-11-11 L Pt
-
1-
1
P
P
(7)
1=1 1-q
where Pf = Ply = / x )0 ,, and C is a constant. Since the constant C does not affect the ranking of entropy values, we can focus only on the term I-q" For TE to correct the bias of SE, we require the inequality ((P. P (-plogp)
to hold. The numerical value of F (p. q) reflects the
degree to which TE corrects the bias entropy of SE. We analyze the behavior of this function for tail category probability p E c), where > 0 is a small value:
(1) .As +000 we have limp- F(p, q) 0 and W/ <9 F
(2) .As g+1+, we have lim +0+ F(p, q) oo and =<
and (0 <0< (3) .As 0+ we have so F(p. [[p.4)=11 11
(4) .As 8-11, we have limp F(p. = +00 and V41 < F F
See the Appendix B.3 for the detailed proof. Based on Property (when + 1, TE and SE become equivalent), conclusions (2) and (4) are not applicable. Conclusion (1) also does not meet our requirements since F(p.g) q) < 0. Conclusion (3) shows that when 0 < q < 1, TE can naturally mitigate the effect of VLM bias, with the correction magnitude increasing 9 decreases.
Woggrat22
22.
650
630
3..50
214
2010
2013
120
630
K30X
2013E
Figure 3: TE at different y values SE; the red dashed line marks the optimal q of TE.
4.3 ADAPTIVE DEBIASING TSALLIS ENTROPY (ADTE)
A limitation of the standard TE formulation is that q is manually hyperparameter. A value of g > 1 can exacerbate the bias, while a value too close to 0 can overcorrect it. As shown in Figure 3, the optimal q varies across different test distributions, making manual tuning impractical in a streaming environment. To address this, we generalize TE into Adaptive Debiasing Tsallis Entropy (ADTE), which customizes class- specifc parameter o for each category I, allowing the model to adapt to any test distribution. Building upon Equation 7, ADTE is defined as:
py
H H (P)
Σ
(8)
1
g
1=1
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Algorithm 1 Estimating the bias b
Algorithm 2 Pipeline of Adaptive Debiasing Tsallis Entropy (ADTE) for Test-Time Adaptation (TTA)
1: Input: Estimated E. Bx- [P]])))
maximum number of iteration T. con-
1: Input: Estimated bias b, test input image x!**, the number of image augmentation N, the num- ber of selected confident views Nº
vergence threshold &
2: Output: Estimated
3: aw == Px]P(x((') [(
2: Output: Prediction y
3: views set X < augment(x*at, num views=N)
4: p(0)
D
4: Calculate P(- Vxees X
5: for t: 0....,T- ,.....TT11 -
do
5: Calculate o' for each class with Equation 13
6:
Pi (t+1) +- -Eveyes Dp an
(8)
6: Calculate HADTF (P (x)))"")) Vxej E X with
7:
p((+1) + b((tt)/ || [ 1
Equation 8
8: if [p(++2) 110 1 S then
7: Confident views set X + top N, views with the smallest HAWTE values
9: break
end if
8: P a-ggregat (P (-(-))) vsg E X(esr)
11: end for
9: 1 f arg max; P(y = (1-)
return log (())
10: return
Based on our analysis Section 4.2, when < < 1, TE can alleviate the impact of bias, and smaller value of g' results in greater degree of correction. The magnitude of this correction depends directly on the prediction bias of the category. Therefore, we can deduce the relationship between the prediction bias and the corresponding o' value for each category:
} } -ploo((p) Tail class dis P,T] > 0, P,r + P < P.T
Head class Td Pin m. Pmn] > O,P,a - L, Piu
log(
where the term dis b) represents the size of the bias between biased prediction and the true unbiased prediction b. The size of this bias is inversely proportional to (-plog p) - (-p log P), and dis(;; increases, the information entropy (-plog p) for category / is increasingly under- estimated, which requires a smaller o' for effective correction.
Thereeore, the class-specific parameter o' can be calculated indirectly by estimating the bias for each category. We adopt the bias estimation method from Frolic (Zhu et al., 2024) as follows. First, we estimate the prior probability of each class, Pr (l), by solving the following linear equation:
Pr Σ degge
B...E [P(I x)].
(10)
A memory bank with size M is maintained store and update continuously incoming test instances for calculating Ex-P(xx[") (P(2 x)] in 10. Since true labels in yest are not available, we use pseudo-labels [(x) = arg maxq ( = ( x) as a substitute, following the approach Frolic (Zhu et al., 2024), i.e.:
E Ex-P(xI)) [P( x)]
Σ P(Ixx). x),
(11)
N
x|((x)=1'
where P([ x) is predicted by the model and Nr Extix) 1. We solve for Di using Jacobi iteration, with a uniform initialization P Iili
VI yesst The iteration is given by:
((++1) p
Σ
E Exppix)
(P( [()).
(12)
In each iteration, perform LI normalization over ((9) 1p() ..... ......... P so that its L1 norm equals 1. The iterative process terminates when the maximum number of iterations reached or when the convergence condition || [(0)) is met, where is the convergence threshold.
Combining this with Section 4.2, we normalize the estimated bias vector p for all categories into the interval (0, 1). A larger bias Pi corresponds to smaller g¹. We use min-max normalization map

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Published as a conference paper at ICLR 2026
the bias values to the parameter range:
o' a (3 log P: min(p)
(13)
max(p) min(p)
where and 3 define the normalization interval. After computing the class-specific parameter s', we plug it into Equation 8 to calculate HADTE for each augmented view, which is then used select high-confidence views. After obtaining the probability distributions of the selected high- confidence views, we simply average (aggregate) these distributions to produce the final prediction. The algorithm for estimating the bias p is summarized in Algorithm I, and the overall TTA pipeline is summarized in Algorithm 2.
5 EXPERIMENTS
5.1 EXPERIMENTAL. SETUP
Benchmarks. Two standard benchmarks: (a) Out-of-Distribution (OOD): evaluates generaliza- tion to distributions different from training. including ImageNet (Deng et al., 2009) and variants (ImageNet-A (Hendrycks et al., 2019), -V2 (Recht al., 2019), -R (Hendrycks al., 2020), and -K (Wang et al., 2019)); ; (b) Cross-Domain: classification across diverse domains-generts -entrii objects (Caltech (Fei-Fei al., 2005)), scenes (SUN (Xiao et al., 2010)), textures (DTD (Cimpoi et al., 2014)), satellite images (EuroSAT AT (Helber et al., 2019)), actions (UCF (Soomro et al., 2012)), and five fine- mene-grained datasets (Pets (Parkhi al., 2012). Cars (Krause et al., 2013), Flowers (Nilsback & Zisserman, 2008), Food (Bossard et al., 2014), Aircraft (Maji et al., 2013))-
Implementation Details. Following (Farina et al., 2024; Zhu et al., 2024), we use pretrained CLIP (ViT-B/16, ViT-L/14) with ViT-B/1 serving as the default model for ablation studies. For fair comparison, we use two types of text prompts: hand-crafted templates from methods (Shu al., 2022; Farina et al., 2024; Karmanov et al., 2024; Zhou al., 2025), and text descriptions generated by GPTs, as CuPL (Pratt et al., 2023; Zhu et al., 2024). We do not tune any hyperparameters, instead adopting the setup from Zero (Farina et al., 2024), with N 64 augmented views and a confidence-biie
filtering ratio of 0.1. The memory bank size for each category set to 10. The normalization interval for the class-specific parameter q' is [0.01, 0.9]. All experiments were conducted on a single NVIDIA A.1 00 GPU, with results averaged over seeds.
5.2
COMPARISONS WITH STAEE-OF-TIEE-AR
Table Accuracy comparison (%) on ImageNet and variants for CLIP WiI-V/1-- and ViT-L/14.
Method
IN
IN-V2
IN-K
IN-A
IN-R
Average
OOD Avg
CLIP [CML 2022
68.7
62.2
48.3
50.6
77.7
61.5
59.7
TPT
NNerPPS 2022)
68.9
63.4
47.9
54.7
77.0
62.4
60.8
TDA
JCVPR 2024]
69.5
64.6
50.5
60.1
80.2
65.0
63.9
ViT-B/16
7cro [NeurPS 2024]
70.9
65.1
50.3
64.0
80.8
66.2
65.0
Dyna
[CCR 2025
64.7
48.2
56.2
78.2
BCA CCVPR
70.2
64.9
50.9
61.1
80.7
65.6
64.4
ADTE ADTE Eemplatees
71.8
65.6
53.5
65.5
81.4
67.5
66.5
CuPL [JCCV 2023]
69.9
64.4
49.4
59.7
79.5
64.6
63.3
Frolic [NeudPP 2024)
70.9
64.7
$3.3
60.4
80.7
66.0
64.8
ADT
72.7
66.2
54.3
63.5
80.9
67.5
66.2
CLIP
[ICML 2022]
75.9
70.2
59.7
70.9
87.9
72.9
72.2
VIT-L/14
TPT
[NeurDSS 2022)
75.5
70.0
59.8
74.7
87.9
73.6
73.1
TDA
JCVPR
76.3
71.5
61.3
77.9
89.8
75.4
75.1
Zero
NNustPS 2024]
77.2
71.9
61.1
80.7
90.2
76.2
75.9
ADTE
ADTF Prepllates
77.8
72.8
63.5
81.1
90.6
77.2
77.0
CuPL [IOCV 2023)
76.2
71.9
60.7
77.9
89.6
75.3
75.0
Frolic [NeurtPS 2024)
77.4
72.5
63.1
78.9
90.3
76.4
76.2
ADTE
78.2
73.3
63.9
81.0
90.4
77.4
77.2
We compare ADTE with several state-of-the-ar methods on both OOD and cross-domain bench- marks, including CLIP (Radford et al., 2021), TPT (Shu et al., 2022), TDA (Karmanov al., 2024),
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Zero (Farina et al., 2024), Dyna (Xiao al., 2025), BCA (Zhou al., 2025), CuPL (Pratt al., 2023) and Frolic (Zhu et al., 2024). We present results for ADTE using both types of text prompts.
Results the OOD Benchmark. In Table I, ADTE consistently outperforms other methods both ViT-B/10 and WiT-L/11 backbones, and with both template-based and text-description- based prompts. On ImageNet-Ik, ADTEremplates achieves 71.8% accuracy, 0.9% higher than Zero. ADTEcupr reaches 72.7%, outperforming Frolic by 1.8%. For OOD datasets, AD TDmpTelpate surpasses state-of-the-art methods IN-V2 (65.6% vs Zero's 65.1%), IN-K (53.5% vs BCA's 50.9%), IN-A (65.5% vs Zero's 64.0%), and IN-R (81.4% vs Zero's 80.8%). ADTECuPT. also consistently outperforms Frolic on all datasets, with a significant 3.1% lead on IN-A. For the ViT-L/14 backbone, ADTEremplater achieves 77.2% average accuracy and 77.0% OOD average accuracy, both 1.1% higher than Zero. Compared to Frolic, ADTEcuEL shows the best performance with 77.4% overall average and 77 27. OOD average, confirming its consistent superiority.
Table Accuracy comparison (%) on 10 cross-domain datasets for CLIP and ViT-L/14 1/14.
Method
Pets.
Flow.
Airc.
DTD.
Euro.
Cars.
Food.
SUN.
Calt.
UCF
Avg.
CLIP
[CML 2023]
88.9
70.4
24.8
44.3
47.7
65.2
86.1
62.5
92.9
66.7
64.9
TPT NeutPP 2022
87.7
68.9
24.7
47.7
42.4
66.8
84.6
65.5
94.1
68.0
65.0
TDA
[CVPR
88.6
71.4
23.9
47.4
58.0
67.2
86.1
67.6
94.2
70.6
67.5
VIT-B/16
Zero
NNudPPS 2024
87.2
66.8
24.4
45.9
43.8
68.5
84.6
66.9
94.1
68.6
65.1
Dyna
[CLR 2025]
88.3
69.9
24.3
48.0
42.3
67.7
85.4
66.3
94.3
68.7
65.5
BCA CVPR 2025]
90.4
73.1
28.6
53.5
56.6
66.8
86.0
68.4
94.7
67.6
68.6
ADTE ADTEremplaees Templates
89.7
72.6
28.9
49.5
53.8
70.9
86.3
70.4
94.8
73.1
69.0
CuPL [OCVV 2023]
92.0
73.2
27.7
54.3
52.7
66.4
86.2
68.5
94.6
70.7
68.6
Frolic [NeurIPS 2024]
92.9
74.8
31.5
56.1
58.5
69.1
70.8
95.2
75.2
71.1
ADT
92.7
75.4
33.5
57.2
58.2
71.2
86.9
71.3
95.7
75.5
71.8
CLIP [023)
93.5
79.3
32.4
53.0
58.0
76.8
91.0
67.5
94.8
74.2
72.0
TPT NNwtPP 2022
93.6
76.2
31.9
55.2
51.8
77.7
88.9
70.2
95.5
74.9
71.5
VIT-L/44
TDA
[CVPR 2024
93.5
80.5
34.7
56.7
64.1
78.3
90.9
71.5
95.9
76.6
74.2
Zero
NeurlDS 2024]
93.4
79.2
33.9
53.7
54.1
78.5
90.2
72.1
96.0
77.1
72.8
ADT ODTEramplater
93.7
79.4
37,2
59.7
56.2
79.4
91.8
73.2
96.4
80.6
74.8
CuPL [ECCY 2023]
94.3
79.8
35.5
62.7
61.2
78.0
91.3
72.4
96.7
75.9
74.7
Frolic [NeurIPS 2024]
94.9
82.4
40.0
64.1
66.2
80.8
91.8
74.5
97.2
80.0
77.1
ADTECaPL
94.6
83.8
40.8
65.6
65.9
81.8
91.7
74.8
97.4
80.4
77.7
Results on the Cross Domain Benchmark. Table demonstrates the significant advantage of ADTE in cross-domain image recognition. On the ViT-B/ 16 backbone, ADTE ADDErroplatess (69.0%) outperforms all template-based methods, while AD ADTFcuPI. (71.8 (7188) surpasses Frolic (71.1%). Simi- larly, on ViT-L/14 4, ADT ADTETempp Erempl ates (74.8) and ADTEcues (77.7%) both significantly outperform their respective counterparts, TDA (74.2%) and Frolic (77.1%). ADTEremplates also ranks at or near ViT-B/15 it improves performance by
the top on multiple individual datasets. For instance, 2.4%, 2.0%, and 2.5% on the Cars, SUN, and UCF datasets, respectively, compared to the best competing method. On ViT-L/14, it achieves state-of-the of-the-art results Aireraft 37,2%, +2.5% improvement over TDA), DTD (59.7%, +3.0% improvement over TDA), and UCF (80.6%, +3.5% improvement over Zero).
5.3 ABLATION STUDIES
We evaluate the contributions of our proposed components, ADTE and Logit Adjustment (LA), through an ablation study. All experiments in this section are conducted on both ViT-B/11 and ViT-L/14 architectures, with results shown in Table 3.
Effectiveness of ADTE. Removing ADTE leads to a notable performance decline across all met- rics compared to the full ADTErempiates model. For ViT-B/16, accuracy drops by 1.1% on IN- Variants 0.7% on IN, and 2.1% on the 10-datasets. For ViT-L/ 14, accuracy decreases by 0.7%, 0.5%, and 1.6% the same benchmarks. The performance drop is most significant the
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Published as a conference paper at ICLR 2026
Table 3: Accuracy (%) of different models 10-datasets, including ImageNet and its five variant datasets.
ViT-B/16
VIT-L/14
Module
IN-Variants
IN
10-datasets
IN-Vinaants
IN
10-datasets
ADTE remplates
66.5
71.8
69.0
77.0
77.8
74.8
A
w/o ADTE
65.4
71.1
66.9
76.3
77.3
73.2
A w/o Logit Adjustment (LA)
66.1
71.6
68.8
76.7
77.6
74.1
A w/o ADTE and LA
65.0
70.9
65.1
75.9
77.2
72.8
10-datasets (-2.1% and -1.6%), indicating that ADTE is particularly effective enhancing the model's generalization across diverse cross-domain tasks.
Contribution of Logit Adjustment. LA adjusts the model logits by using bias estimation (Zhu et al., 2024). The experiments show that removing LA also decreases performance, but this decline generally smaller than removing ADTE. For Vi ViT-B/1 6, the accuracy drops are 0.4%, 0.2%, and 0.2%, while ViT-L/14 experiences decreases of 0.3%, 0.2%, and 0.7%. Both ADTE and LA contribute positively to the model's accuracy. Furthermore, LA can be seamlessly integrated with ADTE to boost performance without adding extra computational cost.
5.4 FURTHER ANALYSIS
Comparison Among SE, TE, and ADTE. Table compares the performance of ADTE, SE, and TE, all with logit adjustment (LA). ADTE demonstrates the highest performance. This highlights ADTE's 's distinct advantages tasks that rely on entropy information.
Table 4: Results for SE, TE, and ADTE.
Module
IN IN-V2 IN-K IN-A IN-R
LA-SE SE-LA
70.7 64.1
52.3
64.0
80.2
71.0
64.3
52.5
64.1
80.3
TE-LA (q50.5)
71.6 65.2
53.0
64.8
80.7
ADTE
71.8
65.6
53.5
65.5
81.4
Table 5: Computational cost and effect of different intervals.
Interval
IN
IN-V2
IN-A IN-K
Avg
0.9]
71.7
65.5
53.4
67.4
72.
0.01, 0.9
71.8
65.6
53.5
65.5
81.4
67.5
88.0
0.0001 0.9
71.8
65.6
53.6
65.6
81.2
67.5
80.3
0.00011 0.9]
71.7
65.5
53.6
65.6
81.2
67.5
IN-1k
65.0
81.3
Metric
TPT
Zero
ADTE
Imagelvet
Time[s]
0.57=0.01 17.66
0.06+0.01 1.40
0.07+0.01
100
Imagehoce
Mem[GB]
1.46
Number augmented views
Figure 4; Different number of views.
Normalization Intervals and Computational Cost. Table 5 shows the performance ADTE using different normalization intervals. As the lower bound of the interval decreases from 0.1 to 0.0001, perfor- mance generally improves and then stabilizes. This demonstrates that ADTE is effective when the class-specific parameter is less than and that the method is robust as does not require precise pa- rameter tuning; long the lower bound is sufficiently small, excellent performance is achieved. Furthermore, ADTE adds only a negligible computational cost compared to Zero, primarily for the bias estimation step.
Number of Augmented Views. Figure 4 shows that increasing views (N) improves performance until convergence. And more views help ADTE select more confident views, boosting accuracy.
Memory Bank Size. We systematically evaluated the impact of varying memory bank sizes on ADTE's performance on ImageNet-Ik, with guantitative results presented in Table 6.
Table 6: Impact of memory bank size on performance (%).
Size
2
5
10
20
30
40
ADTE 71.71
71.73
71.74
71.83
71.81
71.85
71.86
The results show that the memory bank size has a minimal impact on ADTE's performance: with size of the model already achieves 71.71% accuracy. As the size increases 10, the accuracy

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Published as a conference paper at ICLR 2026
stabilizes around 71.83%. Further expansion to 40 yields only marginal fluctuations (71.86%). A small number of high-conee cegh-confidence samples is sufficient to support reliable adaptive adjustments.
Note that 71.71% accuracy achieved with size 1 does mean the memory bank can be removed. To see this, consider 200 categories, using a memory bank size of 1 yields 200 samples in total. The statistical information used calculate bias for specific category is derived not only from its sample but from all 200 pseudo-labeled samples the bank.
Improvements on tail Categories. To further validate ADTE's effectiveness tail classes, we conducted quantitative experiments on t 1 categories in ImageNet-lk 1k. We selected the last 10 tail classes in ImageNet- Ik and compared the performance between CLIP and ADTE.
Table 7: Performance improvement on representative tail classes.
Class Index
670
193
981
157
533
168
316
106
50
156
Accuracy (CLIP)
17.4
16.7
16.1
15.0
14.5
12.5
0.00
0.00
0.00
Confidence (CLIP)
0.01
0.11
0.05
0.18
0.09
0.13
0.15
0.09
0.13
0.19
Accuracy (ADTE)
16.7
33.3
33.3
38.5
25.0
59.4
35.0
32.2
41.7
56.5
Confidence (ADTE)
0.16
0.31
0.28
0.35
0.24
0.44
0.33
0.25
0.34
0.47
As shown in Table 7, ADTE achieves significant improvements in both accuracy and confidence for these categories. For instance, classes that originally had zero accuracy show enhanced accuracy ranging from 32.2% to 56.5% under ADTE, while confidence scores simultaneously increase. This directly validates ADTE's effectiveness improving tail class performance.
Table Comparative analysis between head and tail classes.
Module
Head (avg pred)
Head (avg.cmm entropy)
Tail (avg pred)
Tail (avg entropy)
CLIP
0.6687
5.2956
0.1466
5.2972
ADTE
0.8112
3,2156
0.3638
3.3761
Table 8 presents results of prediction confidence and entropy values for head classes (top 50) and tail classes (bottom 50). The results demonstrate that ADTE not only enhances the average prediction confidence for tail classes (from 0.1466 to 0.3638) but also reduces prediction uncertainty by decreasing the entropy value (from 5.2972 to 3.3761). These improvements indicate that the model achieves definitive and reliable predictions for tail categories.
Effect of Different Normalization Functions. As shown in Table 9, ADTE's performance not highly dependent on a specific normalization function. While some methods may offer minor advantages on certain datasets, no single method is universally optimal. This demonstrates the robustness of our approach.
Table 9: Results with different normalizations.
Normalization
IN IN-V2 IN-K IN-A IN-R
Z-Score
71.8 65.9
53,5
65.5
81.3
Decimal Scaling
72.0
65.8
53.5
65.7
81.3
Sigmoid
72.0
66.1
53.5
65.4
81.2
Min-Max
71.8 65.6
53,5
65.5
81.4
CONCLUSION AND LIMITATION
Conclusion. This paper introduces novel Test-Time Adaptation (TTA) approach called Adaptive Debiasing Tsallis Entropy (ADTE), which is designed to handle the inherent prediction biases in Vision-Language Models (VLMs). We show that Shannon Entropy can be considered special case of Tsallis Entropy, and that its performance serves as a lower bound. By generalizing Tsallis Entropy with class-specific parameters g' tailored for each category I, ADTE effectively reduces the biases encountered during TTA. Our experimental results demonstrate that ADTE outperforms state- of-the-art methods across multiple datasets, proving its robustness and effectiveness in improving the adaptation performance of VLMs.
Limitation. Due to the specific nature of its design, ADTE is highly effective in scenarios with significant prediction bias. However, its advantages may be less apparent in scenarios where the model has almost biased predictions.
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ACKNOWLEDGEMENTS
This work is supported by the NSFC (62276131, 62506168), Natural Science Foundation of Jiangsu Province of China under Grant (BK20240081, BK20251431).
The authors gratefully acknowledge financial support from the China Scholarship Council (CSC) (Grant No. 202506840036).
REFERENCES
James Urquhart Allingham, Jie Ren, Michael W. Dusenberry, Xiuye Gu, Yin Cui, Dustin Tran, Jeremiah Zhe Liu, and Balaji Lakshminarayanan. A simple zero-shot prompt weighting technique to improve prompt ensembling in text-image models. In ICMI, 2023.
David Berthelot, Nicholas Carlini, Ian J. Goodfellow, Nicolas Paperoo, Avital Oliver, and Colin Raffel. Mixmatch: A holistic approach to semi-supervised learning. In NeurIPS, pp. 5050-5060, 2019.
Lukas Bossard, Matthieu Guillaumin, and Luc Van Gool. Food-101 mining discriminative com- ponents with random forests. In ECCV, pp. 446-461, 2014.
Mircea Cimpoi, Subhransu Maji, lasonas Kokkinos, Sammy Mohamed, and Andrea Vedaldi. De- scribing textures in the wild. In CVPR, 2014.
Lu Dai, Yijie Xu, Jinhui Ye, Hao Liu, and Hui Xiong. Seper: Measure retrieval utility through the lens of semantic perplexity reduction. In ICLR, 2025.
Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hierarchical image database. In CVPR, 2009.
Johan Edstedt, Georg Bökman, and Zhenjun Zhao. Dedode v2: Analyzing and improving the dedode keypoint detector. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 4245 4253-4253, 2024.
Matteo Farina, Gianni Franchi. Giovanni Iacca, Massimiliano Mancini, and Elisa Ricci. Frustrat- ingly easy test-time adaptation of vision-language models. In NeurIPS, 2024.
Li Fei-Fei, R. Fergus, and P. Perona. Learning generative visual models from few training examples: An incremental bayesian approach tested on 101 object categories. In CVPR, 2005.
Chun-Mei Feng, Kai Yu, Yong Liu, Salman Khan, and Wangmeng Zuo. Diverse data augmentation with diffusions for effective test-time prompt tuning. In ICCV, pp. 2704-271 2714, 2023.
Obsa Gilo, Jimson Mathew, Samrat Mondal, and Rakesh Kumar Sandoniya. Subdomain adaptation via correlation alignment with entropy minimization for unsupervised domain adaptation. Pattern Anal. Appl., 27(1):13, 2024.
Yves Grandvalet and Yoshua Bengio. Semi-supervised learning by entropy minimization. In NeurlPS, volume 17, 2004.
Patrick Helber, Benjamin Bischke, Andreas Dengel, and Damian Borth. Eurosat: A novel dataset and deep learning benchmark for land use and land cover classification. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, pp. 2217-2226, 2019.
Dan Hendrycks and Thomas Dietterich. Benchmarking neural network robustness to common cor- ruptions and perturbations. arXiv preprint arXiv: 12261, 2019.
Dan Hendrycks, U Berkeley, Kevin Zhao, Steven Basart, Jacob Uchicago, Dawn Steinhardt, and U Song. Natural adversarial examples. In arXiv, 2019.
Dan Hendrycks, Steven Basart, Norman Mu, Saurav Kadavath, Frank Wang, Evan Dorundo, Rahul Desai, Tyler Zhu, Samyak Parajuli, Mike Guo, Dezhen Song, Jacob Steinhardt, and Justin Gilmer. The many faces of robustness: A critical analysis of out-of distrribution generalization. In arXiv, 2020.
11

---

Published as a conference paper at ICLR 2026
Ping Hu, Ximeng Sun, Stan Sclaroff, and Kate Saenko. D Fast and effective adaptation to multi- recognition with limited annotations. TPAMI, 2023.
Longfei Huang, Xiangyu Wu, Jingyuan Wang, Weili Guo, and Yang Yang. Refining Visual Percep- tion for Decoration Display: A self-enhanced deep captioning model. In ACML, volume 260, pp- 527-542, 05-08 Dec 2024.
Yuheng Jia, Xiaorui Peng. Ran Wang, and Min-Ling Zhang. Long-tailed partial label learning by head classifier and tail classifier cooperation. In AAAI, pp. 12857-12865, 2024.
Qing-Yuan Jiang, Longfei Huang, and Yang Yang. Rethinking multimodal learning from the per- spective of mitigating classification ability disproportion. In NeurIPS, 2025.
Adilbek Karmanov, Dayan Guan, Shijian Lu, Abdulmotaleb El Saddik, and Eric Xing. Efficient test-time adaptation of vision-language models. In CVPR, pp. 14162-14171, 2024.
Zong Ke, Yuqing Cao, Zhenrui Chen, Yuchen Yin, Shouchao He, and Yu Cheng. Early warning of cryptocurrency reversal risks via multi-source data. Finance Research Letters, pp. 107890, 2025.
Jonathan Krause, Michael Stark, Jia Deng, and Li Fei-Fei. 3d object representations for fine-grained categorization. In ICCV, 2013.
Jae-Hong Lee and Joon-Hyuk Chang. Stationary latent weight inference for unreliable observations from online test-time adaptation. In ICML, 2024.
Jae Yun Lee, Jae Hyeon Park, Gyoomin Lee, Bogycong Kim, Min Hee Cha, Hyeok Nam, Joo Hyeon Jeon, Hyunse Lee, and Sung In Cho. Duet: Dual-perspective pseudo labeling and uncertainty- aware exploration & exploitation training for source-free free domain adaptation. In The Thirty-ninth Annual Conference on Neural Information Processing Systems.
Jonghyun Lee, Dahuin Jung, Sachyung Lee, Junsung Park, Jubyeon Shin, Uiwon Hwang, and Sun- groh Yoon. Entropy is not enough for test-time adaptation: From the perspective of disentangled factors. In ICLR, 2024a.
Jonghyun Lee, Dahuin Jung, Sachyung Lee, Junsung Park, Juhyeon Shin, Uiwon Hwang, and Sun- groh Yoon. Entropy is not enough for test-time adaptation: From the perspective of disentangled factors. arXiv preprint arXiv:2403.07366, 2024b.
Mengke Li, Yiu-Ming Cheung. and Yang Lu. Long-tailed visual recognition via gaussian clouded 2022.
logit adjustment. In CVPR, pp.
Ruoxuan Li, Xiangyu Wu, and Yang Yang. Noise self-correction via relation propagation for robust cross-modal retrieval. In ACM MM, pp. 4748-4757, 2025.
Hong Liu, Jianmin Wang, and Mingsheng Long. Cycle self-training for domain adaptation. Ad- vances in Neural Information Processing Systems, 34:22468-229993 2021.
Jiaming Liu, Senqiao Yang. Peidong Jia, Renrui Zhang, Ming Lu, Yandong Guo, Wei Xue, and Shanghang Zhang. Vida: Homeostatic visual domain adapter for continual test time adaptation. In ICLR, 2024.
Menglong Lu, Zhen Huang, Zhiliang Tian, Yunxiang Zhao, Xuanyu Fei, and Dongsheng Li. Meta- tsallis-entropy minimization: new self-training approach for domain adaptation text classifi- cation. arXiv preprint wrXiv:2308.02744 2023.
Subhransu Maji, Esa Rahtu, Juho Kannala, MatthewB. Blaschko, and Andrea Vedaldi. Fine-grained visual classification of aircraft. arXiv, 2013.
Aditya Krishna Menon, Sadeep Jayasumana, Ankit Singh Rawat, Himanshu Jain, Andreas Veit, and Sanjiv Kumar. Long-tail learning via logit adjustment. In ICLR, 2021.
Wenjun Miao, Guansong Pang, Xiao Bai, Tianqi Li, and Jin Zheng. dittr--distribution detection in long-tailed recognition with calibrated outlier class learning. In AAAI, pp. 4216-4224 2024.
12

---

Published as a conference paper at ICLR 2026
Maria-Elena Nilsback and Andrew Zisserman. Automated flower classification over a large number of classes. In 2008 Sixth Indian Conference on Computer Vision, Graphics and Image Processing, 2008.
Kaichen Ouyang, Zong Ke, Shengwei Fu, Lingjie Liu, Puning Zhao, and Dayu Hu, Learn from global correlations: Enhancing evolutionary algorithm via spectral gnn. arXiv preprint arXiv:2412.17629, 2024.
Shubham Parashar, Zhiqiu Lin, Tian Liu, Xiangjue Dong, Yanan Li, Deva Ramanan, James Caverlee, and Shu Kong. The neglected tails of vision-language models. arXiv preprint arXiv:2401.12225, 2024.
O. M. Parkhi, A. Vedaldi, A. Zisserman, and C. V. Jawahar. Cats and dogs. In CVPR, 2012.
Sarah M. Pratt, Ian Covert, Rosanne Liu, and Ali Farhadi. What does a platypus look like? generat- ing customized prompts for zero-shot image classification. ICCV, pp. 15645-15655, 2023.
Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sandhini Agar- wal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, Gretchen Krueger, and llya Sutskever. Learning transferable visual models from natural language supervision. In JCMI,, volume 139, pp. 8748-8763, 2021.
Benjamin Recht, Rebecca Roelofs.
Ludwig Schmidt, and Venkatesh Shankar. Do imagenet classi- fiers generalize to imagenet. In CVPR, 2019.
Kuniaki Saito, Donghyun Kim, Stan Sclaroff, Trevor Darrell, and Kate Saenko. Semi-supervised domain adaptation via minimax entropy. In ICCV, pp. 8049-8057, 2019.
Christoph Schuhmann, Romain Beaumont, Richard Vencu, Cade Gordon, Ross Wightman, Mehdi Cherti, Theo Coombes, Aarush Katta, Clayton Mullis, Mitchell Wortsman, al. Laion-5b: An open large-scale dataset for training next generation image-text models. In NewrlPS, volume 35, pp. 222944,,,,, 2022.
Claude E. Shannon. A mathematical theory of communication. Bell Syst. Tech. J., 27(3):379-422 1948.
Piyush Sharma, Nan Ding, Sebastian Goodman, and Radu Soricut. Conceptual captions: A cleaned, hypemymed, image alt-text dataset for automatic image captioning. ACL, pp. 2556-2565, 2018.
Manli Shu, Weili Nie, De-An Huang, Zhiding Yu, Tom Goldstein, Anima Anandkumar, and Chaowei Xiao. Test-time prompt tuning for zero-shot generalization in vision-language models. In NeurlPS, 2022.
Junha Song, Jungsoo Lee, So Kweon, and Sungha Choi. Ecotta: Memory-efficient continual test-time adaptation via self-distilled regularization. In CVPR, pp. 11920-11929, 2023.
Khurram Soomro, Amir Zamir, and Mubarak Shah. Ucf101: A dataset of 101 human actions classes from videos in the wild. arXivv, 2012.
Constantino Tsallis. Possible generalization of boltzmann-gibbe statistics. Journal of statistical
physics, 52:479-487, 1988.
Constantino Tsallis. Generalized based criterion for consistent testing. Physical Review E, 58(2):1442, 1998.
Fengqiang Wan, Xiangyu Wu, Zhihao Guan, and Yang Yang. Covlr: Coordinating cross-modal consistency and intra-modal relations for vision-language retrieval. In ICME, pp. 1-6, 2024.
Dequan Wang, Evan Shelhamer, Shaoteng Liu, Bruno A. Olshausen, and Trevor Darrell. Tent: Fully test-time adaptation by entropy minimization. In ICLR, 2021.
Haohan Wang, Songwei Ge, EricP. Xing, and ZacharyC. Lipton. Learning robust global representa- tions by penalizing local predictive power In CVPR, 2019.
13

---

Published as a conference paper at ICLR 2026
Chen Wu, Hongwei Huang, and Yi- Yi-Qing Ni. Evaluation of tunnel rock mass integrity using multi- modal data and generative large model: Tunnel rip-gpt. Available at SSRN 5348429, 2025a.
Shuang Wu, Heng Liang, Yong Zhang, Yanlin Chen, and Ziyu Jia. A cross-modal densely guided knowledge distillation based on modality rebalancing strategy for enhanced unimodal emotion recognition. In IJCAI, pp. 4236-4244, 2025b.
Xiangyu Wu, Jianfeng Lu, Zhuanfeng Li, and Fengchao Xiong. Ques-to-visual guided visual ques- tion answering. In ICIP, pp. 4193-4197, 2022.
Xiangyu Wu, Qing- Yuan Jiang, Yang Yang, Yi-Feng Wu, Qing-Guo Chen, and Jianfeng Lu. Tai++: Text image for multi-label image classification by co-learning transferable prompt. In IJCAI, 2024.
Xiangyu Wu, Feng Yu, Qing-Guo Chen, Yang Yang, and Jianfeng Lu. Multi-label test-time adapta- tion with bound entropy minimization. In ICI., 2025c.
Xiangyu Wu, Feng Yu, Yang Yang. and Jianfeng Lu. Text as any-modality for zero-shot classifica- tion by consistent prompt tuning. In ACM MM, pp. 8106-8115, 2025d.
Jianxiong Xiao, James Hays, Krista A. Ehinger, Aude Oliva, and Antonio Torralba. Sun database: Large-scale scene recognition from abbey 7oo. In CVPR, 2010.
Zehao Xiao, Shilin Yan, Jack Hong. Jiayin Cai, Xiaolong Jiang, Yao Hu, Jiayi Shen, Qi Wang, and Cees G. M. Snoek. Dynaprompt: Dynamic test-time prompt tuning. In ICLR, 2025.
Xin Xing, Zhexiao Xiong, Abby Stylianou, Srikumar Sastry. Liyu Gong, and Nathan Jacohs. Vision- language pseudo-labels for single-positive multi-label learning. CVPR, pp. 7799-7808, 2024.
Xiaohang Xu, Renhe Jiang, Chuang Yang, Zipei Fan, and Kaoru Sezaki. Taming the long tail in
human mobility prediction. In NeurlPS, 2024.
Yang Yang. Fengqiang Wan, Qing-Yuan Jiang, and Yi Xu. Facilitating multimodal classification via dynamically learning modality gap. In NeurlPS, 2024.
Xinlei Yu, Chengming Xu, Guibin Zhang, Yongbo He, Zhangquan Chen, Zhucun Xue, Jiangning Zhang, Yue Liao, Xiaobin Hu, Yu-Gang Jiang, et al. Visual multi-agent system: Mitigating hallucination snowballing via visual flow. arXiv preprint arXiv:2509.21788 2025.
Shuang Zeng, Xinyuan Chang, Mengwei Xie, Xinran Liu, Yifan Bai, Zheng Pan, Mu Xu, and Xing Wei. Futuresightdrive: Thinking visually with spatio-temporal cot for autonomous driving. arXiv preprint ar 2rxi 2025a.
Shuang Zeng, Dekang Qi, Xinyuan Chang, Feng Xiong, Shichao Xie, Xiaolong Wu, Shiyi Liang, Mu Xu, and Xing Wei. Janusvin: Decoupling semantics and spatiality with dual implicit memory for vasion-language navigation. arXiv preprint arXiv:2509.22544 22548, 2025b.
Yan Zeng, Xinsong Zhang, Hang Li, Jiawei Wang, Jipeng Zhang, and Wangchunshu Zhou. X2-vlm: All-in-one pre-trained model for lingun-language tasks. TPAMI, (165)3156-3165 2024.
Marvin Zhang, Sergey Levine, and Chelsea Finn. Memo: Test time robustness via adaptation and augmentation. NeurIPS, 2022.
Bowen Zhao, Chen Chen, and Shu-Tao Xia. Delta: Degradation-free fully test-time adaptation. In ICLR, 2023a.
Liang Zhao, Yao Teng, and Limin Wang. Logit normalization for long-tail object detection. IJCV, 132(6), 2024.
Sichen Zhao, Zhiming Xue, Yalun Qi, Xianling Zeng, and Zihan Yu. Non-intrusive graph- based bot detection for e-commerce using inductive graph neural networks. arXiv preprint arXiv:2601.22579. 2026.
14

---

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Yuchang Zhao, Shuai Feng, Chang Li, Rencheng Song, Deng Liang, and Xun Chen. Source-free free domain adaptation for srevacc-preservinn seizure prediction. IEEE Transactions on Industrial Informatics, 20(2):2787-2798 2023b.
Zhenjun Zhao. Balf: Simple and efficient blur aware local feature detector. In Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision, pp. 3362-3372, 2024.
Kaiyang Zhou, Jingkang Yang. Chen Change Loy, and Ziwei Liu. Learning to prompt for vision- language models. IJCV, 130(9):2337-234) 2022.
Lihua Zhou, Mao Ye, Shuaifeng Li, Nianxin Li, Xiatian Zhu, Lei Deng, Hongbin Liu, and Zhen Lei. Bayesian test-time adaptation for vision-language models. In CVPR, 2025.
Beier Zhu, Kaihua Tang, Qianru Sun, and Hanwang Zhang. Generalized logit adjustment: Calibrat- ing fine-tuned models by removing label bias in foundation models. In NeurIPS, 2023.
Xingyu Zhu, Beier Zhu, Yi Tan, Shuo Wang. Yanbin Hao, and Hanwang Zhang. Enhancing zero- shot vision models by label-free prompt distribution learning and bias correcting. In NeurIPS, 2024.
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Appendix for Adaptive Debiasing Tsallis Entropy for Test-Time Adaptation
A ADDITIONAL EXPERIMENTS
Detailed Analysis of Estimated Bias Statistics. We conduct statistical analysis of prediction bias on ImageNet variants and cross-domain datasets to explore the correlation between performance gains and the degree of bias. Table 10 shows results on five ImageNet variants.
Table 10: Bias statistical analysis ImageNet variant datasets.
Dataset (Classes)
IN-A (200)
IN-R (200)
IN-K (1000)
IN-V (1000)
IN-1 (1000)
Variance
0.9527
0.7650
1.5858
1.1603
1.0833
Std_Dev
0.9621
0.8747
1.2953
1.0772
1.0408
Acc (CLIP)
50.6
77.7
48.3
62.2
68.7
Acc (ADTE)
65.5
81.4
53.5
65.6
71.8
Gain
14.9
4.7
5.2
3.4
3.1
As shown in Table 10, datasets with larger bias variance and standard deviation (e.g.. IN-A and IN-K) correspond to greater disparity in bias between head and tail classes. Consequently, the performance gains ADTE, are higher on these datasets (14.9% and 5.2%). This indicates that ADTE is particularly effective in scenarios with prominent biases, which also explains the variation in performance improvements across different datasets.
For the cross-domain benchmark, we analyzed the average prediction accuracy and confidence across different percentile intervals. As shown in Tables 11 and 12, all cross-domain datasets exhibit significant long-tail distribution characteristics and CLIP demonstrates pronounced prediction bias across them. These results validate the universality of CLIP's prediction bias.
Table 11:
Quantitative analysis of prediction bias on cross-domain datasets (Part 1). The values in each cell represent (Accuracy, Confidence).
Class Percentile
Flower102
DTD
Pets
Cars
UCF101
0%--10%
(1.0, 0.85)
(0.98, 0.82)
(1.0, 0.95)
(0.99, 0.88)
(L.0, 0.95)
10%-200%
(1.0, 0.91)
(0.86, 0.67)
(0.99, 0.96)
(0.94, 0.81)
(0.98, 0.86)
20%-30%
(0.98, 0.86)
(0.74, 0.59)
(0.98, 0.93)
(0.89, 0.71)
(0.94, 0.80)
30%-40%
(0.93, 0.82)
(0.54, 0.32)
(0.96, 0.87)
(0.82, 0.65)
(0.90, 0.74)
40%-50%
(0.87, 0.69)
(0.42, 0.29)
(0.95, 0.87)
(0.73, 0.51)
(0.82, 0.63)
50%-60%
(0.81, 0.63)
(0.34, 0.23)
(0.93, 0.80)
(0.64, 0.44)
(0.72, 0.55)
60%-70%
(0.62, 0.45)
(0.22, 0.16)
(0.90, 0.81)
(0.56, 0.38)
(0.57, 0.41)
70%-80%
(0.50, 0.35)
(0.07, 0.08)
(0.81,
(0.42, 0.34)
(0.32, 0.27)
80%-90%
(0. 0.14)
(0.01, 0.04)
(0.63, 0.52)
(0.21, 0.22)
(0.19, 0.19)
90%-100%
(0.00, 0.01)
(0.00, 0.03)
(0.00, 0.00)
(0.06, 0.11)
(0.06, 0.08)
Table 12: Quantitative analysis of prediction hias on cross-domain datasets (Part 2). represent (Accuracy, Confidence).
The values in each cell
Class Percentile
Caltech101
Food101
SUN397
Aireraft
Eurosat
0%-100%
(1.0, 0.96)
(0.96, 0.93)
(0.96, 0.84)
(0.86, 0.66)
(0.82, 0.51)
10%%-20%
(1.0, 0.96)
(0.94, 0.87)
(0.90, 0.75)
(0.53, 0.24)
(0.77, 0.63)
20%-30%
(1.0, 0.97)
(0.93, 0,84)
(0.85, 0.69)
(0.37, 0.14)
(0.76, 0.57)
30%-40%
(1.0, 0.97)
(0.91, 0.85)
(0.79, 0.60)
(0.24, 0.12)
(0.72, 0.43)
40%-50%
(1.0, 0.96)
(0.89, 0.82)
(0.72, 0.52)
(0.17, 0.12)
(0.47, 0.35)
50%-60%
(0.98, 0.90)
(0.87, 0.79)
(0.64, 0.47)
(0.10, 0.12)
(0.29, 0.32)
60%-70%
(0.93, 0.87)
(0.85, 0.76)
(0.56, 0.39)
(0.07,0.07)
(0.15, 0.24)
70%-80%
(0.88, 0.79)
(0.82, 0.72)
(0.47, 0.32)
(0.04, 0.07)
(0.14, 0.13)
80%-90%
(0.81, 0.72)
(0.76, 0.65)
(0.32, 0.24)
(0.00, 0.04)
(0.00, 0.08)
90%-100%
(0.49, 0.42)
(0.64, 0.54)
(0.12, 0.12)
(0.00, 0.03)
(0.00, 0.04)
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Correlation between Terk and Prediction Accuracy. We examine the correlation between Terk and prediction accuracy on ImageNet-A to validate the reliability of Ter, as an intermediate eval- uation metric.
Table 13: Correlation between Terk and accuracy ImageNet-A.
Value of q
Teri
Ter:
Ters
Terio
Ter20
Accuracy
0.01
29.3069
27.0006
25.9538
24.6061
23.7410
63.48
0.1
29.3283
26.9548
25.9067
24.5704
23.7164
63.45
29.3293
26.8951
25.8540
24.5383
23.6985
63.24
0.9
29.3189
26.8414
25.8114
24.5162
23.6892
62.80
29.3043
26.8000
25.7808
24.5020
23.6841
62.58
1.5
29.2820
26.7511
25.7460
24.4864
23.6785
62,68
2,0
29.2682
26.7257
25.7291
24.4798
23.6771
60.95
As shown in Table 13, when keeping K constant while decreasing 9, both Terk and accuracy demonstrate increasing trend. This suggests that Terx and accuracy be considered approx- imately equivalent metrics, as the former evaluates model performance through prediction confi- dence, while the latter directly measures performance via top-1 prediction correctness.
Integration with DEYO Method. We further investigate the modularity of ADTE by integrating it with DEYO (Lee al., 2024b). By simply replacing the Softmax Entropy used in DEYO with our ADTE while keeping all other parameters and pretrained weights unchanged, we achieve significant performance improvements. Table 14 demonstrates that the modified method obtains 2.26% boost
Tahle 14: Integration with DEYO method ColoredMNIST.
Method
Avg Acc (%) Worst-Group Ace (%)
Time (s)
DEYO
78.24
67.39
0.073
DEYO ADTE
79.29
69.65
0.074
in Worst-Group Accuracy with almost no additional computational overhead.
Estimated Bias Stability, We tracked the changes in the estimated bias's mean and variance as the size of the memory bank increases, with results presented in Table 15. As the size of the memory
Table 15: Stability of estimated bias memory bank size ImageNet-II.
Size
10
20
30
40
Mean
-5.2248
-4.3044
-4,2567
-3.8658
-3.9067
-3,8224
-3,8825
Variance
2.2897
2.0415
1.7100
1.5247
1.4618
1,4537
1.4752
bank increases, the variance of the estimated biases gradually decreases. When the size reaches 10, both the mean and the variance tend to stabilize, indicating that only 10 samples per category are needed reach a stable bias estimation. This trend is consistent with the results of the performance experiment, where the performance also stabilizes around the size of 10. ADTE can quickly converge reliable bias estimation during the test without relying on an excessively large memory bank.
Experiments on Corrupted Datasets (ImageNNet-C, CIFAR-10-C, CIFAR-100-C), To further demonstrate the effectiveness of CGPO, we conducted experiments on ImageNet-C, CIFAR-IO-C and CIFAR-100-C datasets (Hendrycks & Dietterich, 2019). For ImageNet-C, we randomly select representative corruption families (Defocus Blur, Glass Blur, Motion Blur). For CIFAR-10-C and CIFAR-100-C, evaluated the models on 7 diverse corruption types, covering blur, noise, and geometric distortions.
As shown in Tables 16, 17 and 18, across all datasets and nearly all corruption types, ADTE consis- tently outperforms both the original CLIP and SE. Importantly, (1) SE often degrades performance compared the CLIP model, especially under severe blur and noise; (2) ADTE remains stable and delivers consistent improvements, demonstrating stronger robustness even in settings where SE becomes unreliable.
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Table 16: Accuracy (%) on ImageNet-C across severity levels (1-5).
Model
defocus. blur
glass blur
motion_ blur
3
4
2
2
3
4
16
58.78 53.82 43.36 34.42
26.12
56.47
48.27 26.75 20.88 16.96 62.51
56.91
47.46
34.37
26.55
SE
58.62 54.06
43.15
34.35
26.39
55.74
46.98
26.34
19.87 15.56
62.69
57.18
46.41
33.87 25.31
ADTE
59.43 54.89 44.05 35.06 26.95 57.56 48.52 27.58 21.65 17.84 63.83 58.23 48.22
34.54 27.06
Table 17: Average Accuracy (%) on CIFAR-104
Model
brightness elastic transform gaussian blur impulse noïse motion blur shot.noise speckle noise
CITI-VVT/B-16
90.94
84.33
90.54
87.94
87.33
84.73
85.01
83.71
86.88
86,98
84.39
84.86
ADTE
91.32
84.86
88.43
87.65
85.56
85,42
Table 18: Average Accuracy (%) on 1IFAR-100-G-
Model
brightness elastic transform gaussian blur impulse.nos noise motion blur shot noise speckle noise
ELIP-VIT/B-11
68.29
57.83
68.05 66.56
62.46
62.17
57.27
57.66
SE
67.92
58.05
61.78
61.32
$7.01
56.22
ADTE
68.80
59.32
67.68
62.65
61.98
57.56
57.43
Consistent gains in 3 datasets and most corruption severities indicate the generalization ability of ADTE, reinforcing our main claim: ADTE provides a more robust correction mechanism than SE under distribution shifts, even when SE partially completely fails
Analysis of Pseudo-Label Noise Effects on Class-Wiss Bias Estimation. To directly measure the effect of noisy pseudo-labels, conducted controlled experiments in which manually inject pseudo-label noise on the ImageNet- A dataset. Specifically, for each sample, with probability p {20%, 40%, 60%, 80%, 100%), the true label is replaced by random incorrect label. This allows us to isolate the impact of degraded pscudo-label quality under varying noise intensities.
Table 19: ImageNet-A Accuracy (%).
Model
Zero-shot True Label Pseudo Label| 20 % Noise 40% Noise 60% Noise 80% Noise 100% Noise
CIJP-ViT-B/66
50.6
64.0
ADTE
65.9
65.5
65.9
65.8
65.6
65.4
64.6
The results are shown in Table 19. We observe important trends: (1) When using the true label to estimate bias, ADTE presents the best performance compared with results under pseudo-label noise; (2) ADTE remains extremely stable under moderate and even severe noise levels: accuracy stays within very narrow band (65.9 - 65.4) even as pseudo-label corruption increases to 80%; (3) Even with 100% incorrect pseudo-labels, ADTE still outperforms SE (64.6 vs. 64.0).
This aligns precisely with our theoretical analysis in Sections 4.1 and 4.2: SE is strict lower bound of TE, and TE is a strict lower bound of ADTE, since SE corresponds to the special case where all category-wist parameters g' are identical. Therefore, ADTE can never perform worse than SE, even under extreme pseudo-label noise.
Overall, ADTE is robust to pscudo-label errors, inseeinnensiiive, and maintains reliable perfor- mance even under worst-case degradation, making it practical for real-world deployment where pseudo-labels are inevitably imperfect.
Performance under Low-Bias Scenarios. To quantify the performance gap between ADTE and SE/TE under low-bias conditions, conducted experiments ImageNet- 1k under progressively lower bias conditions. Specifically, we sort ImageNet- 1k classes by their prediction-bias magnitude and randomly construct subsets:
$1 highest inter-class bias (200 most biased classes)
82:
85: lowest bias (200 least biased classes)
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This setup directly evaluates ADTE, TE, and SE in increasingly unbiased distributions. The results in Table 20 show that: (1) ADTE consistently outperforms SE and TE at all bias levels; (2) The advantage grows as the bias becomes larger, (3) Even in nearly unbiased settings, ADTE still yields notable gains. This quantitatively validates ADTE's applicability limit and supports the theoretical claim of lower-bound.
Table 20: ImageNet-A accuracy (%) across progressively lower bias conditions.
Model
CITT--VT//-16
69.5
58.8
52.3
74.2
76.3
SE
70.4
60.3
53.1
75.9
77.8
ADTE
62.3
55.2
77.1
78.5
Continual or Gradual Domain-Shift Scenarios. To evaluate ADTE under realistic evolving dis- tributions, we conducted new experiments by mixing five ImageNet variants, i.e. ImageNet- ImageNet-A, ImageNet-V, ImageNet-K, and ImageNet-R, in fully randomized interleaved stream. This simulates an online TTT scenario where the domain changes unpredictably from sample to sample, making one of the most challenging continual shift settings.
Table 21: Accuracy (%) on randomized, mixed five ImageNet variants.
Model
ImageNet-1k ImageNet-A
ImageNet-V
ImageNet-K
ImageNet-R
ADTE
71.8
65.5
65.6
53.5
81.4
ADTE_random
72.0
65.8
65.4
53.5
81.2
The results in Table 21 demonstrate: (1) ADTE consistently outperforms SE and the CLIP baseline in all domains; (2) No signs of instability or degradation, even when the domain identity changes every few samples; (3) Memory-based bias estimation remains effective because only small class- wise bank is maintained, which is naturally robust to cross-domain mixing.
Evaluating ADTE's Applicability Unimodal ImageNet Models and CLIP Successors like SigLIP. To verify the effectiveness of ADTE on models other than CLIP, we first conducted addi- tional experiments the MEMO (Zhang et al., 2022) test-time adaptation benchmark. As shown in Table 22, ADTE con- sistently improves performance techniques. The results demonstrate that ADTE is not tied to multimodal encoders, and remains effective on purely vision-based architectures.
the ImageNet-A dataset on unimodal
models, following
ResNext-101 outperforming standard TTA and other adaptation
Table 22: ImageNet-A Error (%).
Method
Error(%)
Method
Error( %)
ResNext- 101 (baseline)
90.0
WSL
54.9
TTA
83.2
TTA
49.1
Single-point BN
88.8
+ Single-point BN
58.9
MEMO
84.3
+ MEMO
43.2
ADTE
81.5
ADTE
41.1
Next, we conduct evaluations on five generalization models of CLIP. As shown in Table 23, across all models, including SigLIP and SigLIP2, ADTE provides consistent improvements, confirming its robustness and wide applicability.
The above experiments confirm: (1) ADTE generalizes across architectures (unimodal or multi- modal); (2) ADTE generalizes
training regimes (contrastive - sigmoid loss); (3) ADTE adapts robustly, even for models with stronger native calibration, such as SigLIP2.
Confidence Intervals Significance Tests.. To verify whether the improvements statistically or practically meaningful, we add more runs to get the confidence intervals of accuracy. Table 24 demonstrates the statistical relevance of improvements.
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Table 23; ImageNet-Ik Ik Accuracy (%) on Generalization Models with ADTE.
Model
ImageNet-Ile IK Acc. (%)
+ADTE
CLIP
68.7
71.8
OpenCIIP
70.2
73.5
EVA-CLIP
74.7
77.4
SigLIP
76.2
78.9
SigLIP2
78.2
80.1
Table 24: Accuracy (%) 95% confidence interval of the results in Table
Model
ImageNet-1k
ImageNet-A
ImageNet-V
ImageNet-K
ImageNet-R
CLIP-ViT/B-16
68.7
50.6
62.2
48.3
77.7
SE
70.9
64.0
65.1
50.3
80.8
ADTE
71.8
65.5
65.6
53.5
81.4
ADTE 95% con. int. 71.78 + 0.44
65.72 + 0.50
65.67 0.17
53.59 = 0.25
81.28 + 0.25
B
PROOF
B.1 PROOF OF PROPERTY
Shannon-Tsallis a 1 equivalences
Property 1. As q + 1, Tsallis Entropy becomes equivalent to Shannon Entropy, i.e.,
H (P(: | H (P( (P())x))))
(14)
Proof. For Tsallis entropy, we have:
H.s (P( xx
Σ Ply = 11 x0 -1
Ply = =1 x
>
P = 11 xg9tt)
- 9
1=1
Ply =1y=11 [[]==1x]]]] 1
Σ Ply = [1 x1x
1-
(15)
The limitation lim only applies to the terms containing q. Thus:
P(y x
H x
P(y=
1|
(16)
1=1
We use I''Hopital's rule to solve the limit in the expression:
x5 -
P 1 x-
P = y² log Ply x
lim
lim 7-40
lim 7-50
-7
x log P(y x) = -o log P(y = =1
(17)
where the second equality uses L. L'Hopital's 's rule. Substituting the above into Equation 16, we have:
lim (Pa (- x)
2
P [ (- ( )
9-
l=1
(18)
Σ
P(y = -|| x1 log P = | x())
1=1
H (P 1)
Therefore, prove Property 1.
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Accuracy
Accursey of IN A
Accuracy IWV
Avarage
Rerrdde log
592
522
092
S7.8
00.00
D00 1883
100 181
IN
18
8. aT WIL
53
52
50
60
90
60
90
11-XRR 35
31
35
35
(--X| db
35
1c-X0u db
31
C292 IT-XIX 31
CE 12-1021
12-1UR
00
52.5
02
0090
2290
0072
9/c
222
002
FB2
0002
CE
0299
0002
0200
00
020
12X
100
100
DE
EL 8o wnges TILL
50
60
60
11
51 1
11
35
35
25
1-3la d5
200
(E-3iA 35
1- 25
R22
622
1E2
252
1N
99c
89c
090
932
077
722
73 DO 190
1921
183
150
100
100
18
TE 10 jo urge INLL
23
50
52
00
00
11
60-XiR 35
CI-MIRL T1
St-win 35
OE-MUA 35
SI-MIRL TE
OE D0
CE-MAAL 75
DE VIEH A1
CE-MIR 31
AE-MIL 31
DE HIPI
OC-XIAL
F2
05t
TV 100 1482
O0 1982
00 1083
00 163
TE
13 1E
TE bi jojo argen TNLL
11 60
102--MA 35
102-N/1 35
(0C- 35
(or (oz= 18s
10E 125
10c-X0i db
31
10C- 10C-VIRL
(0l MIP
102-1172
Figure Average Terx values for different g TE SE on ImageNet-IRe and its variant datasets.
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B.2 EXPERIMENTAL ANALYSIS PROPERTY 2
Higher Terk under TE as y and Comparison with SE:
Property 2. Through experimental analysis, we find that as the parameter decreases, the set of high-confidence views selected by TE tends to have a higher average Terk value (for > 1), For two different parameter values qı and q2 with qı < .2, and their corresponding selected view sets Ny. and Xgz of equal size, we observe:
Σ X1 EXE
(xIx(x1) >
Σ x2E
Ter (X2).
(19)
X
Furthermore, there exists a particular o" and corresponding view set Xq., TE outperforms SE in this regard, with the view set selected by SE denoted as X
Σ
Terx(x1)
Σ X2EX
Ter (x2).
(20)
ATTE
SE
XIEXS
Experimental analysis. Equation 19 describes that when K 1, as the parameter q of TE decreases, the selected confidence views exhibit higher average Terk values. For example, in Figure of ImageNet- 1k and its five variants, the q value decreases from 10 0.001, except for Tcr(K (K' 1), all other Ter values show a gradually increasing trend. This implies that the lower the value, the more the TE tends to select views with higher similarity scores.
As shown in Figure 5, when the value of TE is relatively large, the Ter value of TE is generally smaller than that of SE. As the g value decreases, the Ter value of TE gradually exceeds that of SE. This further indicates that SE is special case of TE, and appropriate selection of values can make exhibit better performance than SE.
B.3 PROOF OF CONCLUSIONS 4.2
Let p E c), where e ensures the probability p of tail category being close zero, and we have the following conclusions:
As - 0o, we have limp- F(p.g) = and F(p.q)<F(p. (2) <0, Aqn < co.
Proof. a. Find the limit of the function F(p, 4) = pº 1-4 + pllogpas +o0 and p - p 0+
First term: pd_ o as g + too and p - 0+ -
Second term: plog p by L'Hospital's rule: limp- 1/p
log p (-p) 0
Conclusion:
lim F(p.q) = +0 -
(21)
0 +00
P+0+
Compare the magnitudes of F(p 4)), F(p, 92), and 0 as 4ı 92 + too and p 0+.
Sign ana mallysis For E (0 and > 1:
F(p. g) = D
+ p logg < 0
(22)
Menotonicity: Fix p E e0. The derivative of G(g) = --q.
G'(g) = p"[1 + (1 q) log pl
0 for + +00
(23)
(1 - g)
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Thus G(g) is increasing. For qu 92:
G(n) < (g2)) = F(p. < F(P, <0
(24)
(2) As q q-+1,, we have l p(p.g)=-ov and F(p.:))=((p.0) <0, A1 <<q' <92
Proof. a. Find the limit of the function F(p, -- + ploopaa as + 1+ and p + 0+.
Consider the limit of the entire function F(p. g): Since there are two variables approaching their limits, the path of the limit may affect the result. We consider the iterated limits:
① First, fix > and let + 0+. At this time, we have the limp- F(P, - 0r limp-so [ + p ppplogp. p). Since q > 1 is fixed, limp-ot i- I-g 0-, and we have already found that limp plogp p O-. So, limp F(p,)) 0 +0 = Then, let - 1+, then ( =00=00 =
Next, fix p
(0,c) and let q 7 1
For lim F(p, 4)
lim,-+1
pa 1-q + + plgop) When + 1 - 0-, pd - p. so lim 1-q = 0- = =00
D2
(because p 0), and for fixed p E (0,c). plog is a fixed negative value. So, lim F(p,g) 0 plog -o. Then, let 0+, then limp--o (-00)
Since the results of the two iterative limits are different (one and other is -oo), strictly speaking, the existence of the simultaneous limit depends on the relative rates at which p and q approach However, in this work, the probability of the tail category is usually a very small decimal, but it will not approach 0 infinitely, and we give priority to the case of + 1t. Therefore, lim F(p. g) = -o + p log = -0. Therefore, we determine the limit value to be -00
Compare the magnitudes of F(, q1), F(p, 02). and O as q < Q2 - 1+ and p - 0+.
This part of the proof is the same as part b of Conclusion (1). (3) As q g we have limp-o+ F(p.g)=17, and
v0< 91 <22
Proof. a. Find the limit of the function F(p, 4) 1- + pog a 1+ and p + 0+.
In this condition, both and approach 0 simultaneously. This is limit problem for two-variable function. We need to examine path dependence.
Consider different paths (p,4)
@ First:
Iterated limit with + 0+
first, then p p - 0+
pa
lim F(P. g) lim
+ ppgop =1 + plgg...
(25)
9-
1-q
Thus,
lim (1 + plggp) = 1
(26)
p p
@ Next: Iterated limit with p 0+ first, then q 0+. For fixed q
(0, 1):
lim F(p.q)= = lim pa q p
+ p logp
(27)
p-
Therefore,
lim (0) 0. g+0
(28)
In this work, p represents the probability of category, which may be very small decimal, but it will not approach 0 infinitely. Path can be ignored. Thus, we determine the limit value to be
23

---

Published as a conference paper at ICLR 2026
b. Compare the magnitudes of F(P. 91), F(P: 92). and 0 as 91 < - 0+ and p 0+.
Sign Analysis: As p + 0*, pogg - _ For positivity:
pd > -plogp
p
F(p. 4) > 0
logpl.
(29)
As + 0+, 9 1 -1 and = 1. The inequality simplifies to: logpl. Since diverges
faster than log pl as p = (p. g) for sufficiently small p. Thus:
F(p, gi) > 0 and g(), > 0.
(30)
Monotonicity g: Fix p. The derivative w.r.t. q is:
G4 p + (1 q) logp!
(31)
(1 q)²
For p + 0+, +0. - -0. Since 1- - 2 the numerator is negative, implying G'(4) 0. Thus,
F(p, q) is decreasing in q. For Q < q2:
F() < F(p.
(32)
(4) As q 9-+17, we have limp- -0+ F(p.9) = +o0, and F(p.o))=((pq)))>> 1a < 1.
Proof. a. Find the limit of the function F(p,4) pa 1-9 + +plogp aoggass - 1 and p + 0+.
Compute the iterated limits:
① For fixed q E (0,1):
pa
lim F(p,g) = lim p-00
+ poogp = 0+ - =
(33)
p-+0
1-6 g
Thus,
lim (0*) 0+
(34)
8++1
@ For fixed p (0,e):
pa
lim F(p.g) = lim q->1
1- +
plogp = +o0 + plog 400.
(35)
In this work, the probability of the tail category is usually a very small decimal, but it will not approach 0+ infinitely, and we give priority to the case of q + 1-. Therefore, limg--1 F(p.
+oc. Therefore, we determine the limit value to be +
Compare the magnitudes of (p, 91). F(P. 92). and 0 as q1 92 + 1 and p - 0+.
Sign analysis: Identical to part sign analysis of Conclusion (3).
Comparing g(p.g)) and F(P, 92): Compute the partial derivative:
OF pd q 0g
1
log +
(36)
I-q 9
Since P 0, the sign of depends on log p
By
I-g
1
As g
17,
-
I-g +o0 dominates
log p + -c0. For example:
= 0.01 = logp ~ 4.6; = 0.999 =
1 1-6 1000 = log pogp +
1- 0.
Thus, F(p, q) increases with y near q = 1. For qI Q2 + 11, we have:
F(p,n) < F (2)))))
(37)
24


Reviews:
[{"review_id": "vgYOyE6kfy", "reviewer": "Reviewer_Nqxf", "summary": "This paper addresses the challenge of bias in vision-language models (VLMs) like CLIP during test-time adaptation (TTA). The authors argue that standard Shannon Entropy (SE) used in TTA methods (e.g., for selecting high-confidence augmented views) produces biased uncertainty estimates due to CLIP's pretraining on imbalanced data, leading to suboptimal view selection and adaptation. They propose using Tsallis Entropy (TE), a generalization of SE with a non-extensive parameter $q$, which better handles biased distributions. TE is further extended to Adaptive Debiasing Tsallis Entropy (ADTE), where class-specific parameters $q_l$ are adaptively computed via min-max normalization of estimated label biases from incoming test instances (using a memory bank and logit adjustment). ADTE integrates seamlessly with existing TTA pipelines like Zero, requiring no hyperparameter tuning. My detailed comments are as follows.", "questions": "Please refer to the Weaknesses.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "1. Extensive experiments on ImageNet, its variants, and 10 cross-domain datasets, demonstrate the effectiveness of the proposed method.\n2. The approach is simple yet effective.", "weaknesses": "1. To further demonstrate the effectiveness of the proposed method, it would be better to conduct more experiments on the ImageNet-C, CIFAR10-C, and CIFAR100-C datasets.\n2. The paper overlooks prior studies that have explored the use of Tsallis Entropy in test-time adaptation and domain adaptation. References [1–2] should be discussed in the related works section to better contextualize the novelty of ADTE.\n3. The claim of requiring no hyperparameter tuning is somewhat misleading, as the method still depends on several implicit hyperparameters, such as [α,β] and the memory bank size.\n4. ADTE relies on pseudo-labels to estimate class-wise bias; however, under severe domain shifts, pseudo-label noise may substantially affect the accuracy of bias estimation. The paper does not analyze how such errors impact ADTE’s performance.\n5. The paper concludes that ADTE shows limited advantages when the model is nearly unbiased; however, it does not quantify the performance gap between ADTE and SE/TE under such low-bias conditions. Without empirical or theoretical analysis of these “unbiased” scenarios, it is difficult to assess ADTE’s applicability boundaries or to validate the claim that SE serves as its lower bound.", "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": "6rj7oeu5y1", "reviewer": "Reviewer_okn7", "summary": "This paper proposes Adaptive Debiasing Tsallis Entropy (ADTE), a test-time adaptation method for vision-language models such as CLIP. Conventional approaches rely on Shannon Entropy (SE), which is biased due to class imbalance in pre-trained data. ADTE replaces SE with Tsallis Entropy (TE), a generalized entropy with parameter $q$ that mitigates bias when $0<q<1$ and further introduces a class-specific adaptive parameter $q_l$ estimated from test data using a small memory bank. ADTE can be directly applied to existing TTA pipelines without retraining or hyperparameter tuning. Experiments on ImageNet variants and cross-domain benchmarks show consistent improvements over baseline methods.", "questions": "see Weakness section", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "- Effectively addresses the problem of biased predictions by generalizing SE to TE\n- Plug-and-play design which can integrate into existing TTA frameworks without retraining\n- Achieves consistent performance improvements across OOD and cross-domain benchmarks\n- Computationally lightweight, minimal additional cost or tuning required", "weaknesses": "- In TTA settings like ZERO, where adaptation relies only on confident-view selection per instance, considering class-wise bias may be less relevant or overcomplicated.\n- The paper lacks in-depth analysis explaining why ADTE particularly improves performance on cross-domain tasks, despite showing larger gains there in ablations.\n- When LA is removed, performance becomes similar to competitive baselines, raising doubts about whether ADTE itself is a truly effective standalone TTA solution.\n- The method’s novelty is limited, as several components (e.g., bias estimation, memory bank, LA) are borrowed or slightly modified from Frolic, making ADTE appear incremental rather than fundamentally new.\n- The memory bank-based bias estimation is highly dependent on pseudo-label accuracy; early mispredictions can accumulate and distort class bias, especially for tail classes.\n- In continual or gradual domain-shift settings, where test streams evolve over time, the memory-based adaptation may become inefficient or unstable, limiting its scalability to realistic online scenarios.", "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": "1uJWFiP2Ae", "reviewer": "Reviewer_E5TA", "summary": "This paper proposes Adaptive Debiasing Tsallis Entropy (ADTE), a novel Test-Time Adaptation (TTA) method based on Tsallis Entropy (TE).\nCLIP predictions exhibit bias, with certain classes being predicted more accurately than others.\nConventional CLIP TTA uses Shannon Entropy (SE), but SE treats all classes equally and thus cannot address the prediction bias problem.\nTherefore, this paper proposes using TE, a generalization of SE, which is better suited for such biased predictions.\nFurthermore, this paper proposes a method to automatically estimate q, the class-specific parameter required for TE, using a bias estimation technique that uses a memory bank.\nExperiments on OOD benchmarks and cross-domain benchmarks demonstrate that ADTE achieves higher accuracy than existing TTA methods.", "questions": "I was not aware of the details of the module used in Tables 3 and 4.\nIs ADTE a method that includes LA?\nWhat is the difference between LA-SE and SE-LA?\n\nMinor comment.\nTypo: Line120 Logit Adjustment (EM) -> Logit Adjustment (LA)", "limitations": "", "rating": 6, "confidence": 3, "soundness": 4, "presentation": 2, "contribution": 3, "strengths": "The motivation and proposed method are intuitive and interesting.\nThis paper adopts an intuitive approach of using parameter-free TE to address the prediction bias problem in CLIP. \nDespite its simple concept, the method proves to be effective.\n\nSince TE is a generalization of SE, ADTE can be incorporated into existing SE-based TTA methods.\nIn an era where large-scale models trained on web-scale datasets with inherent prediction biases are mainstream, employing TE is a reasonable approach.", "weaknesses": "This paper lacks experiments with models other than CLIP, raising concerns about the applicability of ADTE.\nFor example, can ADTE be applied to unimodal models pretrained on ImageNet or subsequent models of CLIP, such as SigLIP?\n\nADTE is a method specialized for scenarios with predictive bias, but how common are such scenarios?\nIt is desirable to have a discussion about scenarios where ADTE is effective (such as model or dataset distributions).", "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": "QBnLTB9u1F", "reviewer": "Reviewer_xmGS", "summary": "The paper proposes replacing Shannon entropy (SE) with Tsallis entropy (TE) for selecting confident views in test-time adaptation (TTA), arguing TE better handles prediction bias in vision-language models. It further introduces Adaptive Debiasing Tsallis Entropy (ADTE), which assigns a class-specific parameter $q_l$, derived from an estimated class-prior/bias via a memory bank and pseudo-labels, then picks views with the smallest ADTE to aggregate predictions.", "questions": "1. What is the design rationale of min-max mapping?\n\n1. How sensitive is ADTE to pseudo-label noise in the early phase of adaptation? One experiment could be manually altering the class accuracy and see how ADTE behaves.\n\n1. If we replace ADTE with a fixed q or with Shannon entropy but keep the same view-selection pipeline, how much of the reported gain would remain?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1. The paper offers a fresh perspective by replacing Shannon entropy with Tsallis entropy and further adapting a class-specific parameter $q_l$, giving a tunable lens on confidence that can better reflect skewed priors and domain shift during test time.\n\n1. The entropy perspective is modality-agnostic and should, in principle, transfer to other test-time settings (e.g., VLMs, audio, or tabular) where confidence shaping under shift is crucial.\n\n1. The experiments span multiple datasets and architectures, where ADTE outperforms most of them.", "weaknesses": "1. Table 3 show that “w/o ADTE and w/o LA” already achieves high accuracy; many reported deltas are modest ($\\sim$0.5–2%); without confidence intervals or paired significance tests, it is unclear whether improvements are statistically or practically meaningful.\n\n1. The core of ADTE is a min-max mapping from an estimated bias vector $\\tilde{p}$ into $q_l \\in [\\alpha, \\beta]$ (the paper uses $[0.01, 0.9]$) via Eq.~(13). There’s no theoretical link that this linear rescaling is optimal (or even monotone-calibrated) for view selection risk; it feels ad-hoc and dataset-dependent. Sensitivity is only probed by sweeping the lower bound, not the mapping itself.\n\n1. Estimating class priors from pseudo-labels assumes pseudo-labels are reliable; errors in early iterations can feed back into the prior and $q_l$, potentially harming tail classes the method aims to help.\n\n1. The paper did not specify the details of augmentation strategies; which must highly affect the TTA performance.\n\n1. The use of large memory bank (1~10 samples per each of 1000 classes) might be unfair for comparison with baseline TTA methods.", "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)