Selective Label Enhancement Learning for Test-Time Adaptation
Authors: Yihao Hu
Congyu Qiao
Xin Geng
Ning Xu
Venue: ICLR 2025 Poster (2025)
Keywords: label enhancement
test-time adaptation
distribution shift
Primary area: transfer learning, meta learning, and lifelong learning
TL;DR: We propose the progressive adaptation with selective label enhancement framework for test-time adaptation.

Abstract: Test-time adaptation (TTA) aims to adapt a pre-trained model to the target domain using only unlabeled test samples. Most existing TTA approaches rely on definite pseudo-labels, inevitably introducing false labels and failing to capture uncertainty for each test sample. This prevents pseudo-labels from being flexibly refined as the model adapts during training, limiting their potential for performance improvement. To address this, we propose the Progressive Adaptation with Selective Label Enhancement (PASLE) framework. Instead of definite labels, PASLE assigns candidate pseudo-label sets to uncertain ones via selective label enhancement. Specifically, PASLE partitions data into confident/uncertain subsets, assigning one-hot labels to confident samples and candidate sets to uncertain ones. The model progressively trains on certain/uncertain pseudo-labeled data while dynamically refining uncertain pseudo-labels, leveraging increasing target adaptation monitored throughout training. Experiments on various benchmark datasets validate the effectiveness of the proposed approach.

Published as a conference paper at ICLR 2025
SELECTIVE LABEL ENHANCEMENT LEARNING FOR BEST-TIME ADAPTATION
Yihao Hu Hu,, Congyu Qiaol.2+, Xin Geng Ning Xu
1 School of Computer Science and Engineering, Southeast University, Nanjing, China 2 Key Laboratory of New Generation Artificial Intelligence Technology and Its Interdisciplinary Applications (Southeast University), Ministry of Education, China (yhhu, qiaocy, xgeng, xning) seuu. edu. on
ABSTRACT
Test-time adaptation (TTA) aims to adapt a pre-trained model to the target do- main using only unlabeled test samples. Most existing TTA approaches rely on definite pseudo-labels, inevitably introducing false labels and failing to capture uncertainty for each test sample. This prevents pseudo-labels from being flexi- bly refined the model adapts during training, limiting their potential for per- formance improvement. To address this, we propose the Progressive Adaptation with Selective Label Enhancement (PASLE) framework. Instead of definite labels, PASLE assigns candidate pseudo-label sets to uncertain ones via selective label enhancement. Specifically, PASLE partitions data into confident/uncertainn sub- sets, assigning one-hot labels to confident samples and candidate sets to uncertain ones. The model progressively trains on certain/uncertain pseudo-labeled data while dynamically refining uncertain pseudo-labels, leveraging increasing target adaptation monitored throughout training. Experiments on various benchmark datasets validate the effectiveness of the proposed approach. The source code is available httpt:::////m / con/ 1m-m1//AALLE
INTRODUCTION
Deep neural networks often experience performance degradation when the training and testing data drawn from different distributions. Test-time adaptation (TTA), an emerging paradigm that adapts pre-trained model to different domain using only unlabeled data during testing, aims alleviate this problem. As the practicality of TTA.
been successfully applied across various
fields, including autonomous driving (Wang et al. 2022 Volpi et al.) 2022). medical image seg-
mentation (He et al. 2021 Karani al. 202 and speech processing Kim et al. 2022 Lin al., 2022).
Most TTA approaches utilize pseudo-labeling- -abselig--based methods, which first assign pseudo-labels to the unlabeled target data and then adapt the pre-trained model to the target domain through train- ing on those pseudo-labeled samples. Some approaches utilize non-parametric classifiers to gen- erate pseudo-labels by measuring the distance between samples and prototypical representations (Iwasawa & Matsuo 202I) or leveraging neighboring feature similarities without model adaptation (Zhang et al. 2023). Other methods rely the consistency between prototype-base based pseudo-labela labels
pseudo-labels to guide model updates during adaptation (Jang et al.) 2023) Wang et al.) 2023] (Sun al. 2024). These approaches aim improve the robustness and perfor- mance of TTA by directly using definite pseudo-labels.
or neerest--eighhor-hhee
Due distribution shifts, most previous approaches inevitably introduce false pseudo-labels by adopting definite pseudo-labels. These approaches may experience significant performance dete- rioration. The definite pseudo-labels lose the uncertainty information of each class corresponding to the test sample, lcading to the fact that the unreliable pseudo-labels cannot be flexibly tuned ac- cording to the model's increasing adaptation during the learning process. Therefore, despite making
"quual contribution. Corresponding author.

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efforts in pseudo-labeling including prototype-base baste based Seaueet-neighhor-basse based methods, previous approaches usually do not fully unleash the potential of pseudo-labes labels for improving the performance of TTA.
To address this issue, instead of assigning definite pseudo-labels to test samples, we propose a novel framework named PASLE, i.e., Progressive Adaptation with Selective Label Enhancement. PASLE selectively assigns one-hot pseudo-labels to confident test samples or assigns candidate pseudo- label sets uncertain test samples in label enhancement process (Xu al. 2019 2020). Specif- ically, PASLE partitions test samples into confident and uncertain subsets based on the selective label enhancement strategy, where confident samples receive one-hot pseudo-labels, and uncertain samples are assigned candidate pseudo-label sets. The model is then iteratively trained on certain pseudo-labeled target data and uncertain pseudo-labeled target data in a progressive manner while dynamically refining the candidate pseudo-label sets of uncertain samples by exploiting the model's s evolving adaptation capability to the target domain, which is monitored during the training process. Our contributions can be summarized as follows:
We propose selective label enhancement strategy, where PASLE partitions test samples into confident and uncertain subsets based on the model's predictive confidence scores, with confident samples receiving one-hot pseudo-labels and uncertain samples being assigned candidate pseudo- label sets.
We introduce a progressive learning framework that trains the model on certain pseudo-labeled target data and uncertain pseudo-labeled target data in progressive manner while dynamically refining the candidate pseudo-labe sets of uncertain samples by exploiting the model's s evolving adaptation capability the target domain, which monitored during the training process.
We theoretically establish generalization bound for TTA and assess the effectiveness of pseudo- labels by quantifying them through the pseudo-label error term.
2 RELATED WORK
Test-time adaptation. Domain shifts often cause machine learning systems to suffer substantial drops in performance. To address this challenge, numerous techniques have been developed to enhance model robustness against distribution shifts. Domain generalization (Zhou et al. 2022) attempts train a model on data from one or more source domains, enabling it to generalize effec- tively to unseen target domains. Domain adaptation (Kouw & Loog] (021)) relies on transductive learning, where knowledge from a labeled source domaín is transferred to an unlabeled target do- main. Test-time adaptation (Liang et al. (025)) differs by allowing pre-trained model to adapt to a target domain using only unlabeled test data. Our research centers on online test-time adap- tation (OTTA) (Wang et al. (2024), scenario where test data from the target domain is presented sequentially, requiring real-time adaptation.
Recent advancements in OTTA have explored various strategies. Some methods (Wang et al. 2021 Gong ct al. 2022, Mirza et al. 2022; Zhao et al. (002) focus on batch normalization (BN) calibra- tion since BN layers can incorporate domain-specifie knowledge through the normalization statistics
they learn Li et al. 2017b). Several strategies (Zhang et al. 2022 Jing et al. 2022] Niu et al. 2023
Lee et al. 2024) place emphasis entropy minimization, aiming encourage more confident and distinct predictions by reducing the uncertainty in the model's 's output. Numerous approaches focus on pseudo-labeling. where the model generates pseudo labels for unlabeled data and performs self- training to improve its performance. [wasawa & Matsuo (202T) create a pseudo-prototypee for each class and classify new samples based on the distances. Goyal et al. (2022) introduce a self-training method that utilizes specialized soft label known as the conjugate pseudo label. [Shin et al. (2022) introduce a selective fusion strategy to ensemble predictions from multiple modalities. Meanwhile, Yang et al. (2022) generate soft pseudo labels by averaging the predictions of neighboring samples stored a memory bank. Döbler et al. (2023) use symmetric cross-entropy loss to enforce predic- tion consistency between the teacher and student model. Similarly, Jang et al. (2023) aim to reduce divergence between predictions from prototype-basee based and neighbor- based classifiers. |aan et al. (2023) propose test-time self-distillation for feature uniformity and memorized spatial local cluster- ing for feature alignment. [Sun et al. (2024) combine prototype-base and neighbt methods through a prototype graph model to enhance pseudo-label generation.
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Uncertainty modeling. The previous methods within unsupervised domain adaptation source- free domain adaptation build up the uncertainty at the model or sample level. For example, at the model level, Zhan et al. (2023) leverage Monte Carlo dropout, and Lao et al. (202I) apply deep ensembles. At the sample level. Liang et al. (2020b); Roy et al. (202)) generate weights using prediction entropy, while Litrico al. 2023) derive them by analyzing consensus among neigh- boring samples. TTa et al. (2024) capture both model uncertainty and sample uncertainty using sub-network. Our proposed method models the uncertainty at the label level through candidate pseudo-label sets, where the uncertainty is directly manifested through the cardinality of the can- didate pseudo-label set. Compared existing approaches. our method imposes no constraints on pre-trained models and does not require additional computations during inference, making it partic- ularly suitable for OTTA scenarios.
PROPOSED METHOD
3.1 PRELIMINARIES
To begin with, some necessary notations are briefly introduced. Let X' = R denote the q- dimensional instance space, y = (1, .. the label space with class labels, and - be the c-dimensional probability simplex. A pre-trained predictive model f f: X' + e with param- eters O is initialized to @ on a dataset from the source domain S, i.e. Ds = {x,,, y:) i n} where æ; E X' denotes the g-dimensional instance, Vi Y denotes the correct label annotated to I; and each example (I;, y4 is sampled from the distribution ps (at y). During test-time inference, the predictive model f:: @) streamingly receives R. mini-batch datasets from the target domain T. At the r-th step, the received dataset is denoted by D = { 1 I i m²) where the received instance af X and its unobserved correct label y from the misaligned distribution pr (r, y) with ps (x, y). i.e., (r v) # ps y)- The goal of OTTA is to continuously update the parame- ters θ of the pre-trained predictive model f to obtain the maximization of the following cumulative accuracy on R mini-batch datasets from the target domain T':
R E
RE UV arg max (z) [T)]
Aco(f,T)=
Σ m
where O" is the updated parameters of the model I at the r-th step, and [[:] is the indicator function. To achieve this goal, the process of progressive label enhancement in our framework introduces pseudo-labels through soft labels output by the predictive model to handle the absence of correct labels during adaptation. The pseudo-label of the testing instance x; is denoted by a logical label
vector 17- = 11 m
1T E [0, and the corresponding soft label is denoted by a vec- 1T9T = [fi O"), f2(x=;; e"), fa(::;: @*)] E [0, 1] satisfying the pseudo-label of the testing instance x!! is one-hot
tor di = [d
2
Σj=1 de labud.-label. When 1 "ーー14 4. < the pseudo-label of the testing instance x; is candidate
When Σj=1 1
pseudo-label set. Besides, we prepare buffer D" initialized by 3 with maximum size K to save the received instances not used at the r-th step.
3.2 OVERVIEW
Our framework trains the predictive model with the optimization objective on the split confident sub- set with one-hot pseudo-labels and the uncertain subset with candidate pseudo-label sets, which are constructed by selective enhancement strategy using a dynamic threshold. This strategy follows the derived proposition about uncertainty information. Also, we select and incorporate the received instances that are not used at the current optimization step into the prepared buffer for subsequent use. Finally, as the predictive model becomes increasingly aligned with the target domain distribu- tion, the threshold will decrease to progressively refine the pseudo-labels. In this way, we unleash the power of pseudo-labels in OTTA and improve the performance of the predictive model. Theoret- ically, we demonstrate that our framework achieves tighter generalization bound by incorporating more target domain instances and evaluates the effectiveness of pscudo-labels by quantifying them through the pseudo-label error term.
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3.3 THE PASLE FRAMEWORK
First of all, we introduce the overall objective L of the PASLE framework employed to optimize the predictive model parameters @--1 r-th step:
L
Σ ID DEDH
Σ "(((a';0r-))1))) 1Dial x'EDM M
(2)
where -) the loss function handle each instance æ from the confident subset Djr with its one-hot pseudo-label I while -"(--)) is the loss function to handle each instance x' from the uncertain subset Dir with its candidate pseudo-label I', and represents the cardinality a set. Practically, .(::)) is instantiated as the cross-entropy loss, which has been widely used in supervised learning tasks, while (.).)) is instantiated as the classifier-consiseen loss proposed by Feng et al. 22020
((((=")))));))) - log Σ 1 fa 0
(3)
j=1
which has been validated to deal with candidate labels effecttvvlyy
Note that Eq. (2) model the uncertainty information based on the confident subset Di, and uncertain subset Di which are split from the received dataset Di and the buffer dataset -3"-1" The confident set Dr contains the instances whose correct labels could be determined, while the uncertain set DM, contains the instances whose correct labels could be only determined among some candidate labels. Hence, we assign the one-hot pseudo-label / to each instance x E D and the candidate pseudo-label l' to each instance x' E Di..
Then, a selective label enhancement strategy is induced by the following proposition to construct the confident subset Di, and uncertain subset 2hr by utilizing soft pseudo-labels, generating the one-hot lseudo-label for each instance a Dir and candidate pseudo-label l' for each instance xx DM
Let O be the optimal parameters learned from supervised data from the target domain T, i.c., er arg mine (pp.)))) Uarg maxjey (ar; +) * U)], f(x; θ*) the class-posterior probabilities for the instance on the target domain T. i.c., (=; θ*) pr = j|æ),, p rep- resent the class the highest score of the soft label d;, i..., p = arg maxjey de' and g denote the class with the second-highest score of the soft label d;, i.e., arg maxjex de We provide the following proposition.
Proposition 1 Assume that at adaptation step r, the difference between f(: O²) and (') on (r)),, vj E y. For any
the instance at is bounded by (r), i.e., 15, (af;; Qr) fy(x;;; 5 S a, in the unlabeled data butch Dt,, if d d.3 > Tr)), then j cannot be the correct label of wi Furthermore, if d.. -.."" > Tr)), then p is the correct label of wç.
The detailed proof can be found in the Appendix A On the one hand, Proposition D provides a condition under which the label with the highest predicted score is guaranteed to be correct, allowing for the accurate assignment of a pseudo-single label to a part of the unlabeled samples. Hence, we could split confident subset Dj from the received dataset D and the buffer dataset 1 based on the soft label of each instance and the threshold r(r) at the r-th step:
D4 = ta|Ø E DG U B - d T(r)).
(4)
After splitting the confident subset Djr, we generate the one-hot pseudo-label for each instance Dj, follows:
1, if = pand d' > T(r).
1 = {o. otherwise.
(5)
On the other hand, Proposition [rppositionnppoviieee provides condition under which the label with the low predicted score is guaranteed to be incorrect, allowing for the ambiguous assignment of candidate pseudo- labels to part of the unlabeled samples. Hence, could split uncertain subset Dr, from the
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Algorithm PASLE Algorithm
Require: The pre-trained predictive model f(: O²), total adaption steps R, initial threshold Tstart end threshold Tena. threshold descend constant Tdes, buffer maximum size K;
r(1) < Tstart
2: Initialize the buffer 18" as empty;
3: for = .. do
4: Obtain the confident subset Di and uncertain subset Dār according to Eq. 4 and Eq. (6);
5: Generate the one-hot pseudo-labed I for each instance a E Di using Eq. (5 and the candidate
pseudo-label l' for each instance x' Dis using Eq. (7);
6: Optimize the predictive model parameters @" to e based on Eq.
7: Update the buffer - B following Eq. (8)
8: Adjust the threshold according to Eq.
9: end for
Ensure: The predictive model f(:: O).
received dataset D and the buffer dataset - based on the soft label of each instance and the threshold r(r) at the r-th step:
Dír (x'l0' DJ LU "Ej E y, d d0 T(r)}.
(6)
After splitting the uncertain subset Dir we generate the candidate pseudo-label l' for each instance x' Dj based on the corresponding soft label d' and the threshold ((r) at the r-th step as follows:
0, 1 = (1, otherwise.
df d' > T(r).
Besides, for the received instances which are not used in Eq. ( i.e. (B UD P1)) ), we intend store them in the new buffer B". If the number of samples be stored exceeds the buffer's maximum size during the algorithm's 's operation,
prioritize retaining the samples with the top-K largest margins, as these are likely to contribute to the model's updates carlier. The margin of an instance is defined p(x) d" d Denote Pk the top-K largest margin of the instance formulated as follows:
x E (Dr, U 1)- (Dz U at adaptation step r. Then, the sample selection process can be
B" = {x| E (Dz PBBBB"11 \ (Dr, U DDM) > pk}.
(
where the buffer's maximum capacity is restricted to quarter of the target domain batch size in practice, considering resource consumption.
Finally, since the model becomes increasingly aligned with the target domain distribution as adap- tation progresses, the gap between the scoring function f(; O²)) and the class class- posterior probability f(;:0') O*) supposed to gradually decrease. Hence, to improve the reliability of pseudo-labels, the threshold r(r) is manually reduced over time. In practice, r(r) is initialized at starting value when r = and is gradually decreased by a constant value Técs each step. This process continues until r(r) reaches a predefined lower bound Tand- The adjustment of r(r) can be formulated as:
T(r) = max maxx(T(r- - 1) - Tdes, Tend
In this way, the PASLE framework successfully leverages the uncertainty information and flexibly tunes pseudo-labels according to the model's evolving adaptation capability, thereby unleashing the potential of pseudo-labels and improving the performance of TTA. The algorithmic description of PASLE is presented in Algorithm
3.4 THEORETICAL ANALYSIS
3.4.1 A GENERALIZATION BOUND FOR TTA
We theoretically establish a generalization bound for TTA that by incorporating a greater number of target domain samples with effective supervision, tighter generalization bound can be achieved.
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Suppose that at the r-th step of adaptation, the classifier h receives m" samples. Given the possibility of overlap between the source domain and the target domain, we assume (1 - 5)m" samples are drawn from S, and the remaining 3m" samples are drawn from T. The goal of the classifier is to find a hypothesis that minimizes the target error er (r.)). We focus on classifiers that minimize a convex combination of the empirical errors from the source and target domains (Ben-David al. 2010), defined as:
(h) aêr (h) + (1 (h)
(10)
where E [0,1]. 1]. The corresponding weighted combination of the true source and target errors is denoted by ea (h). To quantify the distributional difference between the source domain and target domain, the disparity discrepancy introduced by /Zhang et al. (2019).
Definition 1 Given hypothesis space H and specific classifier h H. the Disparity Discrepancy induced by E H. is defined by
dp, H (S,7) & sup (dispr (h', h) - disps (h', h))
N'E
(11)
sup M'E
(E,I [N' * h] E [h' + hl)
Based on the above assumptions and definition, we derive the following theorem.
Theorem Lei H be a hypothesis space of VC dimension d. Let S and T be unlabeled sample sets of size m' each, drawn from and respectively. batch of samples of size m is generated by random sampling at the r-th step of adaptation. Given the possibility of overlap between the source domain and the target domain, we assume (1 -3mm samples are drawn from S, and the remaining 3m" samples are drawn from T, which then labeled with the true labeling function. For simplicity in theoretical analysis, we allocate the loss weight proportionally to the number of samples from each domain, specifically setting a and B to be equal. If E H is the empirical minimizer of (h) on this batch and hT- minSEH (T(h) the target error minimizer. then for any 8 >> O, with probability at least - 28.
2d log(m22 + 1)) + 2 2log (
er(h) S ET (hT) + +4V
m
(12)
eny' 2d
log 2m
2 B
+ 2(1 - 9) (n. + +2
4d m'
+ 2
+ x
where À = errs (h*) + errr (h*) and h" arg min (errs(h) + errr(h)) heH
The proof of Theorem is provided in Appendix Theorem provides a generalization bound on the target domain for the empirical minimizer on the given batch. Suppose also have some target domain samples annotated with effective supervisory information provided alongside the well- annotated current data batch guide the model's adaptation. In that case, the empirical minimizer's generalization bound on the target domain becomes tighter. Since the growth rate of the upper
bound's second term is O(V log m ), it decreases as more samples are incorporated into training.
Moreover, the number of target domain samples increases, B will also increase, resulting in reduction of the third term in the upper bound.
3.4.2 PSEUDO-LABEL EFFECTIVENESS QUANTIFICATION
Next, we assess the effectiveness of pseudo-labels by quantifying them through pscudo-label error terms for TTA. Assume that during timt-time inference, the predictive model streamingly receives R mini-batch data from the target domain T, accumulating a dataset DR over R mini-batches, with a total sample size of N For a target domain sample æ. let its Bayes class plass-probabilityy distribution be denoted as p PP (ya æ) P (V2 x) ..... P (ve x)), and its supervision information provided by the algorithm be denoted as (here it refers to the label distribution). We have the following theorem.

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Theorem 2 Suppose the loss function E is bounded by M, i.e., M Fe Fix a hypothesis class F of predictors f : X + IR, with induced class H C [0, 1] of functions h(æ) = é (f (mx4,, q). Suppose H has uniform covering number Nun. Then for any â E (0, 1), with probability at least
([f(()))))
MrR log NR
log Ma
R(F) R(f) & MVC. 1lq pll2)) +
(
+
(13)
NR
where Mya Nint NR: H. and (f) is the empirical variance of the loss values.
The proof of Theorem 2 is provided in Appendix C Theorem 2 demonstrates that the target domain samples' label distribution q provided by the algorithm becomes closer to the Bayes class- probability distribution p. the gap between the empirical risk and the expected risk on the accu- mulated dataset D will decrease. The effectiveness of the supervision information can be quan- tified by the degree of closeness between its corresponding label distribution and the Bayes class- probability distribution and the pseudo-label error term is TE []q p pll2]. Our algorithm provides one-hot pseudo-labels when it is more certain about the samples and candidate pseudo-label set when it is uncertain. These actions can make the corresponding pseudo-labels' label distribution closer the Bayes class-probability distribution, thereby making the empirical risk more closely aligned with the expected risk and thus better guiding the model toward adaptation to the target domain.
EXPERIMENTS
4.1 DATASETS
Following recent works in OTTA (Jang el al. 2023 Wang el al.
2023 Sun et al. 2024), we use do-
main generalization datasets and image corruption datasets to evaluate our method. We employ four domain generalization datasets including PACS (Li al. 2017 VLCS (Torralba & Efros 2011),
off ceHome /Venkateswara al. 2017), and Doma neet (Peng et al.) (219)). Doma i nNet is a large-scale dataset with 586,575 images across 345 classes, covering six domains: clipart, info- graph, painting, quickdraw, real, and sketch. For source training, we designate one domain as the
target and use the remaining domains as source domains. We allocated 20% of the data from the source domains for validation purposes.
Additionally, we employ two image coruppiion datasets: CIFAR-10-C and CIFAR-100-C
[Hendrycks & Dietterich 2019). Both datasets introduce 15 types common image corruptions, categorized into four types: noise, blur, weather, and digital, to the test of CIFAR-10 and CTFAR-100 (Krizhevsky) (009). We use the training sets of CIFAR-10 and CIFAR-100 00 as source domains and the highest level of corruption in CIFAR-10-C and 1MFAAR-100-2 tar- get domains. The validation set partition follows the same approach as that used for the domain generalization datasets.
4.2 BASELINES
We compare the performance of PASIE with ten OTTA approaches.
ERM (Vapnik
1998): A standard approach that directly outputs the model's predictions without
adaptation.
A BN calibration approach that replaces the activation statistics estimated by BN layers on the training set with the statistics of the target domain images.
BN (Schneider al. 2020
TENT (Wang et al. 2021): An entropy minimization approach that optimizes channel-wise affine transformations by reducing the entropy of model predictions on target domain data.
P1. (Lee 2:13): A pseudo-labeling approach that fine-tunes a pre-trained classifier by leveraging connident pseudo-labels derived from the model's predictions.
SHOT-IM (Liang et al., (020a): An information maximization approach that refines the source encoding module by maximizing the mutual information between intermediate feature represen- tations and the classifier's outputs.
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Table Classification accuracy of comparing methods on domain generalization datasets.
Methods
Back
PACS
VI.CS
OfficeHome
DomainNet
Avg.
ERM
79.37
75.14
62.43
35.76
63.18
BN
83.08
68.79
62.29
34.95
62.28
TENT
83.23
69.28
62.51
35.37
62.60
PL
85,66
74.68
62.71
35.24
64.57
SHOT-IM
83.02
70.80
63.91
35.92
63.41
T3A
81.70
75.83
63.90
36.31
64.44
ResNet-18
TAST
84.31
71.69
63.96
35.71
63.92
TAST-BN
86.35
75.17
62.43
35,82
64.94
TsD
87.88
75.47
63.42
35.86
65.66
PROGRAM
83.57
71.64
63.35
35.97
63.63
DEYO
86.26
74.91
63.30
35.37
64.96
PASLE
88.16
77.91
63.99
36.89
66.74
ERM
85.84
76.06
67.84
43,16
68.23
BN
86.00
67.76
66.82
41.50
65.52
TENT
86.51
68.41
67.27
42.38
66.14
PL
85.66
73.80
67.31
42.38
67.29
SHOT-IM
85.27
68.49
67.89
43.41
66.27
T3A
86.54
76.59
68.85
44.00
69.00
ResNet-50
TAST
86.94
67.32
68.70
42.84
66.45
TAST-BN
89.47
75.59
67.97
43.03
69.02
TsD
91.13
74.77
68.97
42.44
69.33
PROGRAM
86.16
68.85
68.03
43.34
66,60
DEYO
88.23
71.59
68.08
42.47
67.59
PASLE
91.36
78.70
69.37
44.91
71.09
Table 2: Classification accuracy of comparing methods on image corruption datasets.
Methods
CIFAR-100-C CIFAR-I0-C
ERM
20.66
5.84
BN
75.33
43.88
TENT
75.41
43.93
75.70
44.24
SHOT-IM
75.85
44.36
T3A
23.52
6.74
TAST
74.13
39.21
TAST-BN
74.56
31.84
TSD
75.14
44.19
PROGRAM
75.00
44.06
DEYO
75.74
44.28
PASLE
76.67
45.32
T3A [wasawa & Matsuo 2021 : A pseudo-labeling approach that predicts test data labels by measuring the distances between the test samples and sseudo-prototyper
TAST (Jang et al. 2023): A pseudo-labeling approach that updates the model by matching the nearest neighbor- based pseudo label and prototype- based class distribution for the data.
TAST-BN (Jang et al. 2023): A pseudo-Labeling approach, which is a modified version TAST and refines the model by adjusting the parameters of the BN layers.
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3000
PARLE-NX
Classification accuracy (mean = std) of PASLE and its variant on target do- mains of the ceHoee dataset. The best performance shown in boldface.
Table 3:
Sample utilization
2500
1500
Domain
PASLE
PASLE-NC
1000
A
56.11 07.25
300
51.30:10.41
50.85+0.68
P
73.31+1.004
72.13+1.43
74.10+00.20
73.87+00.45
Step
Figure 1: Sample utilization during testing.
TSD (Wang et al. 2023): A pseudo-labeling approach that employs dynamic memory bank to compute class prototypes and generate pseudo-labels for refining the model.
PROGRAM (Sun et al., 2024): A pseudo-labeling approach that leverages graph structure that connects prototypes with test test samples, allowing information to flow between them and enhancing the generation of lscudo-labels.
DEYO (Lee al. 2024) An entropy minimization approach that updates the model by minimiz- ing the model output's s entropy of samples with low entropy and high PLPD value concurrently.
We evaluate all methods domain generalization benchmarks using ResNet-18 and ResNet-50 models (He et al. 2016), both equipped with batch normalization (loffe Szegedy 2015). For image corruption benchmarks, employ ResNet- 18 the backbone model.
For source training, the models are trained using the Adam optimizer with a learning rate of 5e 55 for domain generalization benchmarks and 1 for image corruption benchmarks. All weights initialized from ImageNet-1K (Russakovsky et al., (015) pre-trained models. We select the final pre-trained model with the highest validation accuracy.
During testing, we also utilize the Adam optimizer to update all trainable layers without the need for specific selection. The batch size for the online target domain data is set 128, with the buffer capacity K set to one-fourth of the batch size, i.e., 32. The learning rate is selected from the range between le 3 and le The value of Tstn is determined by the number classes each dataset: for example, VLCS contains 5 classes, while Doma nNet. has 345 classes, leading to different Tuan values for each dataset. The threshold gap, represented as T Tenal, is consistently set at 0.1. Furthermore, Tds is uniformly set to 1e 1e-3 for all datasets, except for the large-scale dataset DomainNet where it is adjusted to 14_ It is essential to highlight that all hyperparameters for the OTTA setting finalized prior accessing any test samples. We meticulously select the most suitable hyperparameters for each algorithm based on their performance on the training domain validation datasets (Gulrajani & Lopez- Paz 2021 Wang al. 2023
4.3 EXPERIMENTAL RESULTS
We conduct trials with different random seeds, reporting both the mean and standard deviation of the metrics, with full results detailed in Appendix E Each method's classification accuracy across datasets' target domains is summarized in Table and Table 2 The best performance shown in boldface, and the second-best result is underlined. It is impressive to observe that:
PASLE achieves best performance across benchmark datasets and network architectures, outperforming all the compared upproaches.
PASLE consistently enhances the performance of the classifier domain generalization bench- marks, achieving an average improvement of 5.63% for ResNet-18 and 4.19% for 550
PASLE outperforms the second-best methods on image corruption benchmarks, with an average performance gain of 1.08% CIFAR-1 0-C and 2. 1.6 on CIFAR-1 10-C..

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Published as a conference paper at ICLR 2025
12b
PROGIAM Deva PASLE
Test Acturacy
Test Accuracy (%)
76-
0,5
0.88
1.00
Tatut
0.5
16
32
125
25c
Batch Size
(a) sensilivity Tean and Tend on CIFAR-IC-C. (b) The sensitivity batch size on CIFAR-10-C.
Figure 2: The parameter sensitivity analysis for PASLE.
Especially, find that PASLE significantly improves the performance of the pre-trained classifier on the Doma i nNet benchmark, which a large-scale dataset, indicating that PASLE holds strong potential for real-world applications.
4.4 FURTHER ANALYSIS
To demonstrate the effectiveness of the candidate pseudo-labels in PASLE, conduct abla- tion study using a vanilla variant, PASLE-NC. In PASLE-NC, all samples annotated with candidate pseudo-labels are excluded from model updates. As shown in Table 3 PASLE outperforms PASLE- NC on all target domains of the Offi ceHome dataset with ResNet- 18, highlighting the importance of candidate pseudo- labels in further improving performance during the testing phase.
Furthermore, Figure shows the sample utilization during the testing process for both PASLE and PASLE-NC on the clipart domain of Of ceHome dataset. evident that PASLE utilizes more effectively labeled samples than PASLE-NC as testing progresses, which further explains PASLE'S better test-time adaptation performance.
Besides, we perform parameter sensitivity analysis to examine the impact of two hyperparameters Tstat and Tend on our algorithm using the shot noise corruption of CIFAR-10- 0-C dataset. Tatan and Tend are assigned various values as illustrated in Figure 2(a) with Táes being set to R specifi- cally for the purpose of sensitivity analysis. Clearly, the performance of PASLE remains relatively stable across broad range of each hyperparameter. This robustness is highly desirable, as the PASLE framework consistently delivers reliable test-time adaptation performance.
presents the average accuracy of various methods across different batch sizes shot noise corruption CIFAR-10-C dataset. As depicted the figure, our approach consistently outperforms the other methods under varying batch sizes. This robust performance makes PASLE well-suited for deployment in practical scenarios, where the batch size of real-world data streams fluctuate significantly.
Figure 2(b]
More discussions of PASLE can be found the appendix D
5 CONCLUSION
In this paper, we focus on test-time adaptation and introduce novel framework, PASLE, which selectively assigns one-hot pseudo-labels to confident test samples and candidate pseudo-label sets to uncertain test samples through label enhancement process. The model is then progressively trained on both certain and uncertain pseudo-labeled target data. Throughout this process, the candidate pseudo-label sets for uncertain samples are dynamically refined by leveraging the model's evolving adaptation to the target domain, which continuously monitored during training. Experiments on various benchmark datasets demonstrate the effectiveness and robustness of the proposed approach.
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ACKNOWLEDGMENTS
This research was supported by the Jiangsu Science Foundation (BG2024036), the National Science Foundation of China (62206050, 62125602, and U24A20324), the Fundamental Research Funds for the Central Universities (2242024k30035), and the Big Data Computing Center of Southeast University.
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A PROOFS OF PROPOSITION 1
According to the assumption of Proposition 1 we have the following bounds for fp(x;; (*) and fy(x;:
fp(a;;0") 1 7r) fr (1) 0)) (-) T(),
(14)
[5(();0)) -27(r) (, θ*) [, θ-) (())
(15)
Subtract inequality 15 from inequality 14 we can deduce that:
63" dee fp 6*) faf θ²) S fp(x); fa 0-) +r()).
(16)
Now, if dr d, > (r)), then it follows that:
(r) < fo(=f; fy +*)))))))))))))
(17)
which simplifies to:
1,(0000)) < fp(af;
(18)
Therefore, cannot be the true label of æç.
df te > Tr), then y cannot the true label ay. Moreover, for any j E 3 \ {p, q). follows that d," d.d > T(r), since d. < d. As result, none of the labels in ) {p} can be the true label of æç Therefore, given df d. T(r), p must be the true label of a;. The proof is completed.
B PROOFS OF THEOREM
Suppose that the r-th step of adaptation, the classifier receives m" samples. Given that the source domain and target domain may overlap, we assume (1 8)m² samples are drawn from S, and the remaining 3m" samples are drawn from T. The goal of the classifier is find a hypothesis that minimizes the target error (h)). We focus on classifiers that minimize a convex combination of the empirical errors from the source and target domains (Ben-David et al. 2010), defined as:
e. (h) = aêt (h) + (1 - (h),
(19)
where a E [0, 1]. The corresponding weighted combination of the true source and target errors is denoted by ca (h).
To quantify the distributional difference between the two domains, we use the disparity discrepancy introduced by Zhang et al. (2019).
Definition Given a hypothesis space H and specific classifier H. the Disparity Diserepancy induced by h E H is defined by
dr.H (S,T) A sup (dispy (h', h) disps (h,h)) h)) иER
(20)
sup (E, [ + h] EgI [h' + hl)
MEH
In domain adaptation theory David et al. 2010), the symmetric difference hypothesis space is commonly defined follows:
Define HAH & th h- h & b2 b1 f2 E H. as the symmetric difference hypothe- sis space of H, where & stands for the XOR operator.
Definition 2
We begin by establishing an upper bound on the difference between the target error Ey and the weighted enror (h).
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Lemma Suppose (s(h) - (x.) For any classifier h, we have:
(h) - <r(h)) S (1 - a) (t,, T) + X],
(21)
where x = errs (h*) + errr (1*) and ht arg min {errs (h) + errr(h))
kEH
Proof.
(T(h))
= (1 a) (1) - cT(hi]
$ (1 a) [ETT [h' + EEl [h* + ht) + (es (hh) + ter (h)))]
- (1 a) sup (dispr (1/, disps (K',h) +
+ 1
(22)
LNEE
(1 a) (S, X1
Then, we introduce an upper bound on the difference between the empirical and expected disparity discrepancy.
Lemma 2 Denote S and T the empirical distributions of datasets with and n instances sampled from S and T, respectively. For any ô >> O and binary classifier h E H. with probability 1 - 26,
log 2m
log 3
sup kCH
(d..))))dd < 2m. (HA.s(HHH))+HH
+V
22 (H.H))
(23)
2n
Proof.
ds, (s,n((ST))
sup (dispr (V' h) disps h)) sup (dispy (h", h) disp3 h))
KCHH
W'EH
(24)
S sup (dispr (W/, It) - disps (h', h) dispp (h', h) + dispg (h', MEN
S sup (dispr (h', h)) dispæ (V, + sup (disp3 (h" hh) - disp (h", h)) WEEH
WEH
Take supremum over h E H. we have:
sup (n.,((S - (3.
NEH
< sup
dispp (h', hb) - disp (h] + sup
|ispp (h" h)) disp (h", [)]
N.MEH
h.W"EH
Eri [h' # h] E31 1h' + hi]l
Es # h] EgI [h' # hil
sup
sup AW
N.VEE
sup 9ENAH
Eg.1[g + 1| - E + 1| +
sup S'EAAH
EgI[g' * 1] - E3'lo' + i|
(25)
sup VEHLH
Erg Ezgl + sup d'EHAR
Esg' Egg'
log CR.,.(HAHH +
log
< mms (HA.s(HHH) +
2m
2m
The following lemma provides probabilistic bound on the difference between the empirical and true error rates of the classifier h.
Lemma 3 A batch of samples of size m is generated by taking 3m sumples from T and (1 9)m samples from S, and then labeling them with the true labeling function g(az). Then we can have:
-2me
Pr (r( - (a)) 2052280
(26)
a²
+
(1a)
1-3
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Proof. Let .1....;; represent random variables corresponding to the 3m samples T, taking values:
a 3
[b(x)) g(x)
(27)
Similarly, for the remaining (1 - mm samples x E S, let 1. Fm be random variables that take on the values:
1 - a (h(z)) g(x))
(28)
1 3
The empirical weighted error (h) can be expressed
&o (h) (εr(h) + - (h)
a
Σ [M(x)) - g(a²) + (1 a) (1 3mm
Σ
(1xx))
g(x))
m
Tz-
(29)
3m PET
m
wES
Applying the linearity of expectation, have:
E [E)( 1 ( Bm 3 TeT(h) + (1 3)m 1- a
1- B Es(h) =acr(h) + (1- ca))
(30)
Im It is important to note that 2,,..., Jm E [0, 3] and res+ mm E [0, 1= Thus, Hoeffding's Incquality can be applied as follows:
2m
Pr (h) ca (h)) 2 c] S 2 exx
i== range 2 (3:;)
-2m2222
-2m
2 2exp
2exp
Bm 103
2 + (1 -m)m
1-a
a²
1
+
(1-a)a
1-8
(31)
Building on the above definition and lemma, derive the following theorem:
Theorem Let H. be a hypothesis space of VC dimension d. Let S and T be unlabeled sample sets of size m' each, drawn from S and T respectively. batch of samples of size m generated by random sampling at the r-th step of adaptation. Given the possibility of overlap between the source domain and the target domain, we assume (1 11-3)m² samples are drawn from S, and the remaining 3m2 samples are drawn from T, which are then labeled with the true labeling function. For simplicity in theoretical analysis, we allocate the loss weight proportionally to the number of samples from each domain, specifically setting a and to be equal. If h E H. is the empirical minimizer of (h) on this batch and hy minneH er(h) is the target error minimizer. then for any 8 > O, with probability at least 25.
2d log(2(m + 1)) + 2 log (1)
(T()) S cT (h+) + +4\
m
(32)
2d log
em!
log 2 2m +
+ 2(1 - 3)
dn.x((.T) + +
+ 2\
m'
Proof. According to Lemma
we have:
(T()) s (n) + - (S,T)
(33)
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By applying Lemma
we deduce that:
er(h) S Ea (h) + 2
a²
+
(1 a)2
2d (2 +1) + 2 llo (1)
+ -111aa) a) (da (S,
B
B
m
a²
(1 a)²
2d 2d + 1)) 2 2log (3)
Lo (a(i)
(1 ai) (dh, (o (5,T) X)
1
m
a²
(1 ax2
2d (2 + 1)) + 2 2log (3)
S (h7)
+4
+ (1 - a) (d (S, X).
3
1
m
(34)
Based on Lemma we obtain:
o²
(1-a)²
2dlog(2 1)) + log (4)
(h) & er (hT) + 4
+
3
1-
m
log 3 2mn
log
+ 2(1 aa) a)
(5, 2 (HAH)
+ 2m r (HAH) +
2mn'
(35)
According to Lemma aad Mohri al. (0112), follows that:
a²
(1 a)²
2d Adlo((2(m) + 1)) + 2 log (+)
eT(hi= S ET (17) + 4
+
3
1- 3
m
(36)
sm 2d log m'
log 2/2 2m'
+ +2(1 - a)
ds. + +2V
4d
2
t2)
If we allocate the loss weight according to the number of samples, that is, setting B, we can conclude:
2d log(2(m" + 1)) + 2log (1)
(T()) S cr (h+) +4V
m
(37)
2d m'
em id
log e + ) 2m'
+ 2(1 - 8)
(). 2
+ 2\
This completes the proof.
C PROOFS OF THEOREM 2
First, let Ry = E R ( Then, following the results in Maurer & Pontil 22099, which
provides a uniform convergence form of Bennett's inequality (Bennett) 1962), we can denve:
Rr()) (VVCO)
(V log MyR N N
log MyR
(38)
Moreover, the following holds:
Rv(()) - [Rv(C]]] -E [ $ EE[l pl|2
(ʃ ( (39)
j=1
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Table 4: Running time of different methods on the clipart domain of the Doma i neet dataset.
Table 5: Classification accuracy of PASLE under broader parameter range on the CIFAR-10-C dataset.
Methods
Time (s)
ERM
19.54
Tstert
Tend
Acc
BN
21.03
0.9
0.8
77.90
TENT
57.23
0.8
0.7
77.97
PL
77.94
0.7
0.6
77.96
SHOT-IM
77.02
0.6
0.5
77.99
T3A
46.57
0.5
0.4
77.89
TAST
86.89
0.4
0.3
77.84
TAST-BN
128.46
0.3
0.2
77.84
TSD
105.55
0.2
0.1
77.79
PROGRAM
113.58
DEYO
92.49
PASLE 99.28
Table 6: Classification accuracy of PASLE and its variants (PASLE-NB and PASLE-NR) on the OfficeHome dataset. The best performance is shown in boldface.
Methods
A
C
P
R
PASLE 57.25
51.3010.41
73.31
74.10:10.20
PASLE-NB 56.98=0.82
51.1410.44
73.00:10.25 73.1410.87
PASLE-NR
57.02=#0.76
51.11+0.39
73.09+1.21
72.98=:0.33
Thus, we have
Ry (f) R(f) S M Blllq pl12].
(40)
Finally, combining Eq 38 and Eq 40 completes the proof.
D FURTHER ANALYSIS (APPENDIX)
Running Time Analysis. To evaluate the computational cost, experiments were carried out on the clipart domain of the DomainNers dataset, using ResNet- 18 as the backbone with batch size of 128 on an NVIDIA TITAN Xp GPU. The reported runtime excludes data loading time, ensuring fairness by using torch. cuda synchroni ze accurately measure the computational overhead. The results are shown in Table 4 Our method has a similar time complexity to PL in pseudo-label generation.
bit slower than PL because our sample utilization rate high, and result, better performance has been achieved.
Performance over a Broader Parameter Range. We conducted parameter sensitivity analysis experiment on the CIFAR-10 C-C dataset under shot noise with a broader range of hyperparameters. The value of Tatar: was selected from wider range, specifically between 0.2 and 0.9. The threshold gap represented as |ssart Tendl, was fixed at 0.1. For testing purposes, Tdes was set to
The results are summarized performance when 7 is within the range of 0.5 to 0.8. Within reasonable range of 7, the algorithm also delivers comparable results. However, when 7 is set too low (e.g.. within the range 0.1 to 0.2), many samples with incorrect supervision introduced, leading decline in performance.
Table 5 The results indicate that the algorithm achieves optimal
Ablation Study of Modules PASLE, We additionally conducted ablation studies using two sim- plified variants of our framework: PASLE-NB and PASLE-NR. In PASLE-NB, the buffer is removed from the framework, while in PASLE-NR. the strategy of threshold reduction excluded. For this study, utilized the Offi ceHome dataset and employed ResNet-18 as the backbone. The results
19

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Published as a conference paper at ICLR 2025
Table Classification accuracy of PASLE with different candidate label selection strategies on the of ceHome dataset. The best performance is shown in boldface.
Methods
A
C
P
R
PASLE
57.25 0.75
0..30
73.31+1.004
74.10+0.20
PASLE-TB
57.07=0.63
73.92++0.44 51.13+0.45
73.11+0.94
PASLE-KB
56.31
50.69
72.82:10.69
73.56::0.21
Test Accuracy
Test Accuracy 1aa
660
0.66
650 46
0.00
0.30
0.75
0.30
Fatar
0.48
Tatoy
0.08
(a) The sensitivity of Tunn and Fand OfficeHome. (b) The sensitivity of Tume and Fend DomainNet..
Figure 3: The parameter sensitivity of Tstart and Tend for PASLE.
are shown in Table 6 highlighting that the buffer mechanism and threshold reduction strategy, as pluggable modules in our framework, further improve its performance.
Different Candidate Labels Generation Methods. We further explored two approaches for gen- erating candidate labels. The first is threshold-base approach (PASLE-TB). where threshold is set, and all classes with prediction probabilities exceeding this threshold are selected as candidate labels. This method generates both one-hot pseudo-labels and candidate pseudo-label sets. The sec- ond approach is top-k based (PASLE-KB), where prediction probabilities are sorted in descending order, and the top-A classes are chosen as candidate labels. Unlike the first method, this approach only produces candidate pseudo-label sets. The threshold and & are dynamically adjusted during the adaptation process. Experiments were conducted on the Officelloe dataset using ResNet- 18 as the backbone, and the results are presented in Table 7 It can be observed that PASLE-TI achieves performance comparable to PASLE, while PASLE-KE. KB, which lacks sample selection and directly uses the top-k predicted classes of all samples candidate labels, performs significantly worse than PASLE.
More Parameter Sensitivity Analysis Results We additionally conducted sensitivity analyses on Tstart and Tend using the clipart domain of the Off ceñome dataset and the clipart domain of the Doma i nNet dataset target domains. We also compared the performance of method and the baseline methods under varying batch sizes, using the sketch domain of DomainNet and the shot noise corruption in CIFAR-I 1AAR-100- 100-C target domains. The results are shown in Figure and Figure 4 It can be observed that PASLE is robust to hyperparameter selection and consistently outperforms other methods across different batch sizes.
FULL EXPERIMENTAL RESULTS
20

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Published as a conference paper at ICLR 2025
Table 8: Full results on the PACS dataset.
Methods
BackBone
A
C
P
S
Avg.
ERM
78.73+1.66
74.84+0.54
95.03+00.3
68.87+33.36
79.37
BN
82.03++0.55
81.09+0.45
96.08+0.33
73.12+00.44
83.08
TENT
82.19:0.59
81.27=0.47
95.85:10.33
73.62:10.68
83.23
PL
85.29:11119
83.72:10.77
95.9911.42
77.65+2..51
85.66
SHOT-IM
84.75+00.66
81.83+1.27
96.33+0.78
69.18+0.55
83.02
T3A
80.75+1.45
18.16+0.61
95.89+0.55
72.01+2.99
81.70
ResNet-18 18
TAST
83.32:10.88
82.44=0.92
96.2710.54
75.19:10.89
84.31
TAST-BN
87.09:10.32
83.89=1.37
96.6910.39
77.74+1.45
86.35
TSD
87.81+00.64
87.09+0.50
96.71+0.57
79.89+0.32
87.88
PROGRAM
84.72+00.55
80.36+0060
96.05++0.39
73.14+0.40
83.57
DEYO
8.184
83.3910.56
96.1310.48
79.67
86.26
PASLE
88.1911.42
87.09
96.8310.48
80.51
88.16
ERM
8..84
19.7
96.4710.37
81.27
85.84
BN
86.73+00.2
84.13+1.98
96.79+0.07
1.53
86.00
TENT
87.00+t0.92
14.91=1.89
96.89+0.10
1..65+1.53
86.51
PL
88.80110.8
82.9414.90
95.3511.32
75.5315.00
85.66
SHOT-IM
85.68
83.52.10.47
95.05.10.63
76.83
85.27
T3A
86.51+0044
81.67=1.64
96.85+0.18
81.1242.03
86.54
ResNet-50
TAST
87.8
84.56=2.21
97.35+0.19
78.00
86.94
TAST-BN
89.94.10.31
86.68
97.4910.48
83.77
89.47
TSD
91.06.10.56
90.67110668
97.70.1..15
85.09
91.13
PROGRAM
1..0
1.86
96,89=0.06
76.44+1.66
86.16
DEYO
88.3640094
85.24=1.61
97.05=0.12
82.26+0.54
88.23
PASLE
91.47
89.88 1.53
97.7410.28
86.25
91.36
Table 9: Full results on the VLCS dataset.
Methods
BackBone
L
C
S
Avg.
ERM
95.66:1..33
1..0
17..881..8
72.62.13.70
75.14
BN
42.71112.46
1.55
62.20.10.86
71.42.1.13
68.79
TENT
83.30+2..66
59.26=1.57
62.77+1.02
71.80+1.91
69.28
PL
92.32+11.3
63.87=1141
69.47#0.97
73.05+1.42
74.68
SHOT-IM
88.06.13.50
1..5
63.50
73.06:1...2
70.80
T3A
98.49-11.27
6.602-+1.60
68,9010.82
71.92-14.00
75.83
ResNet-18
TAST
94.74+2.04
56.63+2.07
63.9740.62
71.41+2.11
71.69
TAST-BN
97.3440.84
65.02=1..57
65.71
72.61
75.17
TSD
96.30-10.47
65.47-1..14
67.84.0.53
72.25
75.47
PROGRAM
95.87++1.45
58.71+0.81
10.1141.43
71.85+2.47
71.64
DEYO
95.16
63.93=0.37
67.20
13.33
74.91
PASLE
96.0411.53
66.48=0.51
72.64:0.45
76.48
77.91
ERM
97.15110.43
63.0810.65
70.6310.76
73.37
76.06
BN
77.90+44.52
56.66+2.09
63.36+1.14
73.11+0.37
67.76
TENT
79.15+4..67
57.05++2.06
63.92+1.09
73.50+0.18
68.41
PL
91.31+3.18
61.60
70.9710.05
71.32+2.66
73.80
SHOT-IM
80.60413.95
55.78-1.663
63.51
74.06.10.73
68.49
T3A
18.18+00.11
64.13+1.10
72.04+2.37
71.99+0.81
76.59
Re
TAST
81.70++4.20
52.10+0.42
62.29+1.45
73.20+1.00
67.32
TAST-BN
96.7741.42
61.33-0.06
68.96.14.14
75.30
75.59
TSD
93.92-11.28
58.03-11.04
69.65:12.52
77.4910.99
74.77
PROGRAM
85.05+4..15
58.42+0.40
60.12+1.43
71.82+1.50
68.85
DEYO
84.38+1.70
60.92++1997
67.20+0.97
73.85+0.21
71.59
PASLE
96.0110.89
66.20
76.0111091
76.59
78.70
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Published as a conference paper at ICLR 2025
Table 10: Full results on the Off ceHome dataset.
Methods
BackBone
C
P
R
Avg.
ERM
55.7610.80
48.66:10.43
71.46:10.67
73.84:10.33
62.43
BN
54.96:10.58
49.74=1.37
70.95
73,5010.43
62.29
TENT
55.13:10.65
50.00=0.211
71.27
73.63:0.43
62.51
Pl.
55.09++0.36
50.74+0.19
71.17+1.25
73.83+0.39
62.71
SHOT-IM
1..75++1112
52.03-+0.57
72.77+0005
74.10+0.33
63.91
T3A
56.52:11.12
50.62-10.67
73.45
74.9910.33
63.90
ResNet-18
TAST
55.7511..89
51.71-1.499
73,9311095
74.46.10.4
63.96
TAST-BN
55.28++0.65
50.49+0.64
71.89+1146
72.07+0044
62.43
TSD
57.27+0077
50.60=1.59
72.24+0.85
73.55+0.21
63.42
PROGRAM
56.69111.45
50.9410.51
71.8011..0
73.9810.47
63.35
DEYO
56.5011..30
50.80
71.97.1.02
73.9210.41
63.30
PASLE
07.25+0075
51.30=0.41
73.31+1.04
74.10+0.20
63.99
ERM
63.0440048
53.88=0.18
76.55+0.41
17
67.84
BN
62.00110.81
53.45.10.47
75.06
76.76.10.74
66.82
TENT
62.44:10.72
54.1111.448
75.68
76.8410.57
67.27
PL
03.324+0.9
54.73=0099
73.89+1.22
77.30+0.46
67.31
SHOT-IM
6..95+1.115
54.56=0.44
76.37=0.95
07.66+0.29
67.89
T3A
63.26+0.23
55.30=0.32
78.13:0044
78.72+0.45
68.85
ResNet-50
TAST
63.42.10.59
55.61
78.01
77.74
68.70
TAST-BN
62.76.10.62
55.01-10.43
17.01
77.11
67.97
TsD
64.32+0044
56.91=0.97
77.19+0.67
7..46
68.97
PROGRAM
63,3640.87
54.27=20.23
77.24+0.69
77.24+0.49
68.03
DEYO
63.77-10.23
54.90
76.36.10.51
10.26
68.08
PASLE
65.47-10.83
56.08
78.11
1..30
69.37
Table 11: Full results on the Doma nNet dataset.
Methods
BackBone
clipart
infograph
painting
quickdraw
real
sketch
Avg
ERM
50.48=0.21
15.31:10.15
41.8620.12
11.6620.P 49
51.71:0.20
43.53=0.02
35.76
BN
50.74:10.09
11.3810.03
40.76:1.12
11.2910.39
51.78:10199
43.72-0.26
34,95
TENT
51.13=0.07
12.52:1.19
41.91=0.14
10.57=0.38
51.31:0.25
44.76=0.17
35.37
50.88100066
12.87110.00
41.22-10100
10.8410.74
$1.62:1.229
44.01=0.25
35.24
SHOT-IM
$1.02=0.007
12.75
41.41-0.13
13.714-0.32
$2.26:10.15
44.38 0.21
35.92
ResNer-18
50.34-0..26
15.1140.20
40.35=a0112
16.2440..23
53.13-4..00
42.68-0.17
36.31
TAST
50.31
12.6410.09
40.66=0.05
14.59=0.51
53.58=0..1
42.49=0.26
35.71
TAST-BN
50.44:10.27
13.21:10.13
40.97-0.12
14.7210.49
52.39:1.411
43.19=0.28
35.82
50.74=0.11
13.58:00.77
42.93=00244
11.78:10.4
51.95=0.21
44.20=0.20
35.86
PROGRAM
51.07=0.116
13.27:1.26
41.52:1.12
13.40:10.41
$2.31110288
44.27=0.25
35.97
41.23:10.12
$1.8110.21
43.96-0.23
PaSlE
51.76-0.39
14.98
43.06-+0.15
13.67+00.26
$2.69 18
15.15--..2
36.89
FRM
6..00
40.19
49.58.0.00
13.57
61.95
$2.07
43.16
BN
60.58:0.23
15.1111.117
18.04-10.88
11.9211.220
61.06:1.116
01.70=0.16
TENT
61.6410.15
17.41
50.40.1..11
10.11
61.40
03.30
42,38
17.90+0.20
52.61-0.19
SHOT-IM
61.29=0.21
17.56+0.14
49.81=0.10
16.50=0.52
62.52-00 10
52.79-0.22
43.41
T3a
ResNet-50
61.05=0.23
20.9410.14
48.71=0.08
18.55:0.39
63.19:1.088
$1.57=0.27
44.00
TAST
60.6511.22
17.9310.19
19.03-10.19
15.1710.28
62.62.10.12
51.64=0.07
42.84
TAST-BN
61.03:0.32
18.0410.22
49 09.65
14.75-0.41
62.71
$1.97=0.99
43.03
60.76:10.2
49.82-10.65
12.21:10.66
61.66.10.17
$2.27-0.18
PROGRAM
61.15
18.08 +0.04
49.85-4000
15.53+-0.40
62.14-40.04
53.30-0.20
43.34
61.04-0.22
18.1740.11
11,99-0.23
61.25-10.02
52.50-0.21
42,47
PASLE
62.46=0.39
20.67=:0.12
51.74=0.16
16.73=0.51
63.76:00.99
54.11=0.26
44.91
22

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Published as a conference paper at ICLR 2025
DEvO
44-
PACLI
PASLE
Test Accuracy (%)
Accuracy (%%
40-
38
42
41-
16
256
16
32
64
Batch
Batch
(a) The sensitivity batch size on C1FAR-100-C.
(b) The sensitivity of batch size on Doma nett.
Figure 4: The parameter sensitivity of batch size for PASLE.
Table 12: Full results on the CTFAR-1 0-C dataset.
Methods
shot
motn
SBOW
pixel
Eauss
defoc
brit
Fog
200m
Frost
glass
impul
contr
clast
Avg.
24.93
26.
62
24.52
28.41
13.48
19.53
18:31
24.93
20.66
76.79
75.93
78.17
80.13
77.33
79.13
70.64
79.25
76.05
68.
62.82
76.16
75.33
TENT
76.80
76.11
78.25
80.07
71.29
79.12
85.13
70.80
79.31
76.21
68.57
66.03
63.19
80.24
76.04
75.41
77.07
76.45
78.25
80.42
77.59
79.56
83.20
71.26
79.77
76.50
68.74
66.22
63.95
80.21
76.34
75.70
T3A
29.97
20.27
29.93
26.04
29.
19.81
34.00
13.64
20.02
21 03
21:28
21.91
15.94
28.33
21.29
23.52
TAST
75.27
75.16
77.07
78.99
76.02
78.05
$2.10
69.39
78.01
75.47
66.74
64,42
62.55
78.11
74.64
74.13
TSD
76.54
75.58
78.28
79.96
77.18
78.79
33.16
70.32
78.84
76.03
68.01
66.06
62.10
30.09
76.18
75.14
PROGRAM
76.73
76.22
77.87
79.98
77.10
78.83
83.21
69.86
78.74
76.01
67.88
65.40
61.21
79. 79.95
76.06
75.00
PASLB
78.03
77.40
79.08
81.16
78.23
80.81
33.83
72.31
80.81
77.28
67.07
67.17
80.75
76.77
76.67
Table 13: Full results on the CIFAR- STFAR-100-T 100-C dataset.
Methods
shot
motn
Snow
pixel
gauss
defoc
brit
Fog
200m
Frost
glass
impul
centr
jpeg
clast
Avg.
3.95
5.45
1.08
TENT
44.19
46.23
45.02
.9.97
44.34
48.55
50.47
37.53
48.89
44.07
38.81
34.57
31.68
48.91
45.65
43.93
44.57
47.05
45.09
50.11
44.36
49.27
50.58
37.32
49.49
44.35
39.29
34.94
32.22
49.01
45.92
44.24
49.25
T3A
8.24
5.28
9.14
8.19
8.59
5.04
12.94
2.23
5.50
6.18
6.23
5.97
1.08
9.49
6.98
6.74
TAST
39.65
42.29
40.35
44.83
39.86
43,72
45,00
33.13
43.37
99.13
35.68
31.45
25.91
43.23
40.50
39.21
TSD
44.54
45.32
50.47
44.76
48.92
30.97
37.38
49.46
44.25
39.05
34.62
31.36
49.26
45.95
44.19
PROGRAM
44.19
46.63
44.97
49.91
44.63
48.76
50.36
37.76
48.74
44.37
38.87
34.78
32.42
48.78
45.67
44.06
45.60
51.92
39.12
5042
36.00
32.87
23


Reviews:
[{"review_id": "7jcqSW3mkq", "reviewer": "Reviewer_oudU", "summary": "The paper introduces a new pseudo-learning algorithm that combines one-hot label learning and candidate label learning approaches. Each learning paradigm is conducted on its respective sample set, referred to as the certain set for one-hot label learning and the uncertain set for candidate learning. The key distinction from other pseudo-label learning papers is that the authors propose a theoretical guarantee to ensure that the selected labels in the pseudo-set will correspond to the ground truth if certain conditions are met (Proposition 1). In the initial learning stages, the model focuses more on candidate set learning and gradually shifts toward minimizing the one-hot label loss as it updates more on target samples. The authors provide a theory indicating that the generalization bound becomes tighter as more target samples are incorporated. Experimental results demonstrate the algorithm's performance compared to other TTA learning methods.", "questions": "Please refer to the Weakness.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "1. The proposed method is supported with a theory guarantee.\n2. The experiment is diverse datasets, which confirm the effectiveness of the proposed methods.", "weaknesses": "The reviewer's main concern is the novelty of the proposed approach: adapting pseudo-learning and candidate learning is already popular in TTA and domain adaptation, as the authors discussed in Section 2. The main novelty here comes from Proposition 1, where the authors propose to ensure the correctness of pseudo labels under specific assumptions. The condition is that the learned weight and the optimal one need to be close enough (the closeness is measured by the difference in the probability of each class in the input samples, and $\\tau(r)$ is the threshold). The selected pseudo labels are considered true when this condition is met. However, how can we ensure that this condition is always satisfied? If the reviewers understand correctly, this condition is based on the threshold $\\tau(r)$, which is initialized to 1 and then gradually reduced to a specific value. When $\\tau(r)$ is smaller than 1, how can we ensure that the distance between the learned models and the optimal one is smaller than this threshold?", "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": "Njx8Zf3O2D", "reviewer": "Reviewer_z3cq", "summary": "This paper studies Test-time adaptation (TTA), which aims to adapt a pre-trained model to the target domain using only unlabeled test samples. The authors proposed a new TTA framework, which assigns candidate pseudo-label sets to uncertain ones via selective label enhancement. The model is progressively trained on certain and uncertain pseudo-labeled data while dynamically refining uncertain pseudo-labels, leveraging increasing target adaptation monitored throughout training. Experiments on various benchmark datasets validate the effectiveness of the proposed approach.", "questions": "- In the proposed method, why the authors reduced to improve the reduced threshold could improve the reliability of pseudo labels.  \n- In the experiments, why did the authors only adopt online test-time adaptation approaches as the baselines?", "limitations": "", "rating": 8, "confidence": 5, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "- Instead of assigning definite pseudo-labels to test samples, candidate pseudo-label sets are assigned to uncertain ones via selective label enhancement.\n- The proposed method partitions test samples into confident and uncertain subsets based on the model’s predictive confidence scores, with confident samples receiving one-hot pseudo-labels, and uncertain samples being assigned candidate pseudo-label sets\n- The theory establishes a generalization bound for TTA that by incorporating a greater number of target domain samples with effective supervision, a tighter generalization bound can be achieved.", "weaknesses": "- In the proposed method, the authors need to provide more details about the reduced threshold to improve the reliability of pseudo labels.  \n- Why use image corruption datasets to validate the effectiveness of the proposed method? 15 types of common image corruptions should be shown clearly.\n- This paper uses a vanilla variant that all samples annotated with candidate pseudo-labels sets excluded from model updates to demonstrate the effectiveness of the candidate pseudo-labels sets of the proposed method. More detests could be added in this ablation experiments.", "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": "z343bNEeoC", "reviewer": "Reviewer_mB9B", "summary": "The problem studied in this paper is the conventional test-time adaptation. When assigning pseudo-labels to test samples, the paper assigns one label to samples with high confidence, while assigning a candidate set of labels to less confident samples. It uses a buffer to store samples that could not be labeled, allowing the model to attempt labeling them in subsequent batches. Finally, the model is updated by using cross-entropy with the one-hot encoded pseudo-labels. The effectiveness of the method is validated across multiple datasets.", "questions": "1.\tSince there are many approaches for creating pseudo-label candidate sets, has the paper compared its method with other approaches for selecting pseudo-label candidates? Does this method have any unique advantages specifically for the test-time adaptation (TTA) task? Or is it also applicable to semi-supervised or unsupervised tasks?\n2.\tWhat is the buffer size used in the experiments? Was there any ablation study conducted on the buffer size? If the buffer were removed, would this method still be effective?\n3.\tIn the experiment section, why do ERM and T3A perform so poorly on CIFAR10-C and CIFAR100-C? In the original papers and subsequent TTA studies, their performance was not as weak.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1.\tThe writing of this paper is clear, and both the problem definition and the method description are well articulated.\n2.\tThe motivation behind the proposed label enhancement method is reasonable, and there is substantial theoretical analysis provided.\n3.\tThe experiments in the paper are relatively thorough, demonstrating the superiority of the proposed method.", "weaknesses": "1.\tDespite the relatively comprehensive theoretical analysis, the design of the method in this paper is overly simplistic. Similar approaches using candidate pseudo-label sets have long existed in the field of semi-supervised learning.\n2.\tThe maintenance of this buffer seems somewhat unfair. If a sample’s label remains undecided for an extended period, it will be repeatedly seen by the model in subsequent iterations. Although the buffer size imposes some constraints, the repeated processing of test samples could still introduce bias. Additionally, maintaining a buffer incurs significant overhead. If the buffer becomes too large, the number of samples to be predicted in each batch will be dictated more by the buffer size than by the batch size itself.", "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": "m5hNsGGX2o", "reviewer": "Reviewer_LuhJ", "summary": "This article proposes a method for addressing the TTA problem by dividing confident samples from uncertain samples and progressively updating pseudo-labels, alleviating errors caused by unconfident pseudo-labels in TTA scenarios. The article provides a systematic and comprehensive theoretical generalization error bound and validates its effectiveness on multiple benchmark datasets.", "questions": "The main concerns are as follows:\n1. The novelty of this paper should be emphasized more clearly. From the motivation perspective, dividing confident and non-confident samples and applying progressive training is a fairly conventional approach. Similar ideas have been extensively used in domain adaptation (DA) problems, and several papers in TTA focus on pseudo-labeling. The authors should pay more attention to these closely related works to highlight the novelty of this paper better.\n2. The generalization error bound provided is a little general and offers limited guidance for the current problem. Based on the motivation of the paper, if the so-called more effective supervised information can be quantified? If pseudo-label error terms or confidence levels could be incorporated, it would help reveal how the label-generation process impacts generalization performance, thereby offering more practical insights. Additionally, how is the divergence term in the bound reduced in this paper? How does it influence pseudo-labeling and progressive adaptation?\n3. Regarding the experimental setup, the datasets used in this paper differ from those employed in previous methods. The rationale for these choices should be explained in detail. Furthermore, for certain methods with the same settings like PROGRAM, why do the results differ from the original paper when using the same benchmark and backbone? Could it be due to different settings or other reasons? This should be clarified in the paper, as such vague experimental setups and comparisons make it difficult for readers to accurately assess the actual performance of the method.\n4. The paper lacks ablation studies to evaluate the effectiveness of each module. Additionally, since the proposed method is an online model, time efficiency is an important metric that should be discussed, especially considering the additional computational overhead introduced by the approach.\n5. I am also curious about the sensitivity of the threshold selection strategy. It doesn’t seem highly sensitive, but how does it perform over a broader parameter range or with different thresholding strategies? This could be a point worth discussing in the paper.\n\nIf the authors can adequately respond to these concerns, I would consider increasing my score.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "TTA is a critical research area for machine learning models to adapt to distribution shifts in real-world scenarios, particularly with wide applications in fields such as autonomous driving and medical image analysis. This article enhances model performance on TTA issues by dynamically adjusting pseudo-labels and capturing their uncertainties. Additionally, the detailed derivation of the generalization error bound in the article offers theoretical guarantees.", "weaknesses": "The paper lacks sufficient persuasive experimental evidence, suggesting the need to include relevant ablation studies, discussions on time overhead, and the rationale behind experimental settings. The novelty of the paper is not distinctly highlighted, requiring a more detailed discussion of the differences from related methods. The theoretical guidance is relatively weak; exploring the quantification of pseudo-label errors could strengthen the paper.", "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": "gMefFbn1eX", "reviewer": "Reviewer_b8X9", "summary": "The paper introduces the Progressive Adaptation with Selective Label Enhancement (PASLE) framework for test-time adaptation (TTA). Unlike traditional methods that assign definite pseudo-labels, PASLE assigns candidate pseudo-label sets to uncertain test samples while providing one-hot labels to confident samples. This approach allows the model to adapt progressively, refining the uncertain pseudo-labels based on the model's evolving understanding of the target domain.", "questions": "See weakness", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. PASLE effectively partitions test samples into confident and uncertain subsets, improving labeling accuracy for uncertain samples.\n\n2. The model is trained iteratively on both certain and uncertain pseudo-labeled data, enhancing adaptation capabilities over time.\n\n3. The paper establishes a generalization bound that suggests increased supervision from target domain samples can lead to improved model performance.", "weaknesses": "1. I am confused about some notations in theorem 1, what is the specific meaning of d_{h, H}(S,  T)? It seems that d_{h, H}(S,  T) is a constant with your algorithm. Does theorem 1 show the superiority of your algorithm because there is always a constant gap between the \\epsilon_T(\\hat{h}) and \\epsilon_T (h_T^*)?\n\n2. Whether using the two hyper-parameter to control the iteration is reasonable in equation 9? Since different datasets have different parameters and there is no prior knowledge to guide us in choosing suitable parameters, making hard to achieve the best results\n\n3. More experiments about the sensitivity of the τ_start, τ_end, and batch size on other datasets are expected to be seen.", "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)