ZeroSiam: An Efficient Asymmetry for Test-Time Entropy Optimization without Collapse
Authors: Guohao Chen
Shuaicheng Niu
Deyu Chen
Jiahao Yang
Zitian Zhang
Mingkui Tan
Pengcheng Wu
Zhiqi Shen
Venue: ICLR 2026 Poster (2026)
Keywords: Test-Time Adaptation
Out-of-distribution Generalization
Entropy Minimization
Primary area: transfer learning, meta learning, and lifelong learning

Abstract: Test-time entropy minimization helps adapt a model to novel environments and incentivize its reasoning capability, unleashing the model's potential during inference by allowing it to evolve and improve in real-time using its own predictions, achieving promising performance. However, pure entropy minimization can favor non-generalizable shortcuts, such as inflating the logit norm and driving all predictions to a dominant class to reduce entropy, risking collapsed solutions (e.g., constant one-hot outputs) that trivially minimize the objective without meaningful learning. In this paper, we reveal asymmetry as a key mechanism for collapse prevention and introduce ZeroSiam--an efficient asymmetric Siamese architecture tailored for test-time entropy minimization. ZeroSiam prevents collapse through asymmetric divergence alignment, efficiently achieved by a learnable predictor and a stop-gradient operator before the classifier. We provide empirical and theoretical evidence that ZeroSiam not only prevents collapse, but also regularizes biased learning signals, enhancing performance even when no collapse occurs.  Despite its simplicity, extensive results show that ZeroSiam performs more stably over prior methods using negligible overhead, demonstrating efficacy on both vision adaptation and large language model reasoning tasks across challenging test scenarios and diverse models, including particularly collapse-prone tiny models.

Published as a conference paper at ICLR 2026
ZEROSIAM: AN EFFICIENT ASYMMETRY FOR TEST- TIME ENTROPY OPTIMIZATION WITHOUT COLLAPSE
Guohao Chen' 1 Shuaicheng Niu Deyu Chen', Jiahao Yang', Zitian Zhang?
Mingkui Tan?, Pengcheng Wu', Zhiqi Shen't {guchao. chen, shuaicheng niu, zqshen] @ntu edu. .g
Nanyang Technological University' Joint WeBank-NTU Research Institute on Fintech? South China University of Technology
ABSTRACT
Test-time entropy minimization helps adapt a model to novel environments and incentivize its reasoning capability, unleashing the model's potential during infer- ence by allowing it to evolve and improve in real-time using its own predictions, achieving promising performance. However, pure entropy minimization can favor non-generalizable shorteuts, such inflating the logit norm and driving all pre- dictions to a dominant class to reduce entropy, risking collapsed solutions (e.g., constant one-hot outputs) that trivially minimize the objective without meaningful learning. In this paper, we reveal asymmetry as a key mechanism for collapse prevention and introduce ZeroSiam-aa an efficient asymmetric Siamese architecture tailored for test-time entropy minimization. ZeroSiam prevents collapse through asymmetric divergence aligmment, efficiently achieved by a learnable predictor and stop-gradient operator before the classifier. We provide empirical and the- oretical evidence that ZeroSiam not only prevents collapse, but also regularizes biased learning signals, enhancing performance even when no collapse occurs, Despite its simplicity, extensive results show that ZeroSiam performs more stably over prior methods using negligible overhead, demonstrating efficacy on both vi- sion adaptation and large language model reasoning tasks across challenging test scenarios and diverse models, including particularly collapse-prone tiny models.
INTRODUCTION
Entropy measures the uncertainty of a model's predictions. Since its emergence, entropy optimiza- tion has been widely adopted as an auxiliary objective alongside supervised, reinforcement signals, elc. To be specific, in semi-supervised learning it enforces low-entropy predictions unlabeled data to refine decision boundaries (Grandvalet & Bengio, 2004; Lee et al., 2013; Sajjadi et al., 2016); in domain adaptation it mitigates distribution shifts by promoting confident outputs (Jiang & Zhai, 2007: Long et al., 2016; Morerio et al., 2017); and in reinforcement learning it is often maximized to encourage exploration or minimized to ensure deterministic policies (Ziebart et al., 2008; Ahmed et al., 2019), among others, showing its remarkable success in boosting the learning effectiveness.
Of late, test-time entropy minimization has attracted growing interest, as it operates purely unsuper- vised during inference, without relying any ground-truth supervision. For example, in test-time adaptation (TTA) (Wang et al., 2021; Lee et al., 2024) it encourages confident predictions to miti- gate domain shifts on unseen data streams; in large language models, it helps calibrate uncertainty and improve prediction consistency for alignment (Hu et al., 2025a; Jang et al., 2025). These ad- vances highlight the potential of entropy minimization in unleashing model power during inference, enabling adaptation to novel or out-of-distributtin domains and moving toward greater intelligence.
However, entropy minimization naturally drives the model to increase the maximum predicted logit, regardless of whether it aligns with the true label. In practice, testing often involves noisy real- world data, domain shifts, or novel environments, where models often tend be highly sensitive and uncertain, and the predicted maximum class is frequently incorrect. In this sense, minimizing
Equal contribution. CCorrespondigg author. Source code at: http:///gitaaaacmmm//aaooCC/h///

---

Published as a conference paper at ICLR 2026
similarity
entropy y
entropy
similarity
gradient
h(2z)
gradient
gradient
82
stop-grad
stop-grad
predictor h
classifier
classifier
2
encoder fz
1((2)
classifier
encoder f
2
predictor
encoder f
X1 aug
encoder f
aug
input
test input
test input
(a) BYOL. SimSiam
(b) Tent
(c) ZeroSiam (ours)
Figure 1: Comparisons on architectures. (a) Alignment-oriented SSL methods (BYOL. (Grill et al., 2020), SimSiam (Chen & He, 2021)). (b) Test-time entropy minimization (Tent) (Wang ct al., 2021). (c) Our ZeroSiam, which designs minimal asymmetry for entropy minimization with lightweight predictor and a srop-gradient meanch-withene augmentations, extra encoder passes, or teacher mod- els substantially enhance learning stability and boost performance while retaining efficiency.
entropy alone does not ensure that the corresponding supervised loss (e.g., cross-entropy) on the target task is also reduced. Instead, the model can easily exploit shorteut solution by producing near one-hot outputs for all inputs, which trivially minimizes entropy but fails to capture meaningful predictions, leading to degraded performance. For instance, after TTA, models can deteriorate to predicting all samples to a single class under challenging wild testing scenarios (Niu et al., 2023).
Various TTA methods have been proposed to tackle the above issue, such filtering unreliable gra- dients using predefined thresholds (Niu et al., 2022; Lee et al., 2024; Hu et al., 2025a), or mitigating disturbances through optimization of a sharpness- aware loss surface (Niu et al., 2023). However, the use of heuristic thresholds for gradient selection remains problematic, as such thresholds are difficult to define and generalize across domains. In this sense, filtering or suppressing noisy gradients can only be partial, and the model remains exposed to trivial solutions by optimizing with the remain- ing gradients, for which entropy can still be minimized by collapsing into constant one-hot outputs regardless of the inputs. As result, it is unavoidable that these methods still risk collapse during deployment, particularly under prolonged or more challenging testing scenarios, as in Tables 2 & 6.
In this paper, we reveal asymmetry as key mechanism for collapse prevention, which was intro- duced in the negative-free self-supervised learning (SSL.) (Chen & He, 2021; Zhang et al., 2022a) that seeks to learn meaningful representations by maximizing the similarity between two augmented views of the same image. Negative-free SSL uses an asymmetric structure to prevent the outputs of two branches from collapsing toward the same constant, resolving collapse from architectural design. However, asymmetric structure is tailored for representation learning during pre- trainiinnnn, and naively applying it to context is infeasible or inferior, as: 1) test-time entropy minimization typically has only one prediction branch and optimizes entropy instead of similarity; 2) traditional Siamese design requires extra backbone passes, which impairs efficiency for our test-time learning.
Therefore, we design ZeroSiam, demonstrating how asymmetry can be efficiently implemented in test-time entropy minimization without using augmentations, extra backbone passes, and teacher models. To embed asymmetry within a single backbone pass, ZeroSiam decouples a prediction into two asymmetric outputs based on the same feature: an online branch with a learnable predictor and a target branch with stop- gradient. As shown in Figure 1, we minimize entropy on the online branch learn discriminative features, while performing asymmetric predictor target alignment to prevent collapsed constants. We investigate ZeroSiam's 's behaviors empirically and theoretically during TTA in Section 3.2, demonstrating that our architecture avoids collapse and also meaningful in reg- ularizing biased shortcut learning signals at testing, which improves the performance of entropy optimization even when no collapse occurs. ZeroSiam achieves notable stability and effectiveness with single extra predictor, introducing negligible overhead (see Table 1). Despite its simplicity, ZeroSiam yields superior robustness compared to prior methods across diverse architectures and a wide range of test scenarios, e.g., adapting reliably even with incorrect pseudo labels (see Table 6).
Main Novelty and Contributions: 1) We are the first to study asymmetric structure in TTA and pro- pose ZeroSiam, revealing how asymmetry can be efficiently implemented in test- tit-timm entropy min-
2

---

Published as a conference paper at ICLR 2026
imization for collapse prevention without using augmentations, extra backbone passes, and teacher models. 2) We provide empirical and theoretical insights into ZeroSiam's 's behaviors (Section 3.2), demonstrating that ZeroSiam also helps absorb and regulate non- generalizable shortcut learning signals at testing. which enhances test-time learning performance even when no collapse occurs. 3) Extensive experiments on both language and vision tasks across both transformer and CNN models with varying sizes and a wide range of challenging test scenarios verify our efficacy.
2 PRELIMINARY AND PROBLEM STATEMENT
We briefly revisit test-time entropy minimization in this section for the convenience of our method presentation and put detailed related work discussions into Appendix A due to page limits.
Test-Time Entropy Minimization Formally, given any model with its encoder [(; 0y) and classi- fier 9(::8g) 0g) trained source data Dtrains test-time entropy minimization conducts model learning directly from the testing data Drest { by optimizing
min C(x;0,,00 = Σ p(Uc) logp(ūe), where plú-) = =(((x;0)))00 0c)
(1)
Here, p(Ox) denotes the predicted probability for class c, and represents the learnable parameters.
Based on Eqn. (I), test-time adaptation methods (Wang et al., 2021; Zhang al., 2022b; Marsden
et al., 2024; Zhang et al., 2025a) often leverage it to adapt pretrained model to novel domains under potential distribution shifts, known as distr---dittitttionn generalization. processing, it has also been employed for large language model alignment and improving predictive performance (Hu et al., 2025a; Jang al., 2025). By using the model's own predictive entropy as self-supervised signal during inference, Eqn. (1) requires neither source data nor modifications to the training process, making a practical and lightweight solution for real- world deployment.
natural language
Problem Statement and Motivation As shown in Figure 2 (c-d), model learning with unsuper- vised entropy minimization on test data may favor non-generalizabbl shortcuts, such as (i) inflating the logit norm to reduce entropy, or (ii) aligning all logits towards dominant mode. Such updates converge toward collapsed trivial solutions (e.g., constant one-hot outputs), causing performance degradation. This phenomenon becomes particularly severe in challenging test scenarios or when using weaker base models (e.g., ConyNeXt-Tiny) where the lower source accuracy makes the re- sulting entropy gradients substantially less reliable, thereby increasing the risk of collapse. Existing methods mainly seek to improve TTA stability with heuristic thresholds to remove some unreliable updates (Niu et al., 2023; Lee et al., 2024), but the objective yet trivially minimized by collapsed solutions. Consequently, prior methods remain exposed to collapse and are sensitive to architectures and domains (see Tables 3-6). This gap motivates us to ask: How can we design an efficient, theoret- ically grounded entropy optimization mechanism that inherently avoids undesired trivial solutions?
3 ZEROSIAM: STABLE ADAPTATION VIA MINIMAL ASYMMETRIC NETWORK
We achieve the goal of efficient test-time entropy optimization without collapse by designing a lightweight asymmetric Siamese architecture for entropy minimization, namely ZeroSiam. We draw inspiration from the traditional asymmetric design for similarity learning in SSL., but extend its compatibility to the single-branch entropy minimization via single learnable withictor-without requiring augmentations and extra backbone passes. We depict the design choice of our ZeroSiam in Section 3. and provide further theoretical and empirical evidence of ZeroSiam's 's stability for TTA in Section 3.2. The overall details of ZeroSiam are illustrated in Figure (c) and Algorithm 1.
3.1 MINIMAL ASYMMETRIC SIAMESE ARCHITECTURE FOR ENTROPY MINIMIZATION
Unlike cross-entropy training supervised by ground-truth labels, test-time entropy minimization re- lies on the model's is own predicted labels for self-training. This, however, creates shortcut solution, where the objective can be minimized simply by producing one-hot outputs irrespective of the input. As shown in Figure/ 2 (c-d), pure entropy minimization tends to inflate the logit norm and drive all predictions toward a dominant class to reduce the entropy naively, leading to model collapse into de- generate solutions (i.e., constant one-hot outputs). Similar issues appear in negative-free SSL, where
3

---

Published as a conference paper at ICLR 2026
Algorithm ZeroSiam:
Asymmetric Entropy Minimization.
Input: Test samples Drest {x, 1|11, encoder f(:8g), classifier g(:; 0g), inserted predictor h(:00)
Output:
Predictions {p]] j=1 Initialize predictor h(; 0a) Identity;
// warm start for fully test-time learning
fo E Dtest do
Compute encoder feature: # = 0(
// augmentation free, single-pass Compute target branch oulputs u" = g(2; 0g), p" - softmax(u");
Compute online branch outputs =" g( 0n); 00)) = softmax(u"); // stop-gradient
Update O, and normalization params c Oz via Eqn. (4).
end
the model learns trivial solutions via constant representations regardless of inputs to maximize rep- resentation similarity. SSL (Chen & He, 2021) prevents such collapse by introducing an asymmetry: with a non-identity predictor h on one branch, and a stop-gradient operation on the other (see Fig- ure 1). This ensures that degenerate constant outputs incur non-zero alignment loss, preventing the output of two branches from collapsing toward the same constant, showing promising solution.
Motivated by this, we hypothesize that an asymmetric mechanism, which remains under-explored in entropy optimization, could also prevent undesired trivial solutions and stabilize telf-training. How- ever, constructing asymmetry in test-time entropy optimization remains an open question: (1) Un- like contrastive SSL,, entropy-based learning relies one prediction branch, making it non-trivial to introduce a Siamese asymmetric structure; (2) Its objective optimizes entropy rather than similar- ity, offering no pairwise hop-gradient alignment that enables asymmetry in SSL; (3) Traditional Siamese designs require extra backbone passes, hindering the efficiency for our test-time learning.
To bridge these gaps, our key idea is embed asymmetry within single forward pass. We achieve this by inserting a predictor and the stop- goo-grradent operator before the classifier, which decouples a prediction into two asymmetric views from the same feature: an online branch (through the predic- tor) for optimizing entropy, and a target branch (the original logits) for asymmetric stop- stop-gradient alignment. this way, it establishes an efficient asymmetric Siamese for entropy optimization, using no augmentations or extra backbone passes, yet still exploiting asymmetric predictor-tape alignment to prevent collapsed constants and stabilize adaptation. Formally, let ((; 0y) denote the encoder, g(: 0g) the classifier, and h(;; 0x) lightweight linear predictor. Given a test sample x, ZeroSiam computes the encoder feature = f(x;0) 0y) once, then define two asymmetric branches:
u' = g(2;
(target branch, stop- (oo-ggradent) (online branch).
(2)
u² s(h(2;; 0g);
Let = softmax(u") and nd = softmax (u²). The ZeroSiam objective combines entropy minimiza- tion on the online branch with alignment regularizer to the target branch:
L H (p") + D(p" sg(p"])
(4)
where - Pe log Pe is the prediction entropy, D(-II-) is divergence (e.g.. la KL)", and sg[-] denotes stop- gradient. Here, 0n is initialized as an identity to ensure a warm start, which quickly diverges during online learning,
shown in Figure 2 (a), creating the asymmetry neces- sary to prevent collapsed constant solutions. Even when using a randomly initialized predictor to introduce asymmetry, Table 8 shows that ZeroSiam helps prevent collapse in Tent (Wang al., 2021), revealing asymmetry's 's value. In essence, the asymmetric predictor-stop-ee -top-ggrdent alignment inherently rules out collapsed constant solutions as valid minima, thereby avoiding collapse and im- proving stability during online entropy minimization. Unlike BYOL and SimSiam, which rely on augmentations or extra backbone passes, ZeroSiam shows that asymmetry can also be instantiated within pure online entropy minimization in minimal and efficient manner.
3.2 How ZEROSIAM RESISTS COLLAPSE: EMPIRICAL AND THEORETICAL INSIGHTS
Although asymmetric designs (e.g., SimSiam for SSL) are known to prevent collapsed trivial solu- tions, test-time entropy minimization poses new challenges like logit norm inflation and single-class
'ZeroSiam uses symmetric KI. loss as D(-II-) to penalize both under- and over-cnverage of modes, i.c., D(pll)) DxL. (pllg) + (gl(gllp), and a fixed to 1. Results with KI. and reverse KI. are put in Table 10.
4

---

Published as a conference paper at ICLR 2026
(a) Evolutions ZeroSiam's Predictor
Evolutions Accuracy
(c) Evolutions Logit Norm
[d] Evolutions Center Dominance
15
Accuracy (9)
Logit L2 Norm
2250
Center Dominance
0.8
Preditto Be-
10
36-
1:st
1500
066
Rent
Intelanced 1ofto 14
inbelenced refto 1t
18-
ZortSum (ours)
750-
Thet Zeroiiam (ound)
0.4
Zon55 Sam (ous)
Inbelanced 10
250 Online Batch
500
750
250
500 Online Batch
750
250
500
750
250
500
750
Online Betch
Online Batch
Figure 2: Empirical evidence of ZeroSiam's stabilization effects. (a) records the Frobenius distance between 0n and the identity matrix under the non-i.idd streams with varying imbalance ratios (Niu et al., 2023). (b-d) record the ODD accuracy, logits Lg norm, and center dominance in model pre- dictions under a mild test scenario (Wang et al., 2021). Center dominance is calculated by ||u||/ /|ul|| following (Zhang et al., 2022a). Experiments are conducted on ImageNet-C (Snow, level 5) with ResNe150-GN. For fair comparisons, ZeroSiam and Tent use the same learning rate configuration.
dominance. In this section, we rethink TTA stability from shortcuts, and find that ZeroSiam not only inherits the anti-collapse effect of asymmetry, but also plays broader role in absorbing biased shortcuts and regularizing dynamics during entropy minimization. We present empirical evidence showing these stabilizing effects, and further explain ZeroSiam's 's behaviors with theoretical insights.
Rethinking TTA Stability from Shortcuts During unsupervised TTA, the model can exploit short- cuts (e.g., assigning all predictions to a dominant class) to naively reduce the objective, resulting in model collapse, as shown in Figure 2. Therefore, to improve TTA stability, we seek to identify what shortcuts are and suppress the exploitation of shorteuts during unsupervised learning. Instead of identifying shortcuts specifically for each objective, as in Figures 2 & B, our key insight is that mod- els with different sizes and architectures exploit similar shortcut patterns under the same objective. In this sense, we define shortculs in an objective as patterns learnable by an extremely simple net- work (e.g., the predictor h), which naively reduce the loss value without improving generalization.
Empirical Evidence of ZeroSiam's Stabilization Effects In Figure 2, we visualize the effects of our ZeroSiam under the unsupervised TTA. We conduct experiments with ResNe150-GN on ImageNet-C, and record the evolution of OOD accuracy, representative failure modes of entropy- based TTA, and changes in predictor parameters 0n (i.e., a simple FC layer, learning preliminarily non-generalizzalee modes due to capacity). From the results, we highlight two key observations:
Observation 1: Predictor as an Effective Absorber of Biased Shorteut Signals. Figure (a) shows that the predictor parameters 0, deviate more rapidly and substantially from the identity mapping when facing online data streams with a higher label imbalance ratio (Niu et al., 2023), which pro- duces more shortcut signals for entropy minimization that may result in collapse. In this sense, this pronounced deviation thus suggests an active absorption of biased shortcut signals within predictor h (an extremely simple network), adaptively posing stronger alignment regularization in Eqn. (4) to -ronne stabilize entropy adaptation under more collapse- prone TTA scenarios, as shown in Figure C.
Observation 2: Asymmetry Suppresses Learning Non-Generalizable Collapse Modes. In Figure (c), the logit T22 norm under Tent suffers from a rapid inflation, whereas ZeroSiam grows slowly and then stabilizes. In Figure 2 (d), Tent increasingly aligns logits toward dominant mode (higher center dominance), while our ZeroSiam suppresses such dominance over time. Consequently, Tent collapses into non-generalizable shortcuts, whereas ZeroSiam mitigates them and achieves better generalization as shown in Figure 2 (b), similarly even when no collapse occurs (see Figure B).
Overall, Figure shows that ZeroSiam absorbs and regulates non non- gengeeeallizable shortcuts during TTA beyond collapse prevention. This reveals a distinct ad advantage of ZeroSiam, and provides TTA- specific evidence on the role of asymmetry in generalization that extends prior findings from SSL..
Theoretical Insights of ZeroSiam's Mechanism We provide theoretical analysis to explain Ze- roSiam's 's behaviors, showing that (i) the predictor enhances the online branch's 's dynamism in explor- ing the parameter space, thereby facilitating more efficient entropy optimization; (ii) the alignment term explicitly regulates the biased learning signals induced by entropy minimization, preventing the model from being exposed to collapsed trivial solutions and meanwhile prompting performance.
Theorem 1. (Optimization and Stability of ZeroSiam) Consider the ZeroSiam objective L = (())) + a D(p sglp")) where H-)) denotes the entropy loss, D(-) the alignment regularizer, and pp, .p'" AlCl- are the probability distributions induced by the online and target branches.
5

---

Published as a conference paper at ICLR 2026
Given the encoder f. classifier g and predictor h. Under Assumptions I and 2. the following hold: (1) For a = 0, the entropy variation satisfies (pH()") > [AH("")), and the Hessian of H (p²)
attains its minimal eigenvalue along collapse directions
Aqain HP))) =V''H''
(2) For a > O, the predictor serves as a filtering mechanism that suppresses gradient update directions corresponding over-amplified logits, and the system converges stable equilibrium: there exists hmin > O such that
H(p") Amiin -
Remark 1. Theorem characterizes ZeroSiam's optimization dynamics and convergence behavior. Initially, the online and target branches coincide within the non-collapse region, so entropy mini- mization dominates. In this regime, the online branch exhibits a stronger tendency toward collapse than the larget branch in both magnitude and directional dominance (Conclusion (I)). As opti- mization proceeds, the alignment term D).) constrains the predictor to fitter/ssuperes the gradient components that drive of away from p", i.e., regulating the biased learning signals that may result in collapse, guiding the system toward a stable and non-collonee collassag equilibrium (Conclusion (2)). This show that the predictor in the online branch purposely converts biased signals (e.g., shortcuts) into explicit discrepancies, where these biased signals are then penalized by the alignment loss.
4 COMPARISONS WITH STATE-OF-THE-ARTS
Table Efficiency compari-
son for processing 50,000 im- ages (Gaussian noise, level ImageNet-C) via RTX 3090 GPU on ViT-Base.
Dataset and Methods For image classification, we conduct ex- periments based on ImageNet-C (Hendrycks & Dietterich, 2019), large-scaled benchmark for out-of-distribution generalization. It contains 15 types of main categories (noise, blur, weather, digital) corrupted images and each type has 5 severity levels. For natu- ral language reasoning, we assess logical reasoning capabilities on Math-500 (Lightman al., 2023), CollegeMath (Tang et al., 2024), AIME24, and Minerva (Lewkowycz et al., 2022), ranging from high-school mathematics compare with the following methods. EATA (Niu et al., 2022), SAR (Niu et al., 2023), DeYO (Lee al., 2024), and CETA (Yang al., 2024) are entropy- based methods with sample selection or up- date reweighting. COME (Zhang et al., 2025a) predefines uncertainty mass, implemented based on Yo for comparisons. TLM (Hu et al., 2025a) refines the prediction entropy on input sequences.
Method
Teut (Wang et al., 2021)
193 socs
SAR (Niu 2023)
382
2022)
secs
COMB (Zhong et al,, 2025a)
300 secs
DeYO (Loe et 2024)
280
advanced competition problems. We
ZeroSiam (ours)
secs
Models and Implementation Details We conduct experiments on ResNet50-GN, ViT-Base, ViT- Small, ConvNeXi-Tiny and Swin-Tiny that are obtained from timm (Wightman, 2019) for image classification, and Llama3. 1ettaa..-BB-iie Instrutt (Dubey et al., 2024) for natural language reasoning. We use symmetric KL as the divergence term in Eqn. (4), and a is fixed to without tuning. We update pre- dictor params 6n and the affine parameters in norm layers for the vision task per Tent (Wang al., 2021), and the LoRA (Hu et al., 2022) parameters for LLM. More details are put in Appendix C.
4.1 ROBUSTNESS TO CORRUPTION UNDER VARIOUS WILD TEST SETTINGS
In this section, we evaluate the robustness of ZeroSiam under the wild test scenarios as established by SAR (Niu et al., 2023), which simulate practical TTA scenarios in real- wolldwrldd applications, including 1) online imbalanced label distribution shifts: the samples in a non-i.i.d. data stream come in class order (in Table 3). 2) mixed distribution shifts: the samples in online data stream obtained from a mixture of 15 corruption types (a total of 15 50,000 images) in ImageNet-C, i.e., a prolonged TTA scenario with multiple concurrent shifts (in Table 2), and 3) batch size 1: the samples come one- by-one due to the scarcity of data in online streams (in Table 4). Compared to SAR, we extend the evaluations using more models, including ViT-Small, ConvNeXt-Tingg and Swin-Tiny.
From the results, we have the following general observations: 1) Sensitivity on model choice: While sample selection methods like DeYO perform competitively on ResNet50-GN and ViT- Base, they remain unstable and sensitive to model choices, particularly with weaker models where pseudo labels are highly unreliable, egg., the accuracy of 0.1% (DeYO) vs. 26.5% (ZeroSiam) on

---

Published as a conference paper at ICLR 2026
Table 3: Comparisons with SOTAs on ImageNet-C (level 5) under ONLINE LABEL SHIFTS (im- balance ratio=oo) w.r.t. Acc(%) "N/B/WD" are short for Voise/Blur/Weahhr/Diggee corruptions. RED marks results worse than NoAdapt. Detailed results of each corruption are put in Appendix.
ResNe150-GN
VrT-Base
ViT-Small
ConyNeXt:
Swin-Ting W
Method
N
B
W
D
N
B
W
D
|
B
W
D
N
W
N
Avg.
NoAdope
18.6
19.4
47.7
33.9
8.1
28.4
36.1
41.6
1,8
23,4
27.7
33.5
23.7
24.8
52.1
35.4
25.8
21.7
50,5
25.9
29.0
Tent
2.9
14.6
27.7
38.0
22.9
54.3
41.3
64.7
0.3
40.5
38.5
48.2
22.8
22.9
50.2
34.4
13.6
19.4
34,9
25.3
30.9
SAR
35.0
24.9
47.8
40.6
55.8
65.8
42.2
52.8
35,5
43.3
29.2
39.4
EATA
27.8
20.4
42.7
34,6
35.7
47.4
61.6
51.
16.3
42.2
5488
54.2
35,4
29.0
54.9
42.2
35.6
32.9
53.4
41.1
40.7
COME
18.4
19.2
47.7
33.4
49.8
59.
69.8
67.5
0.2
39.5
56.0
59.6
43.1
24.4
62.9
44.9
42.9
23.9
59.7
27.7
42.5
DeYO
43.7
56.6
69.9
36.0
36.5
22.7
52.1
ZevoSiam
43.7
412
62.1
57.3
52.8
60.1
712
69.6
26.5
50.4
62.0
60.8
43.0
40.0
62.4
53.8
45.3
42.2
59.3
53.6
52.9
Table 4: Comparisons with SOTAs on ImageNet-C (level 5) with BATCH SIZE=1 w.E.t. Acc (%).
ResNet50-GiN
ViT-Baee
ViT-Small
ConvNeXt-Ting -iny
Swin
Method
_V
5
W
D
N
5
D
N
B
D
W
N
W
Avg.
NoAdapt
18.6
1944
47.7
33.9
81
284
36.1
41.7
188
233
27.8
33.6
23.7
24.6
522
35.3
25.9
21.6
50.6
25.8
29.0
Tent
2.6
13.3
27.5
37.9
28.8
51.7
43.7
61.9
23.7
246
522
353
32.0
23.9
51.9
36.5
24.2
23.0
42.1
26.7
31.2
SAR
24.3
23.2
46.9
40.6
39.6
53.7
63.1
64.6
25.9
21.6
50.6
25.8
31.2
25.3
51.0
35.8
25.2
22.8
47.0
26.3
37.2
EATA
26.3
23.3
50.3
43.5
29.8
43.7
5233
56.4
2.2
30.7
36.9
43.6
28.0
25.1
51.
36.4
33.0
25.3
50.6
30,8
36,0
COME
47.6
55.1
69.6
41.8
62.0
39.7
58.3
DeYO
43.2
28.4
50.2
55.5
53.7
59.0
71.7
70.4
0.5
42.4
59.1
60.4
37.7
21.3
44.2
35.3
36.4
24.6
50.1
35.3
44.0
ZemSiom
42.6
40.8
62.9
58.6
52.5
59.9
70.9
69.6
27.1
50.1
61.4
60.5
42.2
39.3
61.7
52.8
44.9
41.5
58.8
52.9
52.5
noise corruptions with ViT-Small under the label shift scenario in Table 3, and SAR and COME also fail to perform TTA (worse than dopd on Swin-
Table 2: Comparisons with state-of-the-ard on ImageNet-C (level 5) under MIXTURE OF 15 CORRUPTION TYPES w.r.t. Acc (%).
Tiny under mixed shifts in Table 2; 2) Sensitivity on test scenario choice: For example, compared to re- sults in Table under label shifts, EATA'S perfor- mance drops significantly
Method
R-50
Vit-B
Vit-S
Con-T
Swi-T
Avg.
NaAdapt
30.6
29.9
22,9
34.7
31,3
29.9
Tent
7.1
27.8
14.3
Swin-Tiny under TTA with a single sample in Table 4, e.g., -...%%%%%%%% regarding the accuracy on blur corruptions. This highlights the instability in prior methods and that achieving robust TTA across diverse architectures and test scenarios remains highly non-trivial: 3) Our ZeroSiam is simple yet effective. ZeroSiam neither relies on careful sample selection strategies as in SAR or Yo, nor requires source data as in EATA, and it achieves consistently stable and high performance across models and scenarios, markedly outperforming prior methods, e.g., 52.9% (ZeroSiam) vs. 38.8% (SAR) in terms of average accuracy under label shifts in Table 3, and an average gain of +8.5% over De under the batch size of in Table 4, suggesting our effectiveness.
SAR
38.1
55.7
41.3
36.5
25,9
39.5
EATA
38.3
57.1
36.9
41.1
41.3
42.9
COME
30.0
58.5
40.9
23.7
19.1
34.4
DeYO
38.6
59.4
35.9
27.8
29.0
38.1
ZenoSiam
40.4
57.1
41.7
42.4
39.3
44.2
4.2 EFFECTIVENESS FOR INCENTIVIZING REASONING CAPABILITY ONLINE
A statistical reasoning model may fail to generalize to the diverse reasoning tasks in roal-world applications, while retraining the model offline is both expensive and time-consuning. We fur- ther explore adaptively incentivizing the reasoning capability in a large language model online, by minimizing the entropy of its own predicted tokens. From Table 5, we have the following obser- vations: 1) Entropy optimization demonstrates a great potential in enhancing the model's reasoning online. i.e., all prior methods achieve an accuracy gain by +3.34% on AIME24. 2) However, for a comprehensive benchmark like CollegeMath, covering algebra, calculus, probability, differential equations, etc, existing methods may suffer from overfitting and poor generalization, e.g., -0.83% % on Tent and -0.75% on SAR. 3) ZeroSiam enhances generalization for online reasoning incentivization with its predictor and asymmetric alignment design, which regularizes non-generalizable shortcuts as discussed in Section 3.2, yielding significant further gains, e.g., + +10.00% on AIME24, +3.40% on Math-500, and +3. 3..94% on average. This suggests the potential of our ZeroSiam to boost both the perception robustness and reasoning capability in a model during inference for greater intelligence.
4.3 ROBUSTNESS TO ADVERSARIAL. ADAPTATION SCENARIOS (STRESS TEST)
Robustness under Blind-Spot Adaptation Existing entropy- based TTA methods largely rely on reliable sample selection strategies stabilize adaptation (Niu et al., 2023; Lee et al., 2024). How-
7

---

Published as a conference paper at ICLR 2026
Table 5: Comparisons with state-of-the-arts for ONLINE ADAPTIVE REASONING in mathematical reasoning benchmarks regarding Accuracy (%).
Method
Math-500
CollegeMath
AIME24
Minerva
Average
Lluma3.1 188B (Duhey al., 2024)
49.20
25.00
3.33
20.96
24.62
* Tent (Wang ot al., 2021)
(0.00)
24.17
6.67(+3.3)
20.59(-0.37)
25. 05.36)
SAR (Nio al,, 2023)
49,20 (-.00)
(-.
6.67(+
(4.32
25.36
EATA (Niu et al., 2022)
48, -..40)
(-.1)
6.67 6.67(45.54)
20.59
25. 25.22
COME (Zhang et al., 2025a)
49,80 (00.0)
25.42(-0.12)
6.67(4
22.74(+1.78)
26. 26.16/+1.54)
TLM (Hu el., 2025a)
50.00, +0.80)
25.58
0..8)
6.67 (43.54)
19.49-11477 1.477
(...5)
ZevoStam (ours)
52.60 (3340)
26.25 1.26)
13.33 (-10,00)
22.06
28,56
Table 6: Comparisons with SOTAs on ImageNet-C (level 5)'s BLIND-SPOT SUBSET (samples ini-
tially misclassified by the NoAdapt model) with BATCH SIZE=1 regarding Accuracy (%).
ResNet50 GN
ViTe
ViT-Small
ConvNeXL Tin
Swin Tiny
Method
_x
5
W
D
N
B
D
B
D
W
N
W
Avg.
NoAdapt
18.6
19.4
47.7
33.9
8.1
28.4
36.1
41.7
1.8
23.3
27.8
33.6
23.7
24.6
522
35.3
25.9
21.6
50.6
25.8
29.0
Tent
42,9
52.0
42.8
17.9
36.3
0.2
SAR
17.9
18.4
35.6
31.6
31.1
55.0
54.0
56.4
2.0
30.4
42.0
43.3
26,4
24.6
50.7
35.1
27.0
22.2
49.3
23.8
33.8
RATA
19.5
19.0
44.2
40.2
26.3
43.5
53.
57.5
2.0
26.5
328
41.7
25.8
24.7
51.6
35.7
27.4
22.4
49.1
26.8
33.5
COME
18.6
47.6
33.8
44.8
69.7
37.0
41.4
31.1
36.1
40.5
25.3
DeYO
0.5
9.4
21.0
40.0
0,2
47.2
72.6
71.4
0.2
38.2
60.2
61.7
35,2
12.2
35.0
33,0
0.2
8.8
25.7
23.9
29.8
ZemSSam
39.9
36.6
53.9
52.7
53.0
60.4
716
70.2
26.1
49.8
61.8
61.1
43.3
40.3
61.9
55.0
46.5
42,
58.8
54.7
52.0
ever, in many real-world scenarios, adaptation inevitably involves numerous erroneous pseudo la- bels that cannot be identified, especially when the model's initial accuracy is very low. This raises critical concern: How safe is existing TTA in the real world? To stress-test this vulnerability, we construct a blind-spot subset consisting only of samples misclassified by the NoAdapt model for each domain and adapt exclusively on this subset, before evaluation on the full dataset. As shown in Table 6, prior methods suffer from severe instability, often collapse and underperform the NoAdapt baseline after TTA, e.g., Yo deteriorates accuracy on out of 20 scenarios. roSiam introduces efficient asymmetry to prevent undesired trivial solutions from optimization, delivering consistent accuracy gains even when adapting with incorrect labels e.g., the average ac- curacy of 29.0% (NoAdapt) 52.0% (ZeroSiam), drastically breaking prior performance ceiling (*33.6%). This underscores ZeroSiam as a more principled and robust solution for real-world TTA.
contrast, Ze-
Resistance to Learning from Noise In dynamic real-world ap- plications, models may frequently encounter test data that are severely corrupted and non-semantic, such as extreme occluded
70
Accuracy (%)
CITA
frames and pure sensor noise where no valid label exists. Mini- mizing entropy these data can then be misled to "confidently learn nonsense", risking model degeneration. To simulate this, we first pre-adapt models on varying amounts of pure Gaussian noise, then perform TTA on ImageNet-C (Fog, level 5) with ViT- Base under the mid scenario (Wang al., 2021). As shown in Figure 3, existing entropy-based methods degrade sharply post- adaptation to noise, e.g., 67.3% -27.227.22 2%% on CETA, indicating an overfit to non-semantic patterns. In contrast, ZeroSiam absorbs and regularizes non-genen non-generalizable shortcuts through the asymmetric alignment (c.f. Section 3.2), maintaining consistently high and stable accuracy (N= 72%) regardless of the exposure to noisy in- puts. This robustness implies that ZeroSiam can be safely deployed even when streams contain meaningless corrupted inputs, a property crucial for reliable deployment in real-world scenarios.
40
10
0
1k
2k
#Noisy Batches
Figure 3: Resistance learning
from noise. Models pre-adapt on N pure Gaussian noise, then run TTA on ImageNet-C' (level 5).
4.4 ADDITIONAL. DISCUSSIONS
Efficacy under Mild Test Setting We further evaluate ZeroSiam in the mild setting (Wang et al., 2021), where data comes with shuffled labels. As shown in Table 7, ZeroSiam delivers superior performance compared to prior method, e.g., the average accuracy of 50.1% (ZeroSiam) vs. 43.0% (COME), suggesting our efficacy across a wide range of scenarios. Moreover, as in Table 1, Ze- roSiam also achieves lower latency compared to prior ofate-of-the-arts are- e.g., 193s (ZeroSiam) 280s (De YO), highlighting the advantages of ZeroSiam regarding both TTA stability and efficiency. We also offer more results under diverse adaptation epochs over the entire test in Appendix E.7.
8

---

Published as a conference paper at ICLR 2026
Table Comparisons with sfate-of-the-arr methods on ImageNet-C (severity level 5) under MILD SCENARIO regarding Accuracy (%). "N/B/W/D" denote Noise/Blur/Weahhr/DDige
corruptions.
ReaNei50--iN
ViT-Base
ViT-Small
ConvNeXi-Tiny
Swin-
Method
B
W
D
N
B
W
D
N
B
W
P
N
8
W
D
N
B
W
D
Avg.
NuAdapi
18.6
19.4
47.7
33,9
28.4
41.6
23.4
23.7
52.1
35.4
25.8
50.5
Tont
5.5
17.7
33
39.0
29.0
51.3
44.7
62.1
0.5
37.2
414
47.2
32.1
24.0
51,9
36.6
24.2
23.1
42.6
26,9
33.5
SAR
29.9
24.6
41.2
41.
34.7
52.4
62.5
62.6
1.5
38.6
44.1
49.0
34.2
25.0
45.4
37.8
32.4
25.1
47.3
29.0
38.0
38.6
328
56.9
514
57.4
67.2
44.7
56.4
36,2
55.5
41.
37.5
56.5
COME
18.4
19.3
47.6
33.6
516
58.9
70.1
69.0
0.3
41.2
56.0
58.4
41.1
26.3
60.5
43.4
42.2
25.5
58.7
38.6
43.0
DEYO
40.8
30.4
44.0
514
53.3
55.0
71.1
69.6
0.2
44.7
57.8
59.0
37.3
22.1
44.3
36.2
36
24.6
$1.0
41.1
43.5
ZemStom
59.7
54.2
58.4
68.3
48.1
59.6
40.2
59.5
43.1
56.6
49.8
Table 8: Ablation on predic- tor design in ZeroSiam on ImageNel-C (level 5) with VīT-Base under label shifts.
Table ZeroSiam's efficacy when used with prior methods. Experiments are on ImageNet- C (level 5) under label shifts.
Table 10: Generality of ZeroSiam
across objective and divergence choices on ImageNet-C (level 5) with ViT-Base under label shifts.
Method
Predictor
Acc.
Method
VIT-B
R-50
Con-T
Avg.
Loss
N/A
sKL
KL
rKL
JS
MSE
Tent
47.3
49.4
31.6
40.7
40.6
SLR
44.0
62.2
63.2
61.0
63.4
61.5
ZeroSium
FC
64.1
ZeroSkan
57.1
48.3
41.7
49.0
CE
43.2
61.6
61.4
61.9
61.4
62.1
Expl
fxed random FC
60.7
DeYO
62.3
43.9
33.2
46.5
-p²
45.8
63.3
63.4
62.1
63.0
Exp2
FCVReLU-FC
64.0
ZeroSiam
65.0
50.7
46.1
53.9
Tent
47.3
64.1
64.0
64.1
63.8
64.1
Ablation on Predictor Design We further examine other predictor designs in Table 8. Interestingly,
replacing the learnable predictor with fixed, randomly initialized predictor (0, = I 0.1 W.
W ~ (O, already improves upon Tent, i.e., 47.3%- w.r.t. accuracy, confirming the value of breaking symmetry alone in collapse mitigation. However, making the predictor deeper and nonlinear brings no further gain (64.0% vs. 64.1%), since the predictor in ZeroSiam is to absorb biased shorteuts for regularization rather than learning rich representations, which do not need large representation capacity. Therefore, we use the single linear predictor for all other experiments.
Integration with Prior Methods with state-of-the-art methods. From Table 9, ZeroSiam consistently enhances the performance of prior methods, e.g., improving the average accuracy by +8.4% on EATA and +7.4% on DeYO, suggesting the efficacy of our asymmetric architecture as a plug-and-play component. However, incorporating with EATA and DeYO does not ensure an improvement over ZeroSiam. This is be- cause while EATA and Yo aim to filter partial noisy samples, ZeroSiam adapts reliably even with incorrect pseudo labels, as verified in Table 6. Thus, ZeroSiam may not directly benefit from the traditional sample selection design and encourages more exploration. We leave it for future work.
We further evaluate the efficacy of our ZeroSiam when integrated
Sensitivity to Learning Rates We further examine the sensi- tivity of ZeroSiam to learning rates. When the predictor learn- ing rate is set to zero, the predictor becomes a frozen identity and ZeroSiam degenerates to Tent. From Figure 4, have the following observations: 1) our ZeroSiam consistently out- performs Tent across wide range of encoder learning rates, Le., by 11. 11.3%-288 28.2% in accuracy, suggesting the benefit of our asymmetric design. 2) For a fixed encoder learning rate,
Encoder LR fr [x0.0 (.001)
10
7.5 38.1
38.4
63.9
64.1
64.1 64.0 63.6
2.5 39.8
62.8
62.9
62.8 62.6 62.3
1 47.3
59.9 59.7 59.3 59.0 58.6
2.5
7.5 10
varying E (1, 5, 7.5, 10} x 0.001 changes accuracy by only 1%. highlighting our effectiveness does not rely on careful hyperparameter tuning. 3) overall, ZeroSiam achieves both high accuracy and a broad performance plateau under diverse learning rate configurations, e.g., above 62.3% when My E [2.5, 10) x10 100 and 7/,, E [1, 10) 10]xx0 1003 3 consistently out- performing the accuracy of 58.0% in SAR. These results suggest that ZeroSiam is not only effective but also robust to learning rate choices, making it practical and easy to use for online deployment. We also provide more sensitivity analysis of learning rates Swin-Tiny and further introduce data-free approach for determining predictor learning rate Th in Appendix E.5 and E.6, respectively.
Predictor LR nr (x0.001)
Figure 4: Sensitivity to learning rates, Results are reported on Im- ageNet-C: (level 5) with ViT-Base under label shifts w.r.t. Accuracy.
Sensitivity of in ZeroSiam To avoid heavy tuning in practical TTA cases, we consistently set a 1.0 in ZeroSiam. From the perspective of learning objective, a = 1.0 strikes a bal- anced and interpretable interaction between the two objectives: 1) comparable gradient scales:
9

---

Published as a conference paper at ICLR 2026
both entropy loss and the divergence loss operate in probability space and are also per-sample normalized, which yield comparable gradient scales for TTA, without any one dominating opti- mization; 2) simplified and interpretable formulations: consider Eqn. (4) with = 1.0 detailed as Dx [g([r"]lpp") By expanding the terms, we derive an overall formu- lation of -p" log #g [p]] sg [p]] log p", which expands to a symmetric cross-entropy between online 17n
(()²) + DxL (p" (p"][sggr [[sg[ls)))
and target branches. This symmetry encourages the two branches to exchange reliable signals while preventing either from drifting too far-an effect we find important for stable adaptation.
Table 11: Sensitivity of a in ZeroSiam. We report Accuracy (%) on ImageNet-C across severities with ViT-Base under ONLINE IMBALANCED LABEL SHIFTS, where the imbalance ratio is co.
Method
No adapt
Tent
0.5
a
1.0
1.5
2.0
2.5
Severity Level=1
67.9
76.8
78.8
78.9
78.6
78.0
77.0
Severity Level=3
53.8
69.5
73.9
74.1
73.8
73.2
71.8
Severity Level=5
29.9
47.3
63.9
64.1
63.9
63.3
62.4
provide sensitivity analysis of under different domain shift severities, As shown in Table 11, by aligning the gradient scale of both terms, ZeroSiam achieves consistently the best results with across severities of domain shift, outperforming Tent's accuracy by 4.6% (at level 3) and 16.8% (at level 5). Extensive results across various test scenarios (Tables 3-7) also validate the efficacy of this setup, making it a reasonable default to avoid careful hyperparameter tuning in TTA.
Generality of ZeroSiam's architecture ZeroSiam introduces a general asymmetric architecture without limiting the use of self-training objectives² and divergence terms. As shown in Table 10, ZeroSiam remains effective across a wide range of combinations and consistently outperforms the single-branch baselines, e.g., 44.0% (SLR) vs. 63.2% (SLR+KL). This arises because collapsed solutions and non- -engrenarllizable shorteuts remain pervasive across many unsupervised objectives, suggesting a promising direction for extending ZeroSiam to wider range of tasks in the future. For entropy minimization, we use symmetric KL as the divergence with a I as discussed in Table 11.
5 CONCLUSION
In this paper, we explore asymmetry as a new principled test-time entropy minimization mechanism that improves learning stability by inherently avoiding collapsed trivial solutions. To this end, we devise a lightweight Siamese architecture for asymmetric entropy minimization (termed ZeroSiam) to prevent the model from being exposed to collapsed solutions, using an injected learnable predictor. The predictor converts collapsed solutions into explicit discrepancies, which are then eliminated by an alignment term. We empirically and theoretically demonstrate that ZeroSiam not only prevents collapse but also absorbs and regularizes biased shortcut signals during learning, thereby boosting the performance even when collapse does not occur. Extensive experiments verify that ZeroSiam performs more stably over prior methods with negligible overhead, proving effective in both vision adaptation and LLM reasoning tasks across challenging models and test scenarios.
ACKNOWLEDGMENT
This research was supported, in part, by the Joint WeBank-NTU Research Institute on Fintech, Nanyang Technological University, Singapore, and Ministry of Education, Singapore, under its Aca- demic Research Fund Tier
ETHICS STATEMENT
This research focuses on improving the stability of test-time entropy minimization through an asym- metric Siamese architecture, to advance robustness and reliability in vision and language models for academic and socially beneficial purposes. The proposed approach is evaluated solely on widely used, publicly available models and benchmark datasets under their respective licenses. The study
Pn Table 10, SL. denotes the soft likelihood ratio (Marsden et al., 2024), CF denotes cross-entropy loss with its own predicted lahels, and -p² denotes the negative squared-probability loss, Le., En pk-
10

---

Published as a conference paper at ICLR 2026
does not involve human subjects sensitive personal data, and thus does not raise privacy, fairesss, or discrimination concerns. No conflicts interest or external sponsorship influence this work, and all experiments were conducted in accordance with established standards of research integrity.
REPRODUCIBILITY STATEMENT
In this work, we implement methods (all compared methods and our ZeroSiam) with differ- ent models (ResNe150-GN) ViT-Base, ViT-Small, ConvNeXt-Tiny, Swin-Tiny. and Llama3. 1-88B- Instruct) on the ImageNet-C, Math-500, College-Math, AIME-24, and Minerva datasets. Reproduc- ing all the results in our paper depends the following three aspects:
1. DATASETS. The first paragraph of Section 4 and Appendix C.1 provide the details of the adopted datasets and the download URLs.
MODELS. All adopted models (with the pre-trained weights) for test-time adaptation are publicly available. Specifically, all vision models: {ResNet50-GN, ViT-Base, ViT-Small, ConvNeXt- Tiny, Swin-Tiny) are from timm repository (Wightman, 2019), and I-ama3.1-8B-Instuuu from its official repository. Appendix C.2 provides the download URLs of them.
3. PROTOCOLS OF EACH METHOD. The second paragraph of Section and Appendix C.2 pro- vides the implementation details of all compared methods and our ZeroSiam. We reproduce all compared methods based the code from their official GitHub, for which the download ur is provided (in Appendix C.2) following each method introduction.
REFERENCES
Zafarali Ahmed, Nicolas Le Roux, Mohammad Norouzi, and Dale Schuurmans. Understanding the impact of entropy on policy optimization. In International conference on machine learning, pp- 151-160. PMLR, 2019.
Adrien Bardes, Jean Ponce, and Yann LeCun. Vicreg: Sirtanceiivvarince--oooo for sule-supe learning. In International Conference on Learning Representations, 2022.
regularization
Alexander Bartler, Andre Bühler, Felix Wiewel, Mario Döbler, and Bin Yang. Mt3: Meta time training for sulf-super test-time adaption. In International Conference on Artificial Intelligence and Statistics, pp. 3080-3090. PMLR, 2022.
Guohao Chen, Shuaicheng Niu, Deyu Chen, Shuhai Zhang, Changsheng Li, Yuanqing Li, and Mingkui Tan. Cross-device collaborative test-time adaptation. In Advances Neural Information Processing Systems, volume 37, pp. 122917-122951, 2024.
Ting Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton. A simple framework for contrastive learning of visual representations. In International Conference on Machine Learning, pp. 1597-1607, 2020.
Xinlei Chen and Kaiming He. Exploring simple siamese representation learning. In IEEE Confer- ence on Computer Vision and Pattern Recognition, pp. 15750-15758, 2021.
MAA Codeforces. American invitational mathematics examination-aine 2024.
Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hierarchical image database. In IEEE Conference on Computer Vision and Pattern Recognition, pp. 248-255,100 2009.
Abhimanyu Dubey, Abhinav Jauhri, Abhinav Pandey, Abhishek Kadian, Ahmad Al-Dahle, Aiesha Letman, Akhil Mathur, Alan Schelten, Amy Yang. Angela Fan, al. The llama 3 herd of models. arXiv e-prints, pp. arXiv-2407, 2024.
Yossi Gandelsman, Yu Sun, Xinlei Chen, and Alexei Efros. Test-time training with masked autoen- coders. In Advances in Neural Information Processing Systems, volume 35, pp. 29355, 2022.
11

---

Published as a conference paper at ICLR 2026
Yves Grandvalet and Yoshua Bengio. Semi-supervised learning by entropy minimization. In Ad- vances Neural Information Processing Systems, volume 17, 2004.
Bean-Bastien Grill, Florian Strub, Florent Altché, Corentin Tallec, Pierre Richemond, Elena Buchatskaya, Carl Doersch, Bernardo Avila Pires, Zhaohan Guo, Mohammad Gheshlaghi Azar, et al. Bootstrap your own latent-a new approach to self-supervised learning. In Advances in neural information processing systems, volume 33, pp. 21271-21284, 2020.
Tuomas Haarnoja, Aurick Zhou, Pieter Abbeel, and Sergey Levine. Soft actor-critic: Off-policy
maximum entropy deep reinforcement learning with a stochastic actor. In International Confer- ence on Machine Learning, pp. 1861-1870. Pmlr, 2018.
Jisu Han, Jaemin Na, and Wonjun Hwang. Ranked entropy minimization for continual test-time adaptation. arXiv preprint arXiv:2505.. 16441, 2025.
Kaiming He, Haoqi Fan, Yuxin Wu, Saining Xie, and Ross Girshick. Momentum contrast for unsupervised visual representation learning. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 9729-9723 2020.
Dan Hendryeks and Thomas Dietterich. Benchmarking neural network robustness to common cor- ruptions and perturbations. In International Conference on Learning Representations, pp. 1-11, 2019.
Dan Hendrycks, Collin Burns, Saurav Kadavath, Akul Arora, Steven Basart, Eric Tang, Dawn Song, and Jacob Steinhardt. Measuring mathematical problem solving with the math dataset. In Thirty-fifth Conference Neural Information Processing Systems Datasets and Benchmarks Track (Round 2), 2021.
Edward J Hu, Phillip Wallis, Zeyuan Allen-Zhu, Yuanzhi Li, Shean Wang, Lu Wang, Weizhu Chen, et al. Lora: Low-rank adaptation of large language models. In International Conference on Learning Representations, 2022.
Jinwu Hu, Zitian Zhang, Guohao Chen, Xutao Wen, Chao Shuai, Wei Luo, Bin Xiao, Yuanqing Li, and Mingkui Tan. Test-time learning for large language models. In International Conference on Machine Learning. PMLR, 2025a.
Zixuan Hu, Yichun Hu, Xiaotong Li, Shixiang Tang, and Lingyu Duan. Beyond entropy: Region confidence proxy for wild test-time adaptation. In International Conference on Machine Learning, 2025b.
Hyosoon Jang, Yunhui Jang, Sungjae Lee, Jungseul Ok, and Sungsoo Ahn. Self-training large language models with confident reasoning. arXiv preprint arXiv:2505. 17454, 2025.
Jing Jiang and ChengXiang Zhai. Instance weighting for domain adaptation in nlp. Annual Meeting of the Association for Computational Linguistics, 2007.
Chi Jin, Rong Ge, Praneeth Netrapalli, Sham M Kakade, and Michael Jordan. How to escape saddle points efficiently. In International conference on machine learning, pp. 1724-1732. PMLR, 2017.
Byungjai Kim, Chanho Ahn, Wissam J Baddar, Kikyung Kim, Huijin Lee, Saehyun Ahn, Seungju Han, Sungjoo Suh, and Eunho Yang. Test-time ensemble via linear mode connectivity: A path to better adaptation. In The Thirteenth International Conference Learning Representations, 2025.
Dong-Hyun Lee al. Pseudo-label: The simple and efficient semi-supervised learning method for deep neural networks. In Workshop on challenges in representation learning. ICML, 2013.
Jonghyun Lee, Dahuin Jung, Saehyung Lee, Junsung Park, Juhyeon Shin, Uiwon Hwang, and Sun- groh Yoon. Entropy not enough for test-time adaptation: From the perspective of disentangled factors. In International Conference on Learning Representations, 2024.
Aitor Lewkowycz, Anders Andreassen, David Dohan, Ethan Dyer, Henryk Michalewski, Vinay Ramasesh, Ambrose Slone, Cem Anil, Imanol Schlag, Theo Gutman-Soo Solo, et al. Solving quanti- tative reasoning problems with language models. In Advances in Neural Information Processing 2022.
Systems, volume 35, pp.
12

---

Published as a conference paper at ICLR 2026
Jian Liang, Ran He, and Tieniu Tan. A comprehensive survey test-time adaptation under distri- bution shifts. International Journal of Computer Vision, 133(1):31-64, 2025.
Hunter Lightman, Vineet Kosaraju, Yuri Burda, Harrison Edwards, Bowen Baker, Teddy Lee, Jan Leike, John Schulman, Ilya Sutskever, and Karl Cobbe. Let's verify step by step. In The Twelfth International Conference Learning Representations, 2023.
Yuejiang Liu, Parth Kothari, Bastien Delft, Baptiste Bellot-Gurlet, Taylor Mordan, and Alexan- dre Alahi. Tu++: When does self-supervised test-time training fail or thrive? In Advances in Neural Information Processing Systems, volume 34, pp. 21808-21820, 2021.
Mingsheng Long, Han Zhu, Jianmin Wang, and Michael I Jordan. Unsupervised domain adap- tation with residual transfer networks. In Advances in Neural Information Processing Systems, volume 29, 2016.
Robert A Marsden, Mario Döbler, and Bin Yang. Universal test-time adaptation through weight ensembling, diversity weighting, and prior correction. In Winter Conference on Applications of Computer Vision, pp. 3565- 2024.
Volodymyr Mnih, Koray Kavukcuoglu, David Silver, Andrei A Rusu, Joel Veness, Mare G Belle- mare, Alex Graves, Martin Riedmiller, Andreas K Fidjeland, Georg Ostrovski, et al. Human-level control through deep reinforcement learning. nature, 51 518(7540):529-333 2015.
Volodymyr Mnih, Adria Puigdomenech Badia, Mehdi Mirza, Alex Graves, Timothy Lillicrap, Tim Harley, David Silver, and Koray Kavukcuogiu. Asynchronous methods for deep reinforcement learning. International conference on machine learning, pp. 1928-1937. PmLR, 2016.
Pietro Morerio, Jacopo Cavazza, and Vittorio Murino. Minimal-entropy correlation alignment for unsupervised deep domain adaptation. arXiv preprint arXi:: 2017.
Michal Nauman, Mateusz Ostaszewski, Krzysztof Jankowski, Piotr Mitos, and Marek Cygan. Big- ger, regularized, optimistic: scaling for compute and sample efficient continuous control. Ad- vances in neural information processing systems, 37:1 1038-113071, 2024.
Shuaicheng Niu, Jiaxiang Wu, Yifan Zhang, Yaofo Chen, Shijian Zheng, Peilin Zhao, and Mingkui Tan. Efficient test-time model adaptation without forgetting. International Conference on Machine Learning, pp. 16888-16905. PMLR, 2022.
Shuaicheng Niu, Jiaxiang Wu, Yifan Zhang, Zhiquan Wen, Yaofo Chen, Peilin Zhao, and Mingkui Tan. Towards stable test-time adaptation in dynamic wild world. In Internetional Conference on Learning Representations, pp. 1-14, 2023.
Shuaicheng Niu, Chunyan Miao, Guohao Chen, Pengcheng Wu, and Peilin Zhao. Test-time model adaptation with only forward passes. In International Conference Machine Learning, 2024.
Shuaicheng Niu, Guohao Chen, Peilin Zhao, Tianyi Wang, Pengcheng Wu, and Zhiqi Shen. Self- bootstrapping for versatile test-time adaptation. In International Conference on Machine Learn- ing, 2025.
Aaron van den Oord, Yazhe Li, and Oriol Vinyals. Representation learning with contrastive predic- tive coding. arXiv preprint arxiv: 2018
Mehdi Sajjadi, Mehran Javanmardi, and Tolga Tasdizen. Regularization with stochastic transfor- mations and perturbations for deep semi-supervised learning. In Advances in Neural Information Processing Systems, volume 29, 2016.
Nikunj Saunshi, Orestis Plevrakis, Sanjeev Arora, Mikhail Khodak, and Hrishikesh Khandeparkar. A theoretical analysis of contrastive unsupervised representation learning. International con- ference on machine learning, pp. 5628-5637. PMLR, 2019.
John Schulman, Sergey Levine, Pieter Abbeel, Michael Jordan, and Philipp Moritz. Trust region policy optimization. In International conference on machine learning. pp. 1899-1897. PMLR, 2015.
13

---

Published as a conference paper at ICLR 2026
John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov. Proximal policy optimization algorithms. arXiv preprint arXiv:1707.06347, 2017.
Max Schwarzer, Johan Samir Obando Ceron, Aaron Courville, Mare G Bellemare, Rishabh Agar- wal, and Pablo Samuel Castro. Bigger, better, faster: Human-level atari with human-level effi- ciency. In International Conference on Machine Learning, pp. 30365-30380. PMLR, 2023.
Yu Sun, Xiaolong Wang, Zhuang Liu, John Miller, Alexei Efros, and Moritz Hardt. Test-time train- ing with self-suuervision for generalization under distribution shifts. In International Conference on Machine Learning, pp. 9229-9248 2020.
Zhengyang Tang, Xingxing Zhang, Benyou Wang, and Furu Wei. Mathscale: Scaling instruction tuning for mathematical reasoning. In Forty-first International Conference on Machine Learning, 2024.
Dequan Wang, Evan Shelhamer, Shaoteng Liu, Bruno Olshausen, and Trevor Darrell. Tent: Fully test-time adaptation by entropy minimization. In International Conference on Learning Repre- sentations, pp. 1-12, 2021.
Ross Wightman. Pytorch image models.
pytorch- wwwaaa-amoeeeee 2019.
Shoukai Xu, Mingkui Tan, Liu Liu, Zhong Zhang, Peilin Zhao, et al. Test-time adapted reinforce- ment learning with action entropy regularization. In International Conference on Machine Learn- ing, 2025.
Hao Yang, Min Wang, Jinshen Jiang, and Yun Zhou Towards test time adaptation via calibrated entropy minimization. In Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pp. 3736-3746, 2024.
Jure Zbontar, Jing, Ishan Misra, Yann LeCun, and Stéphane Deny. Barlow twins: Self-supervised learning via redundancy reduction. In International conference machine learning, pp. 12310- 12320. PMLR, 2021.
Chaoning Zhang, Kang Zhang, Chenshuang Zhang, Trung X Pham, Chang D Yoo, and In So Kweon. How does simsiam avoid collapse without negative samples? unified understanding with self- supervised contrastive learning. In International Conference on Learning Representations, 2022a.
Marvin Mengxin Zhang, Sergey Levine, and Chelsea Finn. Memo: Test time robustness via adapta- tion and augmentation. In Advances in Neural Information Processing Systems, pp. 38629-38642,
2022b.
Qingyang Zhang, Yatao Bian, Xinke Kong, Peilin Zhao and Changqing Zhang. Come: Test-time adaption by conservatively minimizing entropy. In International Conference on Learning Repre- sentations, 2025a.
Yunbei Zhang. Akshay Mchra, and Jihun Hamm. Ot-vp: Optimal transport-guided visual prompting for test-time adaptation. In /EEE/CVF Winter Conference on Applications of Computer Vision, pp. 1122-1132. IEEE, 2025b.
Yunbei Zhang, Akshay Mehra, Shuaicheng Niu, and Jihun Hamm. Dpcore: Dynamic prompt coreset for continual test-time adaptation. In International Conference on Machine Learning, 2025c.
Brian D Ziebart, Andrew L. Maas, J Andrew Bagnell, Anind K Dey, al. Maximum entropy inverse reinforcement learning. In AAAI Conference on Artificial Intelligence, volume 8, pp. 1433-1438. Chicago, IL, USA, 2008
Yuxin Zuo Kaiyan Zhang, Li Sheng, Shang Qu, Ganqu Cui, Xuekai Zhu, Haozhan Li, Yuchen Zhang, Xinwei Long, Ermo Hua, et al. Ttrl: Test-time reinforcement learning. arXiv preprint ar0iv:2504. 16084, 2025.
14

---

Published as a conference paper at ICLR 2026
APPENDIX
CONTENTS
Related Work
16
B Theoretical Analysis
17
B.1 Assumptions
17
B.2 Proof of Lemma 1
17
B.3 Proof of Lemma 2
18
B.4 Proof of Theorem
19
More Implementation Details
22
C.1 More Details on Dataset
22
C.2 More Experimental Protocols on Methods
22
D More experimental results
25
D.I Detailed and Additional Results under Wild Test Scenarios
25
D.2 Detailed Results for TTA the Blind-Spot Subset
25
D.3 Detailed Results under the Mild Test Scenario
25
Additional Discussions
28
ZeroSiam's Efficacy beyond Collapse Prevention
28
E.2 Evolutions of Divergence Loss in ZeroSiam
28
E.3 ZeroSiam for Saving a Collapsed Model
29
E.4 Comparisons between the Entropy and Divergence Term during TTA
29
E.5 More Sensitivity Analysis of Learning Rates in ZeroSiam
30
E.6 Discussions Data-Free Approach for Selecting и/a in ZeroSiam ................................
30
Efficacy of ZeroSiam across Diverse Adaptation Epochs
E.8 Necessity Stop-gradient for Asymmetry
E.9 Statistical comparison
31
E.10 10 More Discussions on the Impacts of Uncontrolled Logit Norm Inflation
31
E.11 More Discussions with Multi-Branch Adaptation Methods
32
F More Discussions with Reinforcement Learning
33
G Large Language Model Usage Statement
33
15

---

Published as a conference paper at ICLR 2026
A
RELATED WORK
In this section, we connect test-time entropy minimization and self-supervvsed learning through their shared challenge of collapse, and relate our approach to these areas.
Test-Time Entropy minimization seeks to promote confident predictions by minimizing the pre- diction entropy on test data. Tent (Wang et al., 2021) first exploits this scheme for test-time model adaptation to novel and out-of-distribution environments. Unlike time training approaches (Sun al.. 2020; Liu et al., 2021; Bartler et al., 2022: Gandelsman et al., 2022), which train an extra auxiliary self-supervised branch to produce learning signals from test data, test-time entropy mini- mization (Wang et al., 2021; Niu al., 2022; Marsden et al., 2024; Lee al., 2024; Zhang et al., 2025a; Hu et al., 2025b; Zhang et al., 2025b) removes reliance on the source training process and adapts an arbitrary model on-the-fly by using its own predicted labels for self-training, rendering it practical in real-world applications (Niu et al., 2024; Liang et al., 2025). Recently, test-time en- tropy optimization has attracted growing interest in various fields, such as incentivizing knowledge in large language models during inference (Jang et al., 2025; Zuo et al., 2025; Hu et al., 2025a), and adapting a fixed policy network to evolving environments real-time (Xu et al., 2025).
Nevertheless, as highlighted by Niu al. (2023), entropy minimization is inherently unstable and prone to collapse, e.g., converging towards constant one-hot outputs that trivially minimize the entropy loss without meaningful predictions. To improve stability, subsequent methods explored strategies such as sample filtering (Niu et al., 2023; Lee et al., 2024; Hu et al., 2025a), uncertainty quantification (Zhang et al., 2025a), and parameter selection (Chen al., 2024; Marsden al., 2024; Zhang et al., 2025c). Despite these advances, collapsed constant solutions remain valid optima in prior methods, so stability often hinges on heuristics, thresholds, or extra compute, leaving methods sensitive to architectures and domains, where robust architectural design is largely underexplored. Our ZeroSiam fills this gap by introducing asymmetry that rules out trivial minima in test-time en- tropy minimization, while remaining efficient by avoiding augmentations and extra encoder passes.
Self-supervised Learning aims to learn discriminative and consistent representations by creating pretext tasks such as contrastive learning (Oord et al., 2018; Saunshi et al., 2019; He et al., 2020; Chen et al., 2020). A central challenge in SSL is trivial collapse, where all outputs degenerate to a constant maximize representation similarity. Contrastive methods such as SimCLR (Chen et al., 2020) and MoCo (He et al., 2020) prevent collapse by pushing apart negative pairs, but rely on large batch sizes, memory banks, or careful negative mining strategies. To remove dependency on negative samples, BYOL (Grill et al., 2020) and SimSiam (Chen & He, 2021) introduce asymmetric architectures, preventing collapse with predictor-stop-grunne
asymmetry break the stability of the collapsed constant solution. Although subsequent methods such as Barlow Twins (Zbontar al., 2021) and VicReg (Bardes et al., 2022) achieve stability without commetry--reakkine maximizing feature diversity within a batch, they implicitly assume large batches and i.i.d. streams, which often fail during testing. Inspired by Simsiam, we revisit asymmetry in the context of single- branch, entropy-based based TTA, and show how it can be instantiated in a minimal and efficient manner.
design by
16

---

Published as a conference paper at ICLR 2026
B THEORETICAL ANALYSIS
Notations. Let L = H(p)) + a D(p") sg[p"]) be the optimization objective of ZeroSiam, where (()) is the entropy loss, (.)) the alignment regularizer, and p",p" p" E A are the probabil- ity distributions induced by the online and target branches. Let the encoder and classifier g be pretrained, and a lightweight linear predictor. At initialization, we set as the identity map- ping so that the online and target branches coincide and both lie in the non-collapse region {p | min, Pe 2 0}.
B. ASSUMPTIONS
Assumption 1. (Lipschitz continuity of the encoder) Let f(; (:;0g) ) be an encoder parameterized by f.. We assume f Lipschitz continuous with respect to its parameters. Specifically, there exists constant Ly > 0 such that for any 01, O2 and any input in the domain,
[a, (x) (x) S Ly][0, - 02l1-
Assumption bounds the sensitivity of the encoder f to parameter perturbations, thereby ensuring stability for subsequent optimization analysis, and is commonly employed in prior theoretical studies on representation learning and model convergence.
Assumption 2. (Standard optimization assumptions) Let L(-) denote the objective function, & (On. 0y) the set of optimization parameters, and Th. the learning rates for the predictor and encoder, rexpectively. Our analysis relies on the following standard assumptions, which are common in the optimization literature:
(1) Smoothness: p-smooth. Specifically, there exists > such that for all Φ1 22.
[VoC(ó1) voL(d2))l S pll@1 Φ2l1;
(2) Descent condition: The learning rates satisfy max(1). 71) } ensuring monotonic descent.
Assumption 2 constrains the appropriate range of learning rates to guarantee monotonic descent of (()), which a common assumption in optimization research.
B.2 PROOF LEMMA
Lemma 1. (Gradient dominance in entropy descent) Let H(-) denote the entropy function, g(:30g) h(:;; and f(=;0)) denote the classifier, the predictor and the encoder, & = (0 (0ns0 0,) the of optimization parameters, and Th, 7f the learning rates for the predictor and encoder, respectively. Then the discrete change in entropy of the target branch satisfies:
IV a H ((p LH l1gl12 Ly max (Th. my)
(p (t) H(p
where LH Ls are the Lipschitz constants of (-) and f. llgll2 denotes the spectral norm of the classifier weight vector, and t is the optimization iteration step.
Proof. Consider the online and target branches:
pp (oftmax(((MM//xxx)))))))) p softmax(g(f(xx) (x); 0,))
(online branch),
(target branch).
By design, the encoder f of the target branch is synchronized with the online branch after each update:
(1++1) + 0 1) (1) ns H()()))
Thus, we bound the entropy change of the target branch ( (t + 1)) Hp)((()) by tracing the propagation of parameter updates through the online branch.
According to the Assumption the encoder f is L, Lipschitz continuous w.r.t. 0,. we have
|z( + 1) 2(1)]l2 (x; 0, 1)) f(x; ()())) s (
0g (5)
17

---

Published as a conference paper at ICLR 2026
where f(x:8y)) is the output feature of the encoder.
Note that in the non-collapse region {p A -1 mine Pe à 0}, the entropy function (() Lipschitz continuous with constant Lи v CT log 1). thus:
is
Hp(t + 1)) - H (p(t)) < LH + 1) - -p((t)l2-
(6)
Since the pre-trained classifier g fixed, and the softmax function is 1-Lipschitz, combining Eqn. (5) and Eqn. (6), we have the following chain:
[H(p' 1)) (t))
s Lulpp"(t p²())
s L (t (t)ll2 [n +1 (())
Lu L o H(P())))
where liglle is the spectral norm of the classifier weight vector.
Let á (0,, 0y) denote the set of optimization parameters, and The 7y the learning rates for the predictor and encoder. Since:
T S max(m), m5))
V H(v V. (p (t)) = =IV
VV, (()
<
we obtain:
| H()(((()))l 2
HHy' (t+ (D)
Lu ||gl|2 Ly max myh
B.3
PROOF OF LEMMA 2
Lemma 2. (Collapse Direction with Maximal Negative Curvature) Let H() denote the entropy
function, g(h(f(x: 8y); 0g) the uncertainty logits, and softmax( u) the induced proba- bility distribution. For any class E C, there exists direction (Vh, vz) didi such that: (1) Pe increases monotonically along v; (2) As Pe 1, it holds that V Hv Amin I))
(3) For any w w.v, we have v V Hv S W 2
Proof. (1) Let z f(x;0 0F) Rd be the encoder output, u ((hhz;0));:0 E R CI the uncertainty logits, and W, P the weight vector of g, h, respectively. Define v = (Vh, vy) such that:
Vv. W.T. vy Ve, TrTz): 2):
T
where r is feature direction satisfying r + 0 and > 0. V, is the direction in normalization layer parameters that amplifies the feature component along
This joint direction v = (Vh. vÿ) induces change in logits:
Au Wvv.)z+ WP 2vy) = a(r z) ZWW + WPr.
By choosing TT 0 and sufficiently large a, ensure:
Aw]e > O, [Au], = O(1) for j #
Thus, moving along increases ue- and hence Pe softmax(u.). monotonically.
(2) The Hessian of entropy H(-) w.r.t. logits u is:
H2H
V H| = Ou,Uuj
= p. (5(5 - P)) - log 1).
18

---

Published as a conference paper at ICLR 2026
As Pe 1, let = 1 - Pe - 0*, and for Pj = |et- for j Then in the Hessian matrix
8 H
Pe (1 Pe) log Pc - 1),
Diagonal for e,
0u
8 H
Py P2) 1o 1),
Diagonal for * c,
0u
8
-PPPj - log log - 1): Off-diagonal,
On;
obtain the following approximation:
ef H Due 0² Su
(1 p))((H H p 1) aajllog [C]-1 1) -4
( log Cl-1 log लল- 1) 1
[C| log C|-1 >
[c|-1
H
R P.Pp (- logP;) > 0.
That is, as Pe + 1, we have
V Hv Amin (2
(3) The parameter space Hessian quadratic form along v is:
VVv VV Σ
OH ou:
V Vgu.v u.V.
v
As pe 1, V.H + 0, so the higher-order terms vanishes. Since Au
By az
x eo. we have:
0 H du?
v
V e VH
0.
For any w w.v,, Auw =
th 56
w not parallel to Ec. S0:
w HW V
B.4 PROOF OF THEOREM 1
Theorem (Optimization and Stability of ZeroSiam) Consider the ZeroSiam objective L. (p") + ou Dpp ||sg]p"]) where H-)) denotes the entropy loss, D(-) the alignment regularizer, and Ale are the probability distributions induced by the online and target branches. Given the encoder f. classifier g and predictor h. Under Assumptions and 2, the following hold: (1) For a 0, the entropy variation satisfies |AH(P") > (H(("")) }, and the Hessian of H
E p",p"
attains minimal eigenvalue along collapse directions V:
Amain (V2))))) +V
(2) For a: > O, the predictor serves as filtering mechanism that suppresses gradient update directions corresponding over-amplified logits, and the system converges a stable equilibrium: there exists hminn > O such that
H(p") Amin, p" p".
Proof. (1) By Lemma 1, the target branch entropy variation is determined by the gradient of the online branch:
1
VoH L Mmax
HH
(F(F(()))
where L = Lu Belllllz,, and Thaax = max(1h. Ty))
Under the Assumption 2 that L = H.)) is pssmoothness and 1/max < J. the descent lemma gives:
H(p 1)) < (t) V.H D. Dr, V.H.
where D, diag(n; 7hh Iá, So have:
AH (1 + 1)) H()((()) > Mmin || Ho Mmin min(m,, m1))
(8)
19

---

Published as a conference paper at ICLR 2026
Combining Eqn. (7) and Eqn. (8), we obtain:
Mmin V 11
7min
VoHl
AH*
L Tmaa
mmax
L
Since L, | and bounded in non-collapse regions, achieving
AH
requires:
AH
Mmii
L
7max
I &
In practice, Th k By with 1: > 1, there always exists k such that
|AH())) > (AH(')))
We further construct the direction v - (Vn, vy) Rdii(()) according to Lemma 2, the correspond- ing directional derivative is given by:
D.H = H.
where u is the uncertainty logits. And the second-order directional derivative is:
=
V V
Amin < 0.
This implies that along v, the loss decreases fastest at second order (Jin et al., 2017).
Moreover, by Lemma 2, Pc. increases monotonically along thus V.H]e. P.(H - log 1)
increases synchronously, creating a self-reinforcing feedback loop that accelerates collapse.
(2) Consider the optimization objective:
- H(D)) + a Dip || sg(p"]).
where Txp sgg["")
Dru(p" |sglp")) + DkL(sg(p") || p²) are symmetric KI. loss.
Under the stop-gres nop-gradient setting on the target branch, the gradient of the shared encoder f is solely determined by the online branch. We have:
Du
V.C
VoL P H(,') + 20r(p - -p")}, Oz
where f(x;0,) 0y) is the encoder output, W. P the weight vector of the classifier g and the predictor h, respectively. Consider parameter update unit direction Vh. l|val12 = 1, then:
>= >= vh TvC = vn T( Ou ( V P V. n- H(') + 2a(p" - p²)]
< V.C,
Oz
During the minimization of L. the predictor encourages the update direction that ensuring
- p",
and suppresses gradient update directions corresponding to wer-ammlified logits.
We further analyze the convergence properties of the optimization system.
By the definition of entropy and KL divergence, we have:
cl
1(p²)
Σ
Pe log Σ pe log DKL((")lp")
Applying Gibbs' inequality,
|cl [ Pe log : 2 H()"), we obtain:
H(p") H(p") DKL (p"llp").
Since DsKL, Dp<i(pp01p>> 2 (rt(0")lp") follows that: H(p²) > H(p") DsKL. (oxu.(p11)) (p"1)p")-
20

---

Published as a conference paper at ICLR 2026
When the target branch is still in the non-collapse region {p" E A|c min. Pt 2 8 >> 0}, the entropy satisfies:
H(p") 2 1 llog(1 (c > 0. Define the Lyapunov function (()) = [()). Since H()) 2 and DSKL. (p"llp") 2 0, we have
(10)
(t) > 0.
Moreover, under the Assumption 2, the descent lemma guarantees:
V(t + 1) 2 v(t)
Mmmn IV [(t(l1) (t)..
Thus, (tt) is monotonically decreasing and bounded below. According to the Monotone Conver- gence Theorem, V(t) V 0. In particular:
DskL (t))l 5 V(0)
(11)
Combining Eqn. (9), Eqn. (10), and Eqn. (11):
H(p") 2 H(y") DSKL. (p "1vlll"))))))))"))) 2 - -log(1 (1 (C])8) V())
Define
hmin log(1 (1 - (C]))) V(0)
((0) Let the hyperparameter o: (1- then Anin 0.
Overall, we have proven that the predictor h serves filtering mechanism that suppresses gradi- ent update directions corresponding to over-amplified logits, and the system converges to a stable equilibrium: there exists hiin > 0 such that
H H(w") > Aming Pº -v.
21

---

Published as a conference paper at ICLR 2026
C MORE IMPLEMENTATION DETAILS
C.I MORE DETAILS ON DATASET
For vision adaptation, we evaluate the out-of-distributie generalization ability of all methods on a large-scale and widely used benchmark, namely ImageNet-CC (Hendrycks & Dietterich, 2019). ImageNet-CI is constructed by corrupting the original ImageNet (Deng et al., 2009) test set. The corruption (as shown in Figure A) consists of 15 different types, i.e. Gaussian noise, shot noise, impulse noise, defocus blur, glass blur, motion blur, zoom blur, snow, frost, fog, brightness, contrast, elastic transformation, pixelation, and JPEG compression, where each corruption type has 5 severity levels and the larger severity level means more severe distribution shift.
Geussien Neiso
Shat
Impusie No
Delocua Blar Prented
Notion Btur
Zoorm Blur
Snow
Frost
Fog
Brightness
Contract
Pixc
Figure A: Visualizations of different corruption types in ImageNet-C benchmark.
For natural language reasoning. we evaluate the effectiveness of online reasoning incentivization on a comprehensive mathematical reasoning benchmark, including Math-500 (Lightman et al., 2023), CollegeMath (Tang et al., 2024), AIME24 (Codeforces, 2024), and Minerva (Lewkowycz et al., 2022). Specifically, Math-500 is derived from the larger MATH benchmark (Hendrycks et al., 2021), consisting of difficult mathematics problems originally taken from high school competitions. It spans domains such as pre-algebra, algebra, number theory, and calculus, emphasizing abstract reasoning and multi-step problem solving. College.Math a college-level mathematics dataset con- structed from nine open-access college textbooks, covering seven areas: algebra, pre-caleulus, calculus, vector calculus, probability, linear algebra, and differential equations. The full dataset contains 2818 test questions, from which we sample 1200 for efficient evaluation. AIME24 consists of 30 advanced problems from the 2024 American Invitational Mathematics Examination (AIME) I and II, designed test extended ffain-of-thougee reasoning. Minerva includes 272 undergraduate- level mathematics and science questions from MIT OpenCourse Ware (OCW), aimed at assessing models' reasoning ability in scientific problem-solving contexts.
C.2 MORE EXPERIMENTAL PROTOCOLS ON METHOODS
All pre-trained models involved in our paper are publicly available, including ResNet50-GNi, VIT- Base ViT-Small ConvNeXt-Tiny" and Swin-Tiny* obtained from timm repository (Wightman,
X2Qpq-xBxca
v0. v0. j.raa=/esatt/eeeeessoooaa..leedd .tt
0. http:///feeaa.oooaaaa..o.....o.2
01 01-res_224.npz out.ahaihettttiiaaaa...00000aa12
http://s.aaaaooooe.a....///aa/a2 03-res_224.np2
0.
v0. oirebbachggtc.oonngcrrrrrffaaaa0
swin aen_:iiyyeercccLLiaaaa01222222_2
22

---

Published as a conference paper at ICLR 2026
2019) for image classification, and Llama3.1 1-8B-Instrue (Dubey al., 2024) for natural language reasoning. In the following, we provide the implementation details of our proposed method and all comparative methods evaluated in our experiments, which help reproduce our results.
ZeroSiam (Ours), We use symmetric KL as the divergence term in Eqn. (4), and a is fixed to 1 without tuning. For vision adaptation, we use SGD the update rule, with a momentum of 0.9, batch size of 64 (except for the experiments of batch size = 1), learning rate VI of 0.0025 / 0.005 / 0.001 / 0.00025 0.0005 with learning rate y) of 0.025 0.005 0.01 / 0.0025 0.0025 for ResNe150-GN/ / ViT-Base ViT-Small / ConnNeXt-Tiny / Swin-Tiny, respectively. The learning rate for batch size is scaled down by 16 for ResNet50- GN and 32 for other models following SAR. The trainable parameters are all the affine parameters of normalization layers. For natural language reasoning. following the configuration for TL.M, we use AdamW as the update rule, with 31 0.9, 82 = 0.999, weight decay = 0.0, and optimize the prediction entropy of the first 8 output tokens. Both learning rates f and 7/, are set to 7.5x10-6 / 5x1000 / 1.25x x 10-5 / 10-6 for Math-500 / CollegeMath / AIME24 / Minerva. Trainable parameters are the LoRA parameters with rank of 8.
Tent 10 (Wang et al., 2021). We follow all hyper-parameters that are set in Tent unless it does not provide. Specifically, for vision adaptation, we use SGD as the update rule, with momentum of 0.9, batch size of 64 (except for the experiments of batch size- = 1), and learning rate of 0.00025 / 0.001 / 0.0001 / 0.000025 / 0.00005 for ResNet50-GN. GN / ViT-Base / ViT-Small / ConwNeXtt-iny / Swin-Tiny, respectively. The learning rate for batch size = 1 is scaled down to (0.00025/32) for ResNe150-GN, (0.001/64) for ViT-Base, (0.0001/64) for ViT-Small, (0.000025/64) for ConvNeXt- Tiny and (0.00005/64) for Swin-Tiny. The trainable parameters are all the affine parameters of normalization layers. For natural language reasoning, we use AdamW as the update rule, with 31 = 0.9, 32- = 0.999, weight decay= = 0.0, and optimize the prediction entropy of the first 8 output tokens. The learning rate is 7.5x 10 /xx10 6 / x.25 10 5 5x100 6 for Math-500 CollegeMath / AIME24/ / Minerva. The trainable parameters are the LoRA parameters with a rank of 8.
SAR" (Niu et al., 2023). We follow all hyper-pann parameerrsssssss that are set in SAR unless it does not provide. Specifically, for vision adaptation, we use SGD as the update rule, with momentum of 0.9, batch size of 64 (except for the experiments of batch size 1), and learning rate of 0.00025 / 0.001 / 0.0001 / 0.000025 / 0.00005 for ResNet50-GN / ViT-Base / ViT-Small / ConvNe / Swin-Tiny. The learning rate for batch size = is scaled down to (0.00025/16) for ResNet50- GN, (0.001/32) for ViT-Base, (0.0001/32) for ViTlSmall, (0.000025/32) for ConvNeXt- (0.00005/32) for Swnn-Tiny. The entropy threshold Eu is set to 0.4x In C. where C' is the number of task classes. The trainable parameters are the affine parameters of norm layers from layer 1 to layer 3 in ResNet50-GN, from blocks to blocks 8 in ViT-Base and ViT-Small, and all affine parameters in other models. For natural language reasoning, Fgg is set to 0.4. We use AdamW the update rule, with 31 = 0.9, 82 = 0.999, weight decay = 0.0, and optimize the prediction entropy of the first 8 output tokens. The learning rate 7.5x 10-6 6 / 5 10 6 / 1.25x 10 5 10-6 for Math-500 / CollegeMaahh / AIME24 / Minerva, trainable parameters are the LoRA parameters with rank of 8.
and
EATA 12 (Niu et al., 2022). We follow all not provide. Specifically, for vision adaptation, the entropy constant Eo (for reliable sample iden- tification) is set to 0.4 In C, where C' is the number of task classes. The e for redundant sample identification is set to 0.05. The trade-off parameter (3 for entropy loss and regularization loss is set to 2,000. The number of pre-collected in-distribution test samples for Fisher importance calculation is 2,000. The update rule is SGD, with momentum of 0.9, batch size of 64 (except for the ex- periments of batch size= = 1). and learning rate of 0.00025 / 0.001 / 0.0001 0.000025 / 0.00005 for ResNet50- GN / ViT- / ViT-Small/ Cenv Tiny / Swin-Tiny The learning rate for batch size = 1 is scaled down to (0.00025/32) for ResNer50-Gr. (0.001/64) for ViT-Base. (0.000 1/041/6) for ViT- Small, (0.000025/64) for ConyNeXt-Ting and (0.00005/64) for Swin-Tiny. The trainable parameters are all affine parameters of normalization layers. For natural language reasoning, Eg is set to 0.4, while the anti-forgetting regularizer not applied due to a lack of knowledge for in-distribution data that the large language model trains on. We use Adam W as the update rule, with 31 = 0.9, 82 = 0.999, weight decay= 0.0, and optimize the prediction entropy of the first 8 output tokens. The
that are set in EATA unless does
2.1- 1--8 82- Instruct
phtrpe://gtthbb..cmmmmmeegg////
23

---

Published as a conference paper at ICLR 2026
learning rate is 7.5 7 11.25x100 1111:11111111x1110 15x10-000001 for Math-500 CollegeMath AIME24 / Minerva. The trainable parameters are the LoRA parameters with a rank of 8.
De (Lee et al., 2024). We follow all hyper-parameters that set in Do unless it does not provide. Specifically, the entropy constant Eg (for reliable sample identification) is set to 0.4 x In 1000, and the factor VEm is set to 0.5 In 1000. The Pseudo-Labe Probability Difference (PLPD) threshold TPLPD is set to 0.2. The update rule is SGD, with a momentum 0.9, batch size of 64 (except for the experiments of batch size 1), and learning rate of 0.00025 / 0.001 / 0.0001 / 0.000025 / 0.00005 for ResNet50-GN ViT-Base ViT-Small ConvNeXt- Tiny / Swin-Tiny. The learning rate for batch size = is scaled down (0.00025/16) for ResNet50-GNY (0.001/32) for ViT-Base. (0.0001/32) for ViT-Small (0.000025/32) for ConvNeXt-Ting and (0.00005/32) for Swin- Tiny. Trainable parameters are the affine parameters of norm layers from layer to ResNer50- GN, from blocks to 8 in ViT-Base and ViT-Small, and all affine parameters in other models.
COME (Zhang et al., 2025a). For vision adaptation, we implement COME based on DeYO for comparisons, following the hyper-parameters set in DeYO unless otherwise specified. Specifically, the entropy constant Eo (for reliable sample identification) is set to 0.4 1000, and the factor Taat is set to 0.5x In 1000. The Pseudo-Label Probability Difference (PLPD) threshold TPLPD is set to 0.2. The uncertainty mass is set to C, where C is the number of task classes. The update rule is SGD, with momentum of 0.9, batch size of 64 (except for the experiments of batch size 1), and learning rate of 0.00025 / 0.001 / 0.0001 / 0.000025 / 0.00005 for ResNer50-GN ViT-Base ViT-Small / TonvNeXt-Tiny Swin-Tiny. The learning rate for batch size 1 scaled down to (0.00025/16) for ResNe150-GN, (0.001/32) for ViT-Base, (0.0001/32) for ViT-Small, (0.000025/32) for ConvNeXt- Tiny and (0. (0.00005/32) for Swin-Tiny. The trainable parameters are the affine parameters of norm layers from layer to layer 3 in ResNe150-GN, from blocks to blocks 8 in ViT-Base and ViT-Small, and all affine parameters in other models. For natural language reasoning, COME implemented based on Tent, and uncertainty mass is set to Z2), where Z denotes the vocabulary size. We use Adam W as the update rule, with 31 0.9, 332 0.999, weight decay = 0.0, and optimize the prediction entropy of the first 8 output tokens. The learning rate is 7.5x 10-6 5 10-6/ / 1.22 10-5 / 15x10-6 6 for Math-500 500 / CollegeMath/ / AIME24 Minerva. The trainable parameters are the LoRA
parameters with rank of 8.
TLM (Hu et al., 2 We follow all syper-parameters that are set in TLM unless does not compare with TLM on the natural language reasoning task. the perplexity
provide. Specifically, threshold P, is set to e². The update rule is Adam with 31 = 0.9, B2 = 0.999, weight decay 0.0. The learning rate is 7.5x 10 / 5 10-6 / x.25x100 5 5 10 for Math-500/ / CollegeMath / AIME24 / Minerva. The trainable parameters are the LoRA parameters with a rank of 8.
24

---

Published as a conference paper at ICLR 2026
D MORE EXPERIMENTAL RESULTS
In this section, we provide the detailed results of Tables 3-6 in the main paper and include additional experiments under both mild and wild testing scenarios to enable comprehensive comparison.
D.1 DETAILED AND ADDITIONAL RESULTS UNDER WILD TEST SCENARIOS
We first provide the detailed results of TTA under label shifts and single sample. From Tables A & B. ZeroSiam achieves superior performance across nearly all cases, e.g., 51.6% (Ours) vs. 43.9% (OeYO) ResNet50-GN under label shifts, and 51.3% (Ours) vs. 42.3% (COME) ViT-Small under the batch size of 1. Similar results are observed even when the data stream exhibits both label shifts and data scarcity, shown in Table C, suggesting effectiveness across test settings.
D.2 DETAILED RESULTS FOR TTA ON THE BLIND-SPOT SUBSET
From Table D. prior methods tend to collapse when adapting on the blind-spot subset, e.g., 18.9% (DeYO) vs. 30.6% (NoAdapt) w.r.t. the average accuracy on R50-GN. In contrast, even under such a challenging setting, ZeroSiam achieves consistent improvement across all domains and models, suggesting that ZeroSiam substantially expands the scope and reliability of TTA the real world.
D.3 DETAILED RESULTS UNDER THE MILD TEST SCENARIO
ZeroSiam is not only effective under challenging test scenarios, but also enhances TTA performance significantly on the mild test scenario (Wang et al., 2021), where data comes with shuffled labels. As shown in Table E, ZeroSiam demonstrates superior performance on out of models and also achieves comparative results on ViT-Base, e.g., the average accuracy of 48.6% (Ours) vs. 41.7% YO) on ResNet50-GN, and 62.6% (Ours) vs. 62.8% YO) on ViT-Base. This suggests that our ZeroSiam's is design helps improve the stability and efficacy of TTA across a wide range of scenarios.
Table A: Detailed results of TTA under IMBALANCED LABEL SHIFTS, Table 3 in the main paper.
Noisc Shot
Blur Motion
Weather
Digital
Modele
Gauss,
Impul.
Defoc.
Glass
Zoom
Snow
Frost
Fog
Brit.
Contr:
Elastic
Pixel
JPEG
Avg.
ResNe55U-GN
18.9
19.8
19.8
21.4
47.3
36.3
52.3
Tent
2.6
3.3
2.7
13.9
7.9
19.5
17.0
16.5
21.9
1.8
70.5
42.2
6.6
49.4
53.7
22.0
SAR
33.1
36.5
35.5
19.2
19.5
33.3
27.7
23.9
45.3
50.1
71.9
46.7
7.1
52.1
56.3
37.2
EATA
27.0
28.3
28.1
14.9
17.1
24.4
25.3
32.2
32.0
39.8
66.7
33.6
41.9
38.4
COME
17.7
19.7
17.7
19.7
11.2
21.2
24.8
40.2
47.8
33.7
68.9
35.6
18.6
27.7
51.8
30.4
DeYO
42.5
51.5
39.7
52.6
59.3
ZensSiam (ours)
42,9
45.1
43.1
35.1
36.1
44.5
49.2
58.1
55.1
62.9
72.3
54.8
$2.5
61.7
60.1
51.6
ViT-Base
9.4
6.7
8.3
29.1
23.4
34.0
27.0
15.8
26.3
47.4
54.7
43.9
30.5
44.5
47.6
29.9
32.7
1.4
58.2
7.7
69.3
66.1
66.4
SAR
46.5
43.1
48.9
55.3
$4.3
$8.9
$4.8
53.6
16.2
69.7
76.2
66.2
60.9
69.6
66.6
58.0
EATA
35.9
34.6
36.7
45.3
47.2
49.3
47.7
56.5
55.4
62.2
72.2
21.7
56.2
64.7
63.7
50.0
COME
45.3
52.1
52.0
56.1
57.4
62.5
60.7
66.6
64.0
71.6
77.1
65.9
61.9
72.9
69.2
62.4
D:YO
53.5
36.0
$4.6
57.6
58.7
63.7
46.2
67.6
66.0
73.2
77.9
66.7
69.0
73.5
70.3
62.3
(ours)
52.3
73.3
70.1
ViT-Small
2.0
2.0
1.5
24.2
17.1
30.3
22.0
9.5
19:2
37.9
44.4
30.1
24.8
38.2
41.0
22.9
Tent
0.3
0.1
43.1
37.0
45.4
36.3
5.5
21.2
58.4
65.8
51.6
26.6
56.6
51.9
34.0
SAR
1.6
2.0
44.3
39.0
46.5
39.0
16.6
45.9
58
65.3
54.7
44.4
56.9
55.2
3%.1
EATA
15.6
15.5
17.8
42.4
40.3
41.8
41.6
46.2
48.7
58.9
65.3
52.9
50.5
57.2
56.2
43.6
0.1
52.8
DeYO
0.1
0.2
0.1
48.4
47.7
53.4
16.2
47.0
54.6
65.0
71.0
59.3
5H.5
64.1
61.0
43.1
ZeroSiam (ours)
25.7
25.9
27.9
48.2
48.3
53.5
51.5
55.7
55.6
65.4
71.2
58.4
59.5
64.2
61.2
$1.5
Con-NeXii-Tay
21.4
27.7
24.5
32.5
52.5
39.5
44.5
55.8
Tent
18.1
25.8
26.6
24,3
4.2
33.9
29.2
41.6
46.
39.7
73.2
$1.6
18:4
10.7
56.9
33.2
SAR
34,8
36.7
34.9
27.1
4.1
35.0
30.8
44.3
47.6
8.4
73.1
$1.1
19.4
24.7
$6.7
35.2
EATA
34.4
36.8
35.0
26.7
19.1
37.0
33.3
47.7
48.4
50.6
73.0
51.9
28.7
31.4
56.9
40.7
COME
42.6
44.5
42.4
38.7
1.2
46.0
11.8
$7.1
56.9
61.8
75.6
601.
1.3
51.9
61.9
43.9
DeYO
38.0
27.9
36.4
52.7
45.3
2.9
56.6
$8.4
ZeroSiam (ours)
42,3
44.5
42.1
37.4
33.5
45.3
44.0
56.5
55.4
62.9
71.7
59.4
41..3
51.7
60.0
50.3
Swin-Tiay
26.6
27.9
22.8
21.7
13.2
26.5
25.4
41.0
45.8
47.7
67.6
39.1
22.6
8.4
33.3
31.3
16.1
14.1
17.1
23.5
28.3
11.3
47.8
43.2
SAR
29.8
28.0
29.8
19.8
10.6
24.4
21.2
33.1
34,3
22.3
67.9
45.9
13.2
4.8
42.9
28.5
EATA
36.2
26.3
38.2
51.4
12.4
COME
41.8
43.6
43.2
36.5
9.8
46.7
2.4
54.6
52.3
60.0
72.0
47.4
4.3
3.1
55.8
38.2
D:YO
35,3
38.5
35.6
18.9
21.6
37.8
9.4
43.7
4LS
52.3
70.6
50.7
21.5
15.6
50.8
36.5
ZeroSiam (ours)
44.4
45.8
45.7
36.4
38.3
47.0
47.0
54.3
51.9
58.7
72.4
54.2
52.7
51.8
55.5
50.4
25

---

Published as a conference paper at ICLR 2026
Table B: Detailed results of TTA with BATCH SIZE=1, i.e,, Table 4 in the main paper.
Noise Shot
Blur Motion
Weather
Digital Elastic
Model Method
Gauss.
Impul.
Defoc.
Glass
Zoom
Prost
Fog
Cont::
JPEG
Avg-
RosNe550-GN
18.0
19.8
17.9
19.8
11A
21.4
24.9
40.4
47.3
33.6
69.3
36.3
18.6
28.4
52.3
30.6
Tent
2.5
2.9
2.5
13.5
3.6
18.6
17.6
15.3
23.0
1.4
70.4
42.2
6.2
49.2
53.8
21.5
SAR
23.4
26.6
23.0
18.4
15.4
28.6
30.4
44.9
44.7
25.7
72.3
44.5
14.8
47.0
56.1
34.5
EATA
24,8
28.3
25.7
18.1
17.3
28.5
29.3
44.5
44.3
41.6
70.9
44.6
27.0
46.8
55.7
36.5
17.8
19.7
21.4
21.9
47.6
33.6
35.7
51.8
D:YO
41.8
44.7
43.0
22.5
24.7
41.8
24.4
54.5
52.2
20.7
73.5
53.5
48.5
60.2
59.8
44,4
ZemSSiam (ours)
41.7
44.4
41.8
92.8
35.8
45.2
49.5
58.4
55.5
63.8
73.7
54.8
55.1
63.6
61.0
VVT.Base
9.5
6.7
29.0
33.9
27.1
15.9
26.5
47.2
14.7
44.1
47.8
29.9
Teut
42.2
1.0
43.3
52.4
48.2
55.5
50.5
16.5
16.9
66.4
74.9
64.7
$1.6
67.0
64.3
47.7
SAR
40.8
36.4
41.5
50..7
59.1
68
65.7
56.3
EATA
29.7
25.1
34.6
44.7
39.2
48.3
42.4
37.5
45.9
60.0
65.9
61.2
46.4
58.2
59.6
46.6
COME
51.7
51.4
52.1
57.6
58.2
63.3
412
67.1
64.8
72.8
77.7
68.1
67.5
73.0
69.9
62.4
DeYO
54.0
52.1
55.1
58.8
59.5
64.2
53.5
68.2
66.4
73.7
68.2
68.9
73.8
70.8
ZeroSiam (ours)
$2.1
52.7
52.8
57.8
58.3
63.0
60.6
67.0
65.7
73.0
77.9
67.6
67.9
72.8
69.9
63.99
Viall
2.0
1.9
1.5
24.3
17.1
30.2
21.8
9.5
19.3
37.9
44.4
29.9
24.9
38.2
41.3
22.9
Tent
21.3
27.7
22.0
21.5
10.6
32.3
30.9
44.6
52.4
39.6
72.3
14.5
23.4
17.6
55.6
34.6
SAR
26.9
27.7
23.0
21.7
13.2
26.4
25.3
41.2
45.8
47.7
67.8
39.2
22.5
8.4
33.2
31.3
EATA
2.4
2.5
32.8
36.3
28.2
48.7
46.1
47.7
COME
0.5
3.5
0.4
48.4
47.3
$2.9
15:4
38.2
53.8
64.3
70.7
58.88
55.8
63.6
60.4
42.3
D:YO
0.4
0.8
49.0
47.4
53.0
20.1
46.4
54.6
64.7
70.9
59.3
57.3
64.1
61.0
43.3
ZeroSiam (ours)
26.0
26.9
28.3
48.6
48.2
52.7
50.7
51.4
55.1
65.0
71.0
59.1
58.6
63.4
60.8
51.3
ConyNeXi-Timg -Tny
21.3
27.7
22.0
21.5
10.6
32.3
30.9
41.6
$2.4
39.6
72.3
41.5
23.4
17.6
55.6
3/16
30.3
33.5
43.7
49.7
SAR
30.3
33.6
29.8
25.9
11.1
33.4
30.8
41.9
47.8
38.3
72.9
46.2
22.6
18.1
56.2
36,1
EATA
26.6
30.5
26.9
25.2
11.4
33.1
31.0
44.8
50.1
40.0
72.2
47.88
23.5
18.5
55.8
35.8
COME
41.1
43,2
41.1
37.3
2.1
44.5
17.9
56.4
55.8
60:7
75.2
59.6
8.6
44.7
61.1
43.3
DeYO
36.8
39.4
37.0
29.5
2.9
38.0
14.6
51.6
46.9
4.5
74.0
55.9
7.8
19.5
$7.9
34.4
ZenSSiam (ours)
41.5
37.2
44.8
42.7
5900
Swin- Tiny
26.9
27.7
23.0
21.7
13.2
26.4
25.3
41.2
45.8
47.7
67.8
39.2
22.5
33.2
31.3
Tent
23.8
26.2
22.5
19.4
18.4
26.9
27.3
40.4
36.0
22.8
69.2
46.5
16.5
2.4
41.4
29.3
25.4
27.1
27.3
38.9
37.5
38.4
39.5
EATA
32.8
34.5
31.7
23.4
17.5
32.0
28.2
43.5
43.6
45.4
69.7
45.8
27.2
10.5
39.6
35.0
COME
38.6
41.4
39.0
34.4
14.9
44.6
7.3
52.9
5L.0
56.9
72.4
51.7
15.7
33,8
$3.3
40.5
D:YO
35.5
38.5
35.3
22.0
23.9
37.1
15.3
42.4
40.4
47.6
70.2
50.8
23.7
18.0
48.8
36.6
ZenoSiam (ours)
44.0
45.4
45.2
34.7
39.0
46.3
46.0
53.9
51.3
57.8
72.1
55.0
51.7
50.3
54.6
49.8
Table C: Additional results of TTA under LABEL SHIFTS with BATCH SIZE=1 w.r.t. Accuracy (%)) (%).
Noisc Shot
Blur Motion
Weather Frost
Dipital
Model-Method
Gauss,
Impul.
Defoc.
Zoom
Snow
Fog
Contr.
Elastic
Fixel
JPEG
Avg.
ResNectU-GiN
18.0
19.8
17.9
19.8
11.4
21.4
24.9
40.4
47.3
33.6
69.3
36.3
18.6
28.4
52.3
30.6
Tent
1.2
1.5
1.3
10.0
2.1
14.3
11.2
8.2
11.7
0.8
70.1
11.6
3.1
19.5
52.3
18.6
SAR
23.4
26.5
23.8
18.3
15.4
28.4
29.5
44.3
44.5
31.6
72.3
44.5
14.9
46.8
56.1
34,7
EATA
19.2
21.7
19.4
17.9
13.0
23.5
25.7
39.7
43.6
34.5
69.4
38.4
20.0
34.9
53.2
$1.6
17.8
19.7
19.7
21.3
40.3
33.6
35.7
$1.7
DeYO
41.0
45.8
42.2
22.9
23.3
41.4
15.9
54.0
52.3
20.7
73.4
53.6
48.
60.1
$9.8
43.5
ZeroSiam (ours)
40.3
42.4
40.5
32.6
33.2
41.2
44.3
53.6
53.1
59.5
72.7
52.1
46.8
58.7
58.7
48.6
ViT. Base
9.4
6.7
29.1
34.0
26.3
47.4
43.9
47.6
29.9
Tent
29.2
7.9
21.1
49.3
46.9
53.77
47.5
18.0
19.2
63.7
71.1
61.4
$1.8
63.6
62.2
44.4
SAR
24.8
18.3
24.1
38.2
31.9
42.1
35.5
31.1
37.5
52.3
61.0
52.3
36.3
52.0
$2.4
39.3
EATA
30.7
26.8
31.3
42.9
39.5
47.8
35.6
38.0
43.7
60.2
65.8
57.7
46.9
59.4
58.0
45.6
COME
51.1
47.9
52.5
57.2
$8.0
63.1
60.5
67.3
61.8
72.8
77.6
67.6
67.4
73.1
69.8
63.4
DeYO
53.2
36.2
58.2
59.3
64.3
68.6
66.7
73.8
67.4
69.3
71.0
ZeroSian (ours)
49.9
50.2
$1.0
56.0
56.4
60.8
55.4
65.5
611.1
71.9
77.4
66.1
65.9
71.5
68.7
62.3
Small
2,0
2.0
1.5
24.2
17.1
30.3
22.0
9.5
19.2
37.9
41.1
30.1
21.8
38.2
41.0
22.9
Teul
0.3
0.3
0.2
43.4
37.2
45.7
36.6
4.6
22.3
58.4
66.0
54.7
27.0
56.8
55.3
33.9
SAR
2.2
2.3
1.7
34.5
26.0
39.2
27.4
19.7
32.1
45.0
53.7
43.4
31.9
44,2
45.9
29.9
EATA
2.1
2.3
29.1
24.8
42.8
39.4
44,2
26.9
COME
0.5
3.5
01.4
47.8
46.9
52.7
16.9
37.3
53.6
64
70.6
$86.8
55.8
63.5
60.4
42.2
D:YO
0.4
0.8
48.7
47.3
53.2
21.2
16.6
51.2
61.9
70.9
59.1
57.5
611.1
61.0
43.1
ZeroSiam (ours)
23.7
23.6
25.01
46.0
44.9
49.6
46.8
50.8
52.8
62.7
69.
56.8
54.8
61.1
58.7
Cony NeXi-eXXT
21.4
27.7
22.1 1
24.5
11.01
32.5
31.2
44,5
$2.5
39.5
72.0
44.8
23.1
17.7
55.8
34.7
18.2
24.8
26.0
24.4
4.3
34.0
29.1
41.8
46-3
42.4
$1.8
18.2
10.4
$6.9
33.5
SAR
30.2
33.6
30.2
25.8
11.1
33.3
31.0
44.9
47.6
37.8
73.0
46.2
22.7
18.2
56.3
36.1
EATA
24.0
28.9
24.5
24.7
11.2
32.5
31.0
44.6
51.4
39.7
72.1
45.9
23.2
18.0
55.8
35.2
COME
41.4
43.4
37.3
44.7
58.7
61.1
75.3
59.6
61.2
DeYO
36.9
39.4
37.0
29.2
3.2
37.7
14.8
51.6
47.6
5.4
74.0
55.8
8,3
23.3
$8.0
34,8
ZemSSia
41.3
43.3
41.1
36.3
31.4
43.8
42.2
54.9
$3.7
61.5
74.2
58.2
41.0
49.8
59.2
48.8
Swin-Tiny
26.6
27.9
21.7
26.5
41.0
45.8
47.7
67.6
39.1
33.3
Tent
14.6
13.1
11.1
17.4
14.3
21.2
20.9
31.4
24.2
12.1
69.7
48.1
9.1
1.0
42.7
23.4
30.5
32.2
29.9
27.9
41.9
39.9
47.5
10.4
10.4
EATA
27.7
29.1
25.0
21.7
14.2
27.7
25.9
40.7
43.5
47.4
68.1
39.9
23.4
9.1
34.3
31.9
COME
38.6
41.0
39.2
34,3
21.6
44.6
5.0
53.1
51.1
57.2
72.2
51.5
21.3
18.3
53.4
40.2
DeYO
35.7
37.6
35.8
21.0
26.0
36.8
14.7
42.3
42.0
49.6
70.4
30.9
24.4
26.2
48.8
37,5
ZeriSiam (ours)
42.8
44.4
43.7
33.3
36.1
44.2
43.9
$2.1
49.6
55.9
71.6
53.5
49.3
47.7
53.4
48.1
26

---

Published as a conference paper at ICLR 2026
Table D: Detailed results of TTA on the BLIND-SPOT SUBSET, ie., Table in the main paper.
Noise Shot
Blur Motion
Weather Fog
Digital Elastic
Methol
Gauss.
Impul.
Defoc.
Glass
Zoom
Snow
Cont::
JPEG
Avrg
RosNe550-GN
18.0
19.8
17.9
19.8
11A
21.4
24.9
40.4
47.3
33.6
69.3
36.3
18.6
28.4
52.3
30.6
Tent
0.2
0.2
0.2
10.5
2.3
5.8
2.3
1.6
2.3
0.2
63.3
16.7
0.5
48.3
46.8
13.4
SAR
17.0
19.6
16.9
15.8
1144
22.2
24.0
5.8
42.0
25.4
69.0
38.9
1.3
31.9
54.2
26.1
EATA
18.6
21.2
18.6
15.6
134
22.7
24.4
37.1
38.8
33.2
67.8
41.6
19.1
47.1
53.0
31.5
18.0
19.8
21.4
24,9
10.4
47.3
33.6
36.2
52.2
D:YO
044
0.6
0.4
7.9
0.2
28. 1
1.6
5.5
7.1
0.1
71.2
47.8
1.3
59.7
$1.4
18.9
ZemSSiam (ours)
38.0
42.7
39.0
27.9
34.0
43.3
$2.1
44.3
59.1
51.2
60.3
45.4
46.2
ViT.Base
9.5
6.7
29.0
33.9
27.1
15.9
26.5
47.2
54.7
47.8
29.9
Teut
0.2
0.2
0.1
56.5
$4.0
60.4
0.5
1.4
1.0
0.2
77.5
67.4
0..3
71.6
68.7 7
30.7
SAR
42.2
7.1
55.3
47.6
71.5
67.1
19.4
67.8
50.3
EATA
26.4
20.3
32:2
45.7
37.5
48.6
42.3
37.2
47.5
62.2
65.7
63.1
46.8
60.1
59.8
46,4
COME
0.1
0.1
56.9
58.4
63.5
0.5
68.3
64.7
73.4
77.1
67.1
69.1
73.4
69.5
49.5
DeYO
0.1
0.5
59.4
3.8
69.7
67.6
74.5
78.5
68.7
70.8
71.2
ZeroSiam (ours)
$2.6
53.2
53.4
57.7
58.6
63.4
61.7
67.8
66.5
73.8
78.2
67.8
69.2
73.7
70.2
64.5
Viall
2,0
1.9
1.5
24.3
17.1
30.2
21.8
9.5
19.3
37.9
44.4
29.9
24.9
38.2
41.3
22.9
Tent
0.1
0.2
0.1
44.6
36.6
45.6
33.2
1.3
16.5
59.5
68.0
56.5
0.5
58.2
56.2
31.8
SAR
2.1
2.2
1.6
31.1
23.7
39.2
27.5
9.8
40.0
51.8
66.4
46.7
23.4
53.2
49.8
31.2
EATA
2.2
2.2
28.4
33.2
44.8
47.4
45.6
COME
0.1
2.6
0.1
47.3
48.0
52.4
0.2
31.2
55.6
65.0
71.7
59.5
0.4
641.4
60.6
37.3
D:YO
0.1
0.3
49.4
48.9
54.0
0.5
45.9
56.3
66.2
72.3
60.6
58.6
65.5
61.9
42.7
ZeroSiam (ours)
25.1
25.4
27.6
48.2
47.9
52.5
50.6
51.3
55.5
65.6
71.8
59.2
59.4
6/1.6
61.2
51.3
ConyNeXi-Timy
21.3
27.7
22.0
24.5
10.6
32.3
30.9
41.6
52.4
39.6
72.3
44.5
23.4
17.6
55.6
311.6
12.9
50.1
56.4
SAR
24.3
30.2
24.8
24.7
10.7
32.5
30.6
42.9
50.1
37.1
72.7
45.1
21.8
17.7
55.7
34.7
EATA
23.7
29.1
24.5
24.6
11.1
32.5
30.7
44.3
50.4
39.9
72.0
46.2
23.2
17.9
55.7
35.0
COME
41.1
42.7
29.4
33.3
2.4
25.1
24.9
0.2
57.7
27.6
58. 3
30.6
DeYO
34,9
35.5
35.3
22.0
0.9
23.0
3.0
38.6
29.1
0.3
72.1
52.3
1.8
22.1
55.6
28.4
ZenSSiam (Durs)
42.4
44.9
44.5
56.3
64.44
44.7
58.5
Swin- Tiny
26.9
27.7
23.0
21.7
13.2
26.4
25.3
41.2
45.8
47.7
67.8
39.2
22.5
8.4
33.2
31.3
Tent
0.2
0.4
0.1
14.0
5.9
7.2
5.0
9.6
8.9
2.6
67.7
16.1
1.4
0.3
34.4
11.6
27.3
29.0
26.7
47.5
39.4
36.5
EATA
27.9
29.0
25.3
20.7
14.6
28.4
25.7
40.1
40.7
47.4
68.1
40.8
23.6
9.2
33.8
31.7
COME
38.1
41.3
42.0
26.2
0.5
10.8
0.5
10.3
8.0
10.2
72.8
52.0
0.1
0.5
55.1
24.6
D:YO
0.2
0.1
0.2
13.8
6.4
11.4
3.7
11.6
16.9
4.3
70.2
44.4
3.7
0.4
47.1
15.6
ZenoSiam (ours)
45.1
47.5
47.0
35.2
40.3
46.1
46.9
56.1
51.9
58.5
68.6
54.8
54.7
52.9
56.3
50.8
Table E: Detailed results of TTA under the MILD SCENARIO, i.e. Table 7 in the main paper.
Noisc Shot
Blur Motion
Weather Frost
Digital Elastic
Model-Method
Gauss,
Impul.
Defoc.
Zoom
Snow
Fog
Contr.
JPDG
Avg.
ResNectU-GN
18.0
19.8
17.9
19.8
11.4
21.4
24.9
40.4
47.3
33.6
69.3
36.3
18.6
28.4
52.3
30.6
Tent
5.1
6.1
5.4
15.0
10.8
22.1 1
22.9
25.8
33.2
3.1
70.1
42.7
11.0
11.1
51.2
25.1
SAR
28.5
31,4
29.7
18.7
19.5
30.2
30.1
43.3
43.7
7.0
70.8
44.0
19.0
48.8
55.2
34.7
EATA
37.3
39.1
39.4
28.1
27.1
36.8
39.1
50.8
49.0
55.8
72.0
50.1
41.8
55.7
58.1
45.4
COME
17.9
19.7
21.4
47.5
35.9
DeYO
39.6
42.1
40.6
22.2
23.3
38. 3
37.7
50.4
49.4
3.0
73.0
50.3
41.9
55.5
57.7
41.7
ZeroSiam (ours)
40.5
42.4
41.7
31.4
31.8
40.8
44.4
53.5
53.3
59.1
72.9
51.5
47.4
58.9
58.8
48.6
Base
9.4
6.7
29.1
34.0
26.3
47.4
43.9
47.6
29.9
Tent
42.4
1.4
43.3
52.2
47.6
55.4
49.9
19:7
18:
66. 1
74.9
64.7
52.5
66.8
64.1
47.9
SAR
44,3
14.0
45.7
$2.9
49.8
56.0
51.1
58.3
50.6
66.5
74.6
64.3
$5.5
66.5
64.00
54.3
EATA
49.7
49.4
51.3
55.9
55.5
60.5
57.8
63.4
63.0
70.4
76.0
67.0
64.7
69.3
67.9
61.5
COME
50.9
51.6
52.1
56.9
$7.4
62.2
59.2
66.1
61.3
72.5
77.4
67.9
66.3
72.4
69.2
63.1
DeYO
52.9
53.1
53.8
58.2
63.0
65.7
73.2
68.0
67.7
73.1
69.8
62.8
ZeroSian (ours)
50.5
$1.0
51.5
$7.1
56.8
61.22
58.6
64.9
61.55
71.9
77.2
67.6
65.6
71.5
68.5
62.6
Small
2.0
2.0
1.5
24.2
17.1
30.3
22.0
9.5
19.2
37.9
41.4
30
21.8
38.2
41.0
22.9
Teul
0.5
0.6
0.4
39.5
33.0
42.5
34.0
10.3
37.1
54.5
63.6
$1.7
31.5
53.1
$2.3
33.6
SAR
1.4
2.1
1.1
40.8
34.9
43.2
35.5
16.3
4L.8
54.7
63.7
51.8
38,5
53.4
$2.5
35.4
EATA
22.4
20.6
47.2
49.9
60.7
56.6
57.2
COME
0.2
0.4
01.2
47.7
46.3
51.3
19.6
37.9
$2.7
63.6
69.88
58.3
$4.1
61.8
59.2
41.6
D:YO
0.2
0.3
47.9
45.8
51.4
33.6
41.5
53.0
63.5
70.1
58.5
55.3
62.4
59.8
43.1
ZeroSiam (ours)
23.8
23.4
25.2
47.6
46.0
50.6
4%.1
$1.9
53.3
63.2
69.9
58.1
55.7
61.8
59.4
Cony -ex--TexTnny
21.4
27.7
22. 1
24.5
11.01
32.5
31.2
44.5
52.5
39.5
72.0
44.8
23.1
17.7
55.8
34.7
30.8
33.6
32.0
24.7
33.6
30.0
43.7
47.3
43.6
49.5
56.3
SAR
33.4
35.6
33.7
27.1
8.1
34.1
30.7
44.6
47.3
17.0
72.8
48.8
22.0
24.4
56.1
35,7
EATA
35.3
37.4
35.8
31.0
2017
37.1 1
33.7
4HL.
49.
51.3
73.2
53.0
29.5
31.3
56.6
41.6
COME
40.4
42.6
36.2
43.2
54.6
54.2
75.0
58.6
44.7
59.9
DeYO
36.3
39.0
36.4
29.1
2.7
37.1
19.6
50.1
48.3
4.5
73.8
54.9
8.6
23.7
$7.4
34,8
ZemSSaa
39.6
41.7
39.3
33.8
27.3
42.0
38.7
53.2
51.8
59.3
73.8
$7.0
36.5
44.2
58.2
46.4
Swin-Tiny
26.6
27.9
21.7
26.5
41.0
45.8
47.7
67.6
39.1
33.3
31.3
Tent
23.7
26.2
22.7
19.4
18.6
27.1
27.4
40.5
36.3
24.4
69.2
46.3
16.9
2.8
41.5
29.5
31.8
32.8
22.3
29.6
39.8
37.6
16.8
43.2
33.5
EATA
40.9
42.9
41.6
33.5
33.6
42.6
40.1
50.1
49.1
54.9
71.8
52.6
44.8
40.0
$1.1
46.0
COME
41.2
43,2
42.1
35.2
15.0
44.7
7.0
52.9
51.9
57.8
72.1
51.1
23.8
25.2
51.3
41.2
DeYO
35,2
37.0
36.0
22.2
25.0
35.8
15.4
42.0
43.8
48.0
70.1
50.3
31.6
34.5
48.0
38.3
ZeriSiam (ours)
42.4
44.0
43.0
31.7
34.9
43.6
42.6
$1.3
48.9
54.7
71.5
53.4
47.5
45.8
52.3
47.2
27

---

Published as a conference paper at ICLR 2026
E ADDITIONAL DISCUSSIONS
E.1 ZEROSTAM'S EFFICACY BEYOND COLLAPSE PREVENTION
ZeroSiam regularize test-time entropy minimization from favoring non-generalizable shortcuts (c.f. Section 3.2), thereby improving its performance even in cases when no collapse occurs. As shown in Figure B, Tent drastically reduces entropy and eventually closes it to zero by inflating the logit norms and aligning all logits toward a dominant mode. Despite the reduction of entropy, it does not involve meaningful learning. and Tent thus fails improve the accuracy on the first 250 batches of samples, where such biased signals can further degrade performance during a prolonged adaptation, as shown in Figure B. In contrast, ZeroSiam maintains stable logit norm and center dominance ratio dur- ing entropy minimization, which successfully enhances TTA efficacy beyond collapse prevention, as shown Figure B (a). Moreover, from Figure B (d), ZeroSiam does not greedily minimize the entropy loss. Instead, ZeroSiam converges to a low but non-zero entropy loss, while still enabling consistent accuracy improvement, i.e., from 250 to 750 batches as in Figure B (a). Such conver- gence toward non-zero loss is also aligned with Theory 1, which shows that ZeroSiam inherently defines a lower bound of hmin for entropy optimization, preventing the model from degenerating into collapsed constant one-hot outputs that trivially minimize (i.e., zero out) the entropy loss.
(a) Evolutions of Accuracy
(b) Evolutionn of Logit 12 Norm
[c]
Evolutions of Center Dominance
(d) Evolutions Entropy
74
8700
Center Domirance
1.0
2.7
Logit 1.2 Narm
Tent
Accuracy
70-
5700
um (oun)
00.
Zeuziam (our)
Enptropy
1.8
(cural
66
2900
0.4
0.9
250
750
250
250
Online Batch
Online Batch
Onlina
Online Batch
Figure B: Empirical evidence of ZeroSiam for boosting stability and efficacy. (a-d) record the ODD accuracy, logits L2 norm, center dominance, and entropy in model predictions under a mild test scenario (Wang al., 2021). Experiments run on ImageNet-C (Bright, level 5) with ViT-Base.
E.2 EVOLUTIONS OF DIVERGENCE LOSS IN ZEROSTAM
We provide additional results of how the divergence loss evolves during adaptation supplement Figure 2. As shown in Figure C, the divergence loss increases more rapidly and substantially under more imbalanced stream. Such phenomenon is also aligned with changes of the predictor as shown in Figure 2 (a), where larger divergence from an identity mapping results in a larger similarity loss. Overall, these results suggest an adaptive regularization strength according to the degree of collapse risk in the scenario, indicating the efficacy of our asymmetric entropy optimization design.
Divergence Loss vs. Imbalanced Stream
1.81
Similarity Loss
imbalanced ratio=1k
imbalanced ratio=3k
imbalanced ratio=5k
0.00
Online Batch
780
Figure C: The evolution of divergence loss during TTA. Results are reported ImageNet-C (Snow,
level 5) with ResNet50-GN under online streams with varying imbalanced ratios (Niu et al., 2023).
28

---

Published as a conference paper at ICLR 2026
E.3 ZEROSIAM FOR SAVING A COLLAPSED MODEL
Interestingly, further demonstrate that ZeroSiam sometimes model that has already collapsed. To illustrate this, we first run Tent on an imbalanced data stream until collapse occurs, and then apply ZeroSiam. As shown in Figure ZeroSiam helps restore strong accuracy after 300 batches of adaptation. This recovery is driven by the asymmetric alignment in ZeroSiam, which makes collapsed solutions no longer stable minimum, encouraging the model escape the col- lapsed mode and re-cluster samples. However, this does not fully explain how class-wise clusters that are consistent with pre-training re-emerge. We hypothesize this is because only the affine pa- rameters in the normalization layers are updated during testing, which introduces small adjustment to the model that makes performance recovery possible. Notably, we observe that the predictor in ZeroSiam has to be randomly initialized (e.g., 8,, = I 0.1 W. W ~N,((, the identity and also remain learnable during TTA to enable the collapse recovering effects. Even so, recovery succeeds in only 4 out of domains, suggesting that while promising, collapse recovery with ZeroSiam remains an open question, and we leave it for future work.
to derive from
Tent
ZeroSiam
60
ZeroSiam Started
Accuracy (%)
30-
400
800
1200
1600
Online Batch
Figure D: Efficacy of ZeroSiam for saving a collapsed model. Results are reported on ImageNet-C C
(Shot, level 5) with ViT-Base under ONLINE IMBALANCED LABEL SHIFTS (imbalance ratio oc).
E.4 COMPARISONS BETWEEN THE ENTROPY AND DIVERGENCE TERM DURING TTA
As shown in Figure E, the alignment loss DDp D(p"")'glp") does not grow infinitely. Instead, the align- ment loss quickly increases then converges, while the entropy term (p²) decreases and stabilizes. Throughout adaptation, the alignment term exhibits smaller loss value than the entropy term, which provides an appropriate regularization strength that prevents the risk of collapse, without hindering the effectiveness of the entropy-basee adaptation.
Entropy vs. Divergence
4.8
entropy loss
divergence loss
3.2
Loss
1.6
0
0
400
800
1200
1600
Online Batch
Figure Comparisons between entropy and divergence during TTA on ImageNet-C (Gaussian, level 5) under ONLINE IMBALANCED LABEL SHIFTS (imbalance ratio oc) with ViT-Base.
29

---

Published as a conference paper at ICLR 2026
E.5 MORE SENSITIVITY ANALYSIS OF LEARNING RATES IN ZEROSIAM
To demonstrate ZeroSiam's 's robustness, we further supplement the sensitivity analysis of learning rates on Swin-Tiny, a challenging architecture on which Tent frequently suffers from collapse.
From Figure F, ZeroSiam consistently outperforms Tent across a wide range of encoder learning rates, confirming the stability trends observed in Figure across architectures. Moreover, on smaller and more collapse-prone models, ZeroSiam can benefit from larger predictor learning rate 7h, e.g., yielding an accuracy of 53.3% with fy 10 5e and 7/ 40 ny; while still outperforming previous methods across broad learning rate configurations, e.g., achieving an accuracy above 45% when My E [5. x 5 and 77 [1. 40) x1y,. showing a substantial gain compared the accuracy of 38.2% in COME and 37.7% in De These results collectively demonstrate the efficacy of ZeroSiam across learning rate choices. In practice, we did not extensively tune the learning rates, where we simply use T/ 10 x 5e 5 and f7 5 ny on ZeroSiam, which yields accuracy of 50.4% for comparisons with other methods.
Encoder LR nr (x0, 00005)
40
6.3
41.7
39.7
41.3
44.1
37.8
26.2
20
49.7
50.3
50.9
51.
51.1
-40
10
12.4
48.6
49.5
50.4
51.3
52.5
53.3
5 14.4
45.9
46.9
47.9
48.6
49.4
50.5
1-
24.0
37.2
38.5
39.7
40.3 40.6
40.7
10
i
2
5
10
20
40
Predictor LR On (xn))
Figure F: Sensitivity learning rates on Swin-Tiny. Results are reported on ImageNet-C (Gaussian,
level 5) under ONLINE IMBALANCED LABEL SHIFTS (imbalance ratio = oc).
E.6 DISCUSSIONS ON A Data-Free APPROACH FOR SELECTING Th IN ZEROSIAM
While the predictor Ir 77,, in ZeroSiam is simply set the same as 7/ on larger models and around 10x larger than 1Ty smaller and more collapse-prome models, we further briefly introduce data-free method to help select 7/h-- The core idea is to leverage random Gaussian noise as the proxy to track TTA dynamics, where ideally, noisy learning signals should be totally absorbed and suppressed in ZeroSiam. To this end, we track the changes in prediction, e.g., prediction entropy A., before and after adaptation on Gaussian noise, and select the perfformino 7/ that leads to minimal change, e.g., min., Ael, which implies an appropriate regularization strength for bias filtration. As shown in Table V, on ResNet50-GN, we can find т) 10 by min,, [Ael using only generated Gaussian before TTA deployment, which also delivers the highest TTA accuracy of 51.4% under label shift.
Table F: Illustration of data-free selection for Vi on ResNer5O-GN based on entropy difference |Ae] before and after adaptation 6,400 random Gaussian inputs. TTA accuracy is measured under the label shift setting. Encoder learning rate πy is set to 0.00125, and r7s. is set to 4x 0.00125.
Metric
7h = 0
7h = 2
Th = 5
7h = 10
7h
20
1h = 40
prediction
0.750
0.085
0.053
0.001
0.061
0.083
TTA Acc. (%)
14.3
49.6
51.0
51.4
50.3
45.3
We acknowledge that some architectures, such as ConvNeXt, can consistently output the highest prediction entropy on Gaussian noise regardless of adaptation and may require tracking other pre- diction metrics for data-free 77, selection. We leave this for future work, and believe that our current focus on collapse prevention and asymmetric entropy-basee ful contributions, as this significantly reduces the risk of TTA across adaptation scenarios while maintaining efficiency for practical and reliable deployment.
architecture already makes meaning-
30

---

Published as a conference paper at ICLR 2026
E.7 EFFICACY OF ZEROSIAM ACROSS DIVERSE ADAPTATION EPOCHS
In our main experiments, all methods are evaluated with only 1 epoch over the test set, following the evaluation settings established by prior works. Here, we further evaluate Tent and ZeroSiam using more adaptation epochs under Tent's default mild setting. As shown in Table G. Tent's performance gradually degrades with more epochs (47.9% - 41.3%), reflecting its known overfitting tendeney. In contrast, ZeroSiam remains stable and even benefits moderately from additional epochs (62.6% + 65.7%). This confirms that ZeroSiam improves generalization while mitigating overfitting in Tent, which maintains stable adaptation across different epoch budgets.
Table G: Accuracy of Tent and ZeroSiam under the k-th epoch of TTA over the entire test set. Results reported with ViT-Base under Tent's default mild setting.
Method
No adapt
Tent (k=1) Tent (k=3) Tent (k=5) ZeroSiam (k=1)
ZeroSiam (k=3)
ZeroSiam (k=5)
Acc. (%)
29.9
47.9
45.5
41.3
62.6
65.7
65.7
E.8 NECESSITY OF STOP-GRADIENT FOR ASYMMETRY
As verified in Theory 1, the online branch in ZeroSiam converges more rapidly towards the collapse solutions during TTA. The stop-gradient on the target branch prevents the target branch from also drifting toward the collapse modes, while providing stable reference for the online branch. As shown in Table H, removing stop-gradient leads to severe collapse, e.g., reducing the accuracy from -1..5% ResNe150-GN. Similar results also observed in SimSiam (Chen & He, 2021) and BYOL (Grill et al., 2020), underscoring too-ggaddeent as a key component in asymmetry.
Table H: Importance of stop nop-gradient operation. Results are reported on ImageNet- (severity level 5) under ONLINE IMBALANCED LABEL SHIFTS (imbalance ratio oo) regarding Accuracy (%)
Noisc Shot
Blur
Weather
Digital
ResNet50-GIN
Gauss.
Impal.
Defoc.
Glass
Motion
Zoom
Snow
Fog.
Blastic
Pixel
Avg.
ZeroSiam (ours)
42.9
45.1
43.1
35.1
36.1
44.5
49.2
58.1
55.1
62.9
72.3
54.8
52.5
61.7
60.1
51.6
w/o stop-grad
2.1
2.7
15.3
2.0
15.2
11.1
11.9
17.7
1.2
71.9
43.5
3.8
50.9
55.5
20.5
WT--aase
Ganss.
Impal.
Glass
Motion
7oom
Snow
Frost
Fog
Flasric
Pixel
JPRG
Aug.
ZenoSia (ours)
52.3
52.6
53.4
57.7
58.7
62.7
61.1
67.6
66.0
73.3
78.0
67.0
67.9
73.5
70.1
64.1
stop-grad
33.7
6.3
69.2
E.9 STATISTICAL COMPARISON
We re-run Table 3 in the main paper with 5 different random seeds. As shown in Table I, ZeroSiam achieves both higher adaptation accuracy and lower standard deviation compared prior methods. Specifically, ZeroSiam increases the average accuracy from 42.6% (DeYO) to 52.9%, while reduc- ing the standard deviation by over /0-fold. This reduced standard deviation further underscores our reliability for robust adaptation in real-world applications.
Table I: Statistical comparison. Experiments follow the settings of Table 3 in the main paper. Results reported with 5 random seeds.
Method
ResNe150-GN
ViT-Base
ViT-Small
ConvNeXI-Tiny
Swin-Tiny
Average
DeYO ZeroSiam
39.7+2.05 51.2.10.66
61.842.19
40.8 50.0
34.3+0.20 49.8
36.5
42.640.82 52.9
63.540.10
50.2
E.
MORE DISCUSSIONS ON THE IMPACTS OF UNCONTROLLED LOGIT NORM INFLATION
During test-time entropy minimization, uncontrolled inflation of logit norm induce the follow- ing issues that hinders robust and reliable model adaptation: 1) Overconfidence: regarding indi- vidual predictions, increasing the logit magnitude |/w]]2 (where the predicted logit) artificially
31

---

Published as a conference paper at ICLR 2026
inflates predictive confidence without improving accuracy, since the predicted class arg max; Wg depends solely on the direction u' = [Iu]la not its magnitude. This leads to overly confident but inaccurate predictions that undermine trust in Al systems. 2) Degraded generalization from gradient interference: while inflating the logit norm does not benefit sample's own generaliza- tion, it adversely affects others through gradient interference during batch updates. Empirically, test-time adaptation with only the objective of -||u||2 to inflate the logit norm would lead a catastrophic collapse of zero accuracy for all models. Theoretically, define the decision margins
as m(x) max; Uy- of Uj and the sharpness of relative boundaries [[=]I given that both m(xx and [|V=m(z)] scale proportionally with || inflating the logit norm can not im- prove the sample's own relative boundary. However, since per-example gradients are generally non- orthogonal, a sample's update can add irrelevant noise to the boundaries of other samples while having no benefit on its current prediction. Such interference accumulates during online TTA, ad- versely affecting generalization and ultimately causing collapse. ZeroSiam mitigates this by aligning with a stable target branch, preventing uncontrolled norm growth, and improving TTA efficacy.
m(z)
E.11 MORE DISCUSSIONS WITH
ADAPTATION METHODS
ZeroSiam advances the entropy-based, self-training TTA by adding both the mechanisms of bias learning signals filtration (c.f. Section 3.2) and asymmetric optimization (c.f. Section 3.1 through a lightweight predictor with theoretical insights (Theorem 1). We further detail our distinctions with multi-branch-baas TTA methods, such as SPA (Niu et al., 2025), REM (Han et al., 2025), and TTE (Kim et al., 2025) from three aspects.
(1) Distinct inspirations from self- sele-uupe learning (objective vs. architecture): SPA and REM augmentation-bast based methods that exploit consistency learning an objective similar to self- supervised approaches-accee end, their efforts focus on devising appropriate augmentations or deteriorations images for infor- mation masking and creating a weak-to-strong consistency learning. In contrast, ZeroSiam is en- tirely augmentation-free and focuses on the asymmetric architecture in SPA and REM-for the single-branch, entropy- -based adaptation, not being limited to images.
different views to promote adaptation to the target domain. To this
to efforts
REM (2) Advantages of model collapse prevention (model-, test data stream- & modality- prevents collapse by depending on the assumption that masked images should exhibit higher pre- diction entropy, which develops architecture-specff masking strategies for the vision transformer equipped with a classification token and explicitly fixes the rank of prediction entropy of masked inputs. However, the assumption and the masking strategy may fail to generalize to broader architec- tures and modalities, while the objective can still be minimized with constant one-hot outputs. TTE prevents collapse by subtracting a moving average center in the predicted logit for self-alignment, which explicitly reduces center dominance in straightforward manner. However, it assumes that the prediction center truly reflects the trends of overfitting, which, however, violates under a long-tail data stream where the center actually reflects the dominant class. In this case, when subtracting the center, TTE can significantly risk flipping correct predictions and producing misguided alignment. In contrast, ZeroSiam develops an assumption-free and theoretically grounded asymmetric archi- tecture that self-induces collapse-resistant alignment to disfavor shortcuts in entropy minimization without relying on heuristic thresholds, making it generally applicable across diverse models, data streams, and modalities (Tables 2-7) and requiring fewer hyperparameters for deployment.
(3) Unique strengths of adaptive bias filtration (improving generalization): Beyond the widely appli- cable collapse prevention mechanism in ZeroSiam compared to prior methods, we also empirically and theoretically demonstrate that ZeroSiam further improves generalization with a bias learning signals filtration mechanism during TTA. Specifically, we show that the predictor in the online branch purposely absorbs and converts biased shorteut signals (e.g., norm inflation) into explicit discrepancies, where biased signals are then penalized by the alignment loss. As shown in Theorem and Figure (b-c), any shortcut representable by the predictor is naturally suppressed, while use- ful signals flow into the backbone encoder update. This bias filtration effect even helps improve the generalization of a large language model during test-time reasoning incentivization, demonstrating a promising research direction enhance future TTA methods.
Finally, we provide further empirical comparisons on both TTA performance and efficiency. As shown in Table J, existing methods improve performance substantial cost of computation and
32

---

Published as a conference paper at ICLR 2026
memory efficiency, due to using additional augmentations and branches, e.g., SPA increases the memory Tent from 7.760MB to 28, 28,147MB (which can not be fitted into an RTX 3090), and the latency from 113s to 275s ViT-Base. In contrast, ZeroSiam is the only method that maintains almost the same memory and latency as Tent, while achieving the highest stability, egg. increasing the accuracy of SPA from 60.3% to 64.5%, while reducing the memory from 28, 147MB to 7, 7,806MB on ViT-Base, which reveals a novel and practical stability-efficinncy Pareto frontier that has not been achieved in prior TTA methods.
Table comparisons on performance and efficiency with multi-branch TTA methods. Accuracy is reported under the blind-spot adaptation scenario. Efficiency is measured by processing 50,000
images under a batch size of via an 100 GPU.
ResNet50-GN Mem. (MB)
ViT-Base Mem. (MB)
Method
Acc. (%)
Time (s)
Acc. (%)
Time (s)
Tent TTE REM SPA
13.4
5,519
30.7
7,760
113
40.8
6,303
136
55.2
8,574
164
56.9
27,438
346
45.0
21,327
220
60.3
28,147
275
ZeroSiam (ours)
46.2
5,584
64.5
7,806
113
F MORE DISCUSSIONS WITH REINFORCEMENT LEARNING
Entropy collapse is also common challenge within reinforcement learning, where policies can degenerate (e.g., become deterministic and lose diversity) due to biased or noisy advantage esti- mation, insufficient exploration, or overly aggressive updates (Mnih al., 2016; Haarnoja al., 2018: Ahmed et al., 2019). To address this, trust-region methods such as TRPO (Schulman et al., 2015) and PPO (Schulman et al., 2017) constrain each update step in policy space through KL- divergence penalties or clipping, ensuring gradual and stable improvement. Similar principles ap- pear in value-based methods (Mnih al., 2015; Schwarzer al., 2023; Nauman et al., 2024), where target networks provide a stable anchor to stabilize bootstrapped updates against rapidly changing estimates. These approaches share with ZeroSiam the key idea of structurally constraining updates to counter collapse. Specifically, ZeroSiam's online branch with gradient updates resembles a fast- updating policy (i.e., with extra updates the predictor), while the stop- gradient target branch serves anchor, effectively forming lightweight trust region in the entropy minimization landscape. This connection situates ZeroSiam as a general Dollapse-prevention mechanism, linking stabilization strategies across TTA, self-supervised learning, and reinforcement learning.
G LARGE LANGUAGE MODEL USAGE STATEMENT
In accordance with the ICLR 2026 policy on the responsible use of LLMs, confirm that our study did not use any LLM to generate scientific content or conduct substantive experiments. The only of LLM (ChatGPT-5) to polish the English writing and improve presentation quality; all core methodology, experiments, and analyses were authored and verified by the human authors.
33


Reviews:
[{"review_id": "JptYwk1xKl", "reviewer": "Reviewer_BMnf", "summary": "ZeroSiam introduces a lightweight, low‑cost asymmetric architecture for test‑time adaptation by inserting a single linear predictor before the classifier and pairing it with a stop‑gradient target branch, enabling adaptation with only one encoder pass. Its test‑time loss function minimizes entropy on the online branch while aligning it to the stop‑grad branch via a symmetric‑KL term, which discourages shortcut solutions such as logit‑norm inflation and single‑class collapse. Extensive experiments across diverse backbones (ResNet, ViT, ConvNeXt, Swin) show consistent gains under mixed corruptions, label shifts, and batch‑size‑1 streams. This paper also shows improvement in LLM reasoning experimentally.", "questions": "- I was wondering if ZeroSiam achieves consistant performance when it negates predictor $h$ and employ only classifier $g$. It would be more favorable to highlight the proposed loss function without any modification of networks.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "- This paper delivers stable improvements over strong TTA baselines under mixed corruptions, online label shifts, batch‑size‑1, and even blind‑spot adaptation. Furthermore, it includes LLM mathematical reasoning underscoring concrete experimental cases.\n\n - The network modification is minimal, instead it requiresa single linear predictor plus a stop‑grad branch. In contrast, it does not depend on augmentations or extra encoder passes. Thus, Its runtime equals to baselines.", "weaknesses": "- This paper lacks a comprehensive understanding of representation adaptation to test-time scalings and the preservation of pre-training knowledge. The proposed loss function, which minimizes the difference from pre-trained knowledge, is driven by KL Divergence. While the paper asserts that $\\alpha = 1.0$ is applicable across all experimental cases, I believe that a deeper understanding and explanation of representations are crucial for forming more concrete and reasonable evidence, rather than elaborating numeric numbers across experimental cases.\n\n- I believe that the theoretical analysis presented in this paper doesn’t align with the empirical contribution. The analysis focuses on entropy minimization and KL Divergence separately. Specifically, it fails to accomodate which dynamic occurs during the training process when two terms are considered at the same time. When applied to test-time adaptation experiments, these concepts serve as loss functions simultaneously. Consequently, I believe that this analysis hinders the accurate understanding of the proposed loss function.", "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": "0R7PzcIHLE", "reviewer": "Reviewer_yJuL", "summary": "This paper addresses the problem of \"model collapse\" in test-time entropy minimization, where models adapting during inference can degenerate to predicting a single dominant class. The authors propose ZeroSiam, a lightweight, asymmetric Siamese architecture inspired by self-supervised learning methods like SimSiam. The key idea is to process a feature from a single encoder pass through two branches: an \"online\" branch, which includes a learnable predictor before the classifier, and a \"target\" branch, which uses a stop-gradient on the original classifier output. The model is then trained to minimize the entropy of the online branch while simultaneously aligning its output distribution to the stop-gradient target branch. The authors claim this approach efficiently prevents collapse without requiring augmentations or extra backbone passes5. This claim is supported by theoretical analysis and extensive empirical results showing stable performance on vision-based test-time adaptation (TTA) tasks.", "questions": "Q1. Could the authors provide a direct comparison (e.g., for Table 3 or 4) where both TENT and ZeroSiam are run for only a small, fixed number of epochs (e.g., 1, 3, and 5) over the entire test set? \n\nQ2.  Does the alignment loss $D(p^o || sg[p^r])$ also grow indefinitely, eventually overpowering the entropy term $H(p^o)$? A plot of the individual loss components over time would be very insightful.", "limitations": "", "rating": 2, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "S1. The primary strength of this paper is the asymmetric, predictor-stop-gradient architecture (inspired by negative-free SSL) to the problem of test-time entropy minimization. While the components (predictor, stop-gradient) are not new, adapting this mechanism to stabilize a single-branch, entropy-driven objective is an architectural contribution.\n\nS2. The authors demonstrate the method's effectiveness beyond standard vision TTA by applying it to incentivize reasoning in large language models.\n\nS3. The organization and the writing of the paper are good. The motivation of the proposed method is natural. The paper is easy for reader to follow.", "weaknesses": "W1. The most significant weakness of this paper is the misrepresentation of the primary baseline, TENT. The original TENT paper and its open-source implementation are designed for online adaptation over a limited number of epochs (e.g., 1-5). It is well-understood that adapting indefinitely on an unlabeled, out-of-distribution data stream is inherently unstable. This paper, however, appears to run TENT for an excessive number of steps to induce the very collapse it aims to solve. This creates a \"strawman\" argument. The plots showing TENT's accuracy dropping to near-zero are a consequence of this unfair experimental setup, not necessarily an inherent flaw of the TENT method under its intended operating conditions. This experimental choice undermines the validity of the central empirical claims.\n\n\nW2. The paper's motivation states that \"minimizing entropy alone does not ensure that the corresponding supervised loss... is also reduced\". This is a trivial observation. The lack of ground-truth labels is the fundamental challenge of all unsupervised test-time adaptation. This framing slightly overstates the conceptual contribution by presenting a foundational premise of the subfield as a problem that this work is uniquely identifying.\n\nW3. The alignment weight $\\alpha$ is a critical hyperparameter that balances the original entropy objective with the new alignment regularizer. The paper fixes this to 1, claiming it works well without tuning24. While Table F provides a sensitivity analysis, this trade-off seems under-explored. It is likely that the optimal balance between exploration (entropy minimization) and stability (alignment) depends on the severity of the domain shift, which is hard to know beforehand.", "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": "GWJGmvCYSQ", "reviewer": "Reviewer_32Pf", "summary": "This paper proposes ZeroSiam, a method inspired by asymmetric self-supervised learning to address the collapse problem of entropy minimization-based approaches, where all predictions degenerate into a single one-hot vector regardless of the input. By introducing an asymmetric structure, ZeroSiam eliminates the need for additional augmentations and enhances efficiency through a single forward pass, effectively preventing model collapse.", "questions": "- In Figure 4, the sensitivity analysis of the learning rate is conducted using ViT-Base, where collapse does not occur seriously, making it difficult to fairly assess the robustness of learning rates across different approaches. \n- Moreover, different learning rates are applied to the predictor depending on the architecture, and the hyperparameters of existing methods are not fully optimized, which complicates fair comparison. If the predictor’s learning rate is treated as a tunable hyperparameter, wouldn’t it also be possible to alleviate the collapse problem in other entropy minimization methods by appropriately adjusting parameters such as the entropy threshold or learning rate?", "limitations": "", "rating": 8, "confidence": 5, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "- The paper presents extensive experimental results across a wide range of benchmarks. In particular, the experiments on the blind spot adaptation effectively demonstrate the limitations of entropy minimization methods when faced with incorrect initial predictions, thereby strengthening the motivation and necessity for the proposed method.\n- The paper addresses an important issue in test-time adaptation by improving inference time through a single forward pass without any augmentation. The utilization of all samples and the reduction in inference time enhance the practicality of the method for real-world applications.\n- The visualization of model collapse in entropy minimization (Figure 2) is clear, and the visualization of recovery possibility (Figure D in Sup. material) is intriguing and provides additional insight.", "weaknesses": "- Although the proposed method is shown to be applicable under various learning rates, the comparison may not be entirely fair since it also updates affine parameters similar to previos methods but applies a higher learning rate. For instance, in Table 5, it is unclear how the learning rate for LoRA was determined, as the optimal value for the proposed method could differ due to the influence of the projector module.\n- While the efficiency achieved through a single forward pass is acknowledged, there are concerns regarding the novelty of the approach compared to prior works that also draw inspiration from self-supervised learning and apply it to TTA. For example,\\\n[1] Self-Bootstrapping for Versatile Test-Time Adaptation, ICML 2025\\\n[2] Ranked Entropy Minimization for Continual Test-Time Adaptation, ICML 2025\\\n[3] Test-Time Ensemble via Linear Mode Connectivity: A Path to Better Adaptation, ICLR 2025\\\nFurthermore, [1] employed the self-supervised learning and [2, 3] addressed the model collpase problem. \n- Some typos should be revised. For example, u^r in eq(2) and u^o in eq (3) are not same to softmax(u_r) and softmax(u_o) (line 190), resepctively.", "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": "mUz7GOv1kP", "reviewer": "Reviewer_UrZX", "summary": "Entropy minimization in test-time adaptation often leads collapse into one-hot outputs without learning meaningful features. To alleviate this issue, the paper proposes to employ asymmetric siamese architecture inspired by negative-free self-supervised learning such as BYOL. More specifically, it simply adds a shallow linear layers of which outputs are trained to minimize the divergence with the target branch designed to have no gradients. The effectiveness of the method was demonstrated with extensive experimental results on both image and natural language reasoning benchmark datasets.", "questions": "1. How small is $L_f$ in practice? Wouldn’t it be arbitrary large for the worst case scenario? Also, I don’t quite understand the meaning of “Given that only the affine parameters of the normalization layers are optimized, this assumption is well justified.”\n2. Does the theorem hold when we update only on one sample? Or does it hold for any arbitrary number of inputs with random order?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "1. The proposed method is simple yet effective.\n2. It provides some theoretical support that shows convergence behavior.\n3. It was validated on extensive experiments for both image and natural language datasets compared to several state-of-the-art methods.\n4. Various ablation studies were provided.", "weaknesses": "1. It is not clear why it is beneficial to have large deviation from identity mapping and what exactly imbalance ratio is in Figure 2(a).\n2. Why is the inflation of logit L2 norm bad (according to Observation 2) in Figure 2(c)? Is there any theoretical connection between increase of logit norm and generalization ability?\n3. What exactly is center dominance in Figure 2(d)? How is it computed? How is it connected to generalization ability in the target domain? \n4. It seems like the experiments were run with one random seed. It is important to have standard deviation to compare significance of the difference between different 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)