Noisy-Pair Robust Representation Alignment for Positive-Unlabeled Learning
Authors: Hengwei Zhao
Zhengzhong Tu
Zhuo Zheng
Wei Wang
Junjue Wang
Rusty Feagin
Wenzhe Jiao
Venue: ICLR 2026 Poster (2026)
Keywords: PU Learning
Non-contrastive representation Learning
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

Abstract: Positive-Unlabeled (PU) learning aims to train a binary classifier (positive vs. negative) where only limited positive data and abundant unlabeled data are available. While widely applicable, state-of-the-art PU learning methods substantially underperform their supervised counterparts on complex datasets, especially without auxiliary negatives or pre-estimated parameters (e.g., a 14.26% gap on CIFAR-100 dataset). We identify the primary bottleneck as the challenge of learning discriminative representations under unreliable supervision. To tackle this challenge, we propose NcPU, a non-contrastive PU learning framework that requires no auxiliary information. NcPU combines a noisy-pair robust supervised non-contrastive loss (NoiSNCL), which aligns intra-class representations despite unreliable supervision, with a phantom label disambiguation (PLD) scheme that supplies conservative negative supervision via regret-based label updates. Theoretically, NoiSNCL and PLD can iteratively benefit each other from the perspective of the Expectation-Maximization framework. Empirically, extensive experiments demonstrate that: (1) NoiSNCL enables simple PU methods to achieve competitive performance; and (2) NcPU achieves substantial improvements over state-of-the-art PU methods across diverse datasets, including challenging datasets on post-disaster building damage mapping, highlighting its promise for real-world applications. Code: https://github.com/Hengwei-Zhao96/NcPU.

Published as a conference paper at ICLR 2026
NOISY-PAIR ROBUST REPRESENTATION ALIGNMENT FOR POSTTIVE-UNLBBLLED LEARNING
Hengwei Zhao
Zhengzhong Tu
Zhuo Zheng
Wei Wang 3,4
Junjue Wang"
Rusty Feagin
Wenzhe Jiao
Texas A&M University, College Station, USA
Stanford University, Stanford, USA
3 RIKEN, Tokyo, Japan
'The University of Tokyo, Chiba, Japan (hengwei. zhao, wenzhe. weezheejiaooeeeee fag twm...aauee.. edu
ABSTRACT
Positiv--Unlabeled (PU) learning aims to train a binary classifier (positive vs. neg- ative) where only limited positive data and abundant unlabeled data available. While widely applicable, state-of-the-arr PU learning methods substantially un- derperform their supervised counterparts on complex datasets, especially without auxiliary negatives or pre-estimated parameters (e.g., 14.26% gap on CIFAR- 100 dataset). We identify the primary bottleneck as the challenge of learning discriminative representations under unreliable supervision. To tackle this chal- lenge, we propose NePU, a non-contrastive PU learning framework that requires no auxiliary information. NcPU combines noisy-pair robust supervised non- contrastive loss (NoiSNCL.), which aligns intra-class representations despite un- reliable supervision, with phantom label disambiguation (PLD) scheme that sup- plies conservative negative supervision via regret-based label updates. Theoreti- cally, NoiSNCL and PLD can iteratively benefit each other from the perspective Expectation-Maxiiizzerr Maximization framework. Empirically, extensive experiments demonstrate that: (1) NoiSNCL enables simple PU methods to achieve compet- itive performance; and (2) NePU achieves substantial improvements over state- of-the-art PU methods across diverse datasets, including challenging datasets post-disaster building damage mapping, highlighting its promise for real-world applications. Code: https: com/ Hengwei PhaP96/NcPU
of the Expectation
INTRODUCTION
Desitie-Unnlabelen (PU) learning aims to train a binary classifier with limited labeled positive data and large pool of unlabeled data (Zhao et al. 2023a| Long et al., 2024 Du Plessis et al.) 2015
which is well-suited for many real-world applications such as product recommendation (Hsieh et al. 2013), medical diagnosis (Yuan et al.) 2025), and remote sensing applications (Zhao et al.) 2022) For example, a real-world case arises in the context of humanitarian assistance and disaster response (HADR), where mapping the spatial distribution of damaged buildings from remote sensing imagery remains highly challenging. Shortly after disaster, specialists are typically able to annotate only subset of damaged buildings (positive samples) (Xia al., (202)). while large amount of the remaining building data remains unlabeled. These unlabeled data inevitably contain both damaged and undamaged (negative) structures, and such ambiguity significantly impedes the effective training of classification models.
Numerous methods for PU learning have been developed over the past decades, and the core chal- lenge in PU learning lies in deriving the reliable binary classification supervision using only PU data. Early studies focused on selecting reliable negative samples, and then training binary clas- sifier with positive and reliable negatives (Gong et al., 2018 Garg al. 1021 Wang et al.) [023a). However, the performance these methods heavily depends on the pscudo- labels of the selected samples. More recent research tries estimate the reliable binary classification supervision using all PU data, and achieving competitive or state-of-the-an performance (Wilton et al., 2022 Tiang
al. 2023 Zhao al. 2023a Long et al. 2024 Yuan et al. 2025). Nevertheless, many these
"Corresponding author.

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Published as a conference paper at ICLR 2026
Aradhu
Dilicennieeas sample
Andiee
Diliverreellss sumple
Aradice
Difizeetoclan sample
Samo-dias samples
Sambola sscples
Semples
SelSpaary from nelf superiition
Cleotepairy from rellable fabels
Nateo-paiz aureliable labels
(6) Self-Saperiied Reprosentation Learning
(b) Superviud Reprosmiation Learning
(c) Noicy-Pair Rebust Represmntaion Learning
Figure I: Illustration of different representation learning methods. Representation learning can acquire discriminative representations either by pulling same-class samples closer the anchor and pushing different-class samples apart (contrastive representation learning), or by only pulling same- class samples closer the anchor (non-contrastive representation learning). (a) Self-supervised representation learning: same-class pairs from augmented anchor. (b) Supervised representation learning: same-class pairs from reliable labels. (c) Noisy-pair robust representation learning: same- class pairs from unreliable labels.
methods rely on auxiliary negative validation data or a pre-estimated parameters (such as the class prior Tp. which denotes the proportion of positive samples within the unlabeled data) to facilitate the estimation of binary classification supervision.
While previous methods have shown promising results, learning discriminative representations from complex PU data remains a significant challenge, causing best-performing methods to fall short compared to supervised counterparts. As shown in Figure 2, the features generated by PU methods, such as LaGAM (Long et al. 2024) and HolisticPU [Wang et al.) 2023a). show substantial overlap between positive and negative distributions, unlike the clearly separable features obtained with pervised learning. Additional t-SNE visualizations are provided the Appendix A In other words, the binary classification supervision derived from PU data in these methods is insufficient to ensure the acquisition of discriminative representations, which adversely affects model performance.
Inspired by recent advances in seffsuupervieedsuperviedd representation learning (He et al. 2020); Grill et al.] 20200]
Khosla et al. 2020 Lu al. (2023). this paper proposes a novel non- con-rantrett PU learning framework (NcPU) to learn more discriminative representations. When represen- tation learning meets PU learning, the challenge of noisy- pair robust representation learning (Figure [ arises: unreli- able supervision inevitably introduces incorrect pairwise re- lations (i.e., noisy pairs), which hinder the effective learn- ing of discriminative representations. To address this, noisy- pair robust supervised non-contrastive loss (NoiSNCL) is proposed to align intra-class representation while tolerat- ing noisy pairs from the perspective of gradients. More- over, based on the discriminative representations learned by NoiSNCL, the phantom label disambiguation (PLD) is pro- posed, which refines supervision through regret-based label updating. Theoretically, NePU can be interpreted under the Expectation Maxiiiiiziaiiiiiiiionoo (EM) framework. with pseudo- label assignment serving the E-step and NoiSNCL minimization the M-step (cluster tight- ening), iteratively updated during training. Remarkably, NoiSNCI. enables simple PU methods to achieve highly competitive performance. The contributions of this paper summarized as follows:
Rosttive Negathve
-50
Pestrive Kangative
100
100
LG0
HolistiPP features
LaGAM features
"Magattve
Faegetive
NoPU Beotures
Supervised featunes
Figure 2: t-SNE visualizations of the representations learned by PU meth- ods CIFAR-10 training dataset.
Methodology. NcPU is proposed to obtain discriminative representations through noisy-pair robust intra-class representations alignment, which consists of NoiSNCL and PLD modules. No- tably, NcPU works well without requiring auxiliary negatives or pre-estimated parameters.
Theories. Gradient analysis demonstrates that noisy pairs dominate the optimization process in representation learning. Furthermore, the proposed NoiSNCL and PLD modules can be theoreti- cally justified to iteratively benefit each other from the perspective of the EM framework.
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Experiments. Extensive experiments demonstrate that (1) NoiSNCL enables simple PU methods to achieve competitive performance; and (2) NcPU outperforms state-of-the-ae methods, achiev- ing performance comparable to its supervised counterpart. Moreover, results post-disaster building damage mapping tasks highlight the broad applicability of NePU.
2 PROBLEM SETTING
Let 2;; E IRd denote a sample and yi denote its label. Here, = O indicates that a; belongs to the positive class, and yi 1 implies that æ; belongs the negative class. The objective of PU learning is to learn a binary classifier f(æ;)= IRd + [0, 1] using the training dataset D = P Ul:
p ( (a,, Vi = -)) Pp = P(æly = 0), + (1-7p))(zm)) 1);
4 { P.. -
(2)
where 7ip and nh denote the numbers of positive and unlabeled samples, respectively, and Pp and P. denote the marginal distributions of positive and unlabeled data, respectively. Besides, "p P(y 0) is the class prior.
The challenge of PU learning is to derive reliable binary classification supervision from the PU data. Let a pseudo target 8; E [0, 1] be assigned to a sample 2;, 8; is expected to become more accurate as it is updated during training without auxiliary information. If the s; is obtainable, the classifier can be optimized by minimizing the following label-disambiguation cross-entrope loss (LDCE):
Le(f(z;), 8:) -s; T log f(:;),
where (ax;) is the softmax output of the classifier. The sample index will be omitted the context clear in the following.
Intuitively, if ideal representations are available, the labels of unlabeled data can be accurately recov- ered by exploiting the available information: the similarity between data points the representation space, and the weak supervision inherent in PU data. For example, an unlabeled sample would be inferred as belonging to the negative class if, the ideal representation space, it lies close to a cluster corresponding to the negative class. However, this reliance on representations gives rise to non-trivial dilemma: the inherent weak supervision adversely affects the process of represen- tation learning (as illustrated in Figure 2), while the quality of the learned representations, in turn, constrains the acquisition of accurate pseudo targets. This dilemma is mitigated in NePU through intra-class representation alignment, which is described in the following section.
3 NOISY-PAIR ROBUST NON-CONTRASTIVE PU LEARNING FRAMEWORK
The NcPU framework (Figure) is designed to obtain more discriminative representations by align- ing intra-class representations. It consists of two key components: NoiSNCL and PLD. The two components work collaboratively; NoiSNCL produces discriminative representations under unreli- able supervision, which in turn benefits subsequent label disambiguation. Conversely, PLD provides more reliable supervision, thereby facilitating the non-contrastive representation learning module in acquiring more discriminative representations. Notably, NePU works well without requiring addi- tional negative samples pre-estimated parameters. A more detailed theoretical interpretation from the perspective of the EM framework is provided in Section
3.1 NOISY-PAIR ROBUST SUPERVISED NON-CONTRASTIVE REPRESENTATION LEARNING
In PU learning, unreliable supervision poses major obstacle to acquiring discriminative represen- tations. To address this, NcPU integrates NoiSNCL with LDCE to facilitate the clustering effect in the representation space, thereby aligning intra-class representations.
Preliminaries. Compared with contrastive representation learning, non-contrastive representation learning acquire discriminative representations by only pulling same-class data closer to the anchor (intra-class representation alignment), thereby mitigating the impact of noisy different-class pairs. Without loss generality, this paper adopts the classical non-contrastive representation learning framework BYOL (Grill al. 2020p. Given each sample (ær, y), two different augmented views
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Psrado Langet
Classificr
LOCE
Pansdr-laell excipenenn!
Auguaa)
Projection head
Prediction
Updnting
Phantommaate
Encoder
EMA
EMA
x
Aug(K)
prossape
protaaye
Projection head
NoISNCL
Cluser tiphernigg
No Basigrquugeiion
Phantom Label Disambiguation
Mossentum
encoder
The proposed NePU framework. NoiSNCL improves representations for label disam- biguation, while PLD enhances supervision for representation learning.
Figure 3:
Aug,(a) and v' Aug, are produced by the image augmentation Aug,()) Because Aug, (-) is stochastic, & v'. From the first augmented view v, the online network outputs the embedding q. The target network outputs the other embedding based on the augmented view v'. Consistent with the original design of B BOL, the target network does not include the prediction head. The encoder and projection head of the target network are momentum-updatee from the online network.
Self-supervised non-contrastive representation learning, such as BYOL, aims to pull the representa- tions of the same sample from different views closer together:
(x.,) = 2(1 (q., k.)),
(4)
where q = |ن and is T are the Lg-nomaalized embeddings. Similar to supervised contrastive loss (Khosla et al., 2020),, the supervised non-contrastive loss (C,) can align intra-class representa- tions through the incorporation of label information. Formally, L, can be formalized as follows:
(xi, 25) = 2(1 (ā: 1 )-
(5)
Minimizing 5) on (x), v.) and (x,, Us) pulls representations of æ; and æ, closer if y: = yj-
Gradient Analysis for Noisy Pairs. In the PU learning setting, the ground-truth labels y for unla- beled data are unavailable, thereby preventing the direct computation of E5. The use of pseudo labels ÿ generated by the classifier NcPU inevitably introduces noisy pairs. These noisy pairs tend to dominate the representation learning process, as their gradient magnitudes overwhelm those from the clean pairs. For example, consider clean pair (æ:, .r with y; yj and noisy pair (x;; am.) with yi Dm * Ym. the representations may have q, 9; + and q, qm O, which will wrongly pull together representations with incorrect labels and ultimately impair the learning of the clean pairs:
(z, 3m
4
4
@.r xz))
(1
(g. )m)
(1
(q.. (;)))
(6)
0q.
1g.112
||
0q.
where the prediction head regarded as an identity function for simplicity. The detailed proof provided in Appendix
Noisy- Pair Robust Supervised Non-Contrastive Loss. The NoiSNCL, as shown in Eq. is proposed to mitigate the problem of noisy pairs dominating the training process and is defined as follows:
L,(x,, = 2/12 (ā., k2) v,3.
NoiSNCL still aims to align representations same-class data, while the gradient magnitudes of clean pairs greater than those of noisy pairs (8)) the representation learning process is pri- marily driven by the clean pairs. Moreover, given that L,(x;, m.)) (r mz)), under some mild
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assumptions, minimizing (zz,, 2;) in NePU is equivalent to maximizing a lower bound of the likelihood function of the unlabeled data (Section
dLr 3mm) ōq.
1 (1 (Ā. (m))
aL. (20 xzj)
2
(1 (q. (,))
(8)
11q.112
|1
àq:
Due to page limit, detailed proofs are provided in Appendix
3.2 PHANTOM LABEL DISAMBIGUATION FOR PU LEARNING
Based on the discriminative representations derived from noisy-pair robust supervised non- contrastive representation learning, the PLD is proposed to generate more accurate pseudo targets. This strategy built upon class prototypes and enables regret-based label updating with the proposed PhantomGate. This strategy facilitates more conservative negative supervision while preserving the integrity of the prototype- disambiguation process, where empirical evidence has demonstrated to be essential for effectively extending prototype-basee label disambiguation to PU learning.
The class-conditional prototype embedding vector Mo serves the representative embedding of class c:
Class-oonditoonal Prototype Updating.
He Normalize (1 aa])).
(9)
where the prototype μe is defined by the moving-average of the normalized embedding q. The normalized embedding q corresponds to the representation of produced by the online network, and the classifier assigns the label the æ. Besides, denotes a momentum hyperparameter.
Phantom Pseudo Target Updating. Benefiting from discriminative representations, the prototype can be employed obtain more accurate pseudo targets:
8' = 38' + (1 B)r, re ( if c= arg J q Hjj
(10)
else.
where denotes the momentum hyperparameter. However, this approach is effective when Tp is explicitly provided as input (Yuan et al. 2025). In the absence of Tp. such naive label disambigua- tion strategy in PU learning may lead to trivial solution caused by the lack of negative information, namely s' = [].
PhantomGate is proposed to prevent this trivial solution by injecting explicit negative supervision during training. Specifically, PhantomGate employs a threshold 7 to assign [0, 1] to reliable pseudo negative samples, while simultaneously incorporating regret-based label updating. That is, when the model identifies that the pseudo target of sample has been incorrectly set to [0, 1] PhantomGate
allows the pseudo target to be updated starting from s' rather than resetting [o, 1)". The pseudo
targets of positive data are fixed as [1, T] throughout training. The pseudo targets of unlabeled samples are initialized as [0, 1]T and updated as follows:
[0, 1]
f1( 2T,
(11)
f1 <T.
where fe(x) denotes the e-th entry of the softmax output produced by the classifier.
To avoid manually setting т. the self-adaptive threshold (SAT) (Wang et al., 2023b) is introduced, which offers two key benefits: it starts low to supply clear supervision for more negative samples in early training, and gradually increases to filter out potentially incorrect negatives as training pro- gresses. The global threshold 7 and the local threshold (p) updated follows:
i= = + (1 - Σ max(f(x:))) p(c) = > +
(1- - +
Σ Sa(wx),
(12)
where b denotes the batch size, 7 is momentum hyperparameter, and p(c) denotes the e-th entry of P. Both and p(c) are initialized to 0.5. The ő is used to modulate 7 in a class-wise manner, and the final threshold can be obtained follows:
p(1)
T max ((1)) F.
(13)
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Finally, NcPU can be optimized as follows:
C
1
E
1
Σ 8.EM
C.
1
(14)
P
u
E.PP
B.ED
where Q denotes the set of same-class pairs associated with 2,, and w, is the weight hyperparameter. In practice, is computed in a batch manner. An entropy regularization term employed to stabilize training. The pscudocode of NePU is provided in Appendix
4 THEORETICAL ANALYSIS OF NcPU BASED ON THE EM FRAMEWORK
By injecting the classifier predictions into the EM framework, the latent variables can linked to the supervision from PU data, thereby enabling more accurate supervision for the unlabeled data during the iterative process. Different from previous works (Wang et al., 2024. Yuan et al. 2025). which conducted their theoretical analyses within the framework of supervised contrastive learning (Khosla et al. 2020) while neglecting the uniformity term, the theoretical analysis in this paper is instead built upon non-connonnnnoo con--ontratttve learning (C,). By adopting the non-contrastive learning framework, this study avoids the complications arising from the uniformity term, thereby providing more comprehensive theoretical perspective. Since the positive data have accurate labels, the following analysis focuses primarily on the unlabeled data. more detailed derivation can be found in Appendix [
E-Step. At the E-step, each unlabeled example is assigned to one specific cluster. Given a network g(-) parameterized by 0, the objective is find O" that maximizes the likeliikkoodd function:
0
arg max
log 0 arg max
log Σ =
(15)
BEW
#EZ
where 2 (0, 1} denotes the latent variable associated with the data. If the classifier predictions are injected into the EM framework: p(= xc 0) p(y az, 0), and considering that the label of each
sample deterministic, have p(y) , 0) (ÿ = yy) Then, O" can be obtained as:
0 arg max
Σ
Σ
1 - v) log p(x; 0)
(16)
DE DEZ
M-Step. At the M-step, minimizing E. encourages embeddings to concentrate around their cluster centers (cluster tightening). For analytical convenience, all data are considered in each iteration:
Rz) - - -
Rx(x) Tu well
(17)
AEER
k.EQ
Since the same-class peer set of is constructed based on the classifier predictions, the unlabeled data can be divided into two subsets S. C (c E (0,1)), where S. = {a) arg max f(x) = c, x E 43. Then (2r) can be reformulated as:
2
Rx(x))
Nu Σ
lØ(x)) vall?
(18)
SEE.
where v. denotes the mean center of S.. Since n, usually large, we approximate 1 simplicity, the augmentation operation is omitted and let q = ğ(x). Under some mild assumptions, minimizing (x:) is equivalent to maximizing lower bound of the likelihood in 15.
[8] R For
Theorem Assume the distribution of each class in the representation space follows d-variate von Mises-Fishe (vMF) distribution, which leads to: h(xlee, k) ca(x)e 3(m), where V. vel |eell, R. is the concentration parameter, and ca(k) is the normalization constant. Under the assumption of a uniform class prior, optimizing Eq. and Eq. (5)) is equivalent to maximizing Lı and Le below, respectively.
SSal nu
See |ell L2. na
L
|
(19)
S.Ell
S.ell
A more detailed proof can be found in Appendix Theorem indicates that minimizing Rx(x)) is equivalent to maximizing a lower bound of the likelihood in Eq. 15). The lower bound becomes tight when ||=]||| is close to 1, which implies that the data with the same label are concentrated the representation space.

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Table 1: Results of different methods (mean=std). The best performance is highlighted in red.
Method
Addirional N Data
CIFAR-IO
CIFAR- 100
STI-10
ARCI)
<HI
OA
P1
OA
OA
F1
OA
F1
OA
F1
CB
60,45461
2.42-44
50,36416
1.86
50.30 30.30440
1.19822
55,70462
20.93424
84.08
25,70
uPU
65.52492
26 26.82499
61,4499
43.
57 0gg0gg
25 88-13
83,76-21
81, 81.4322
86.8293
55.43-28
unPU
87.29-9.5
83.71 10
72,00
74,93m0
80.62-M1
79.28-422
87.73384 4
58
82 22.60
59.66-h7
vPU
85,94464
82.98 4g
69,0 09.01412
70.78442
75.76455
70.524
84.06-7
84,13414
73.604
50.30
ImbPU
87.29
83 80
72.0747
75 15.05mm
80 68
79. 19:4
88, 14
88, 60003
82,51 M01
89, 99,72405
TEDn
86.29 29:24 4
80, 70
69. 8:38
61,73415
66 2636
88 9pell
89. 89.19
85.4 e
52,65546
PUET
78.5
73.85
62,81
71,0gam
75. 75.36
73.56-
78.09229
66.528l49
74,92%L
38.38
HolisticPU
84,20-21
78, 18
51,944151 64.01445
72.81 1du
66.064146
65.4941.
$1.60415
81,9841
53,15434
DisiPU
85.29-7A
83.96 4022
67.65 67.63448
73.68 73.6841s
85 63.62415
85. 45.4
86.25 26.25
87.36*1
82.94
57,58+92
PICO
89.72461
87.40400
69.98444
72.71
60.71 440
71.04-03
74,07
79.27413
49,36
39.52402
LaGAM
95.78465
94, 94.904ma
84. 34.82413
84 42442
88 64444
88.50-01
75 95.0004
78.3844
79,14415
58, 88,78417
WSC
90.55a8. 3
87 97.92
75. 15.3992
73,76558
79.06 09.0664.5
74. 74.16=70
80, 80,
76.12443
84, 84.89
62.17513
NcPU(ours)
97
96,67802
88,2840
88,14
91.40a04
90.82ati
91.10
91,21
87,60410
64.84221
Supervised
96,24902
89.66 20.65993
89.7gan4
92.00992
91 91,96993
88.47903
73,3250
EXPERIMENTS
5.1 EXPERIMENTAL SETTINGS
Datasets. To evaluate the performance of the proposed NcPU, five datasets are employed: three prevalent benchmark datasets (CIFAR-10 10 (Krizhevsky et al. 2009). CIFAR- 100 (Krizhevsky et al.] 2009) and STL-10 (Coates et al. 2011)) )). as well as two remole sensing post-disaster building dam- age mapping datasets (ABCD Fujita et al. (017) and xBD (Gupta et al. 2019),, which can be used to identify damaged buildings after disasters. Experiments on ABCD and xBD demonstrate the sig- nificant potential of PU learning in the field of HADR. More details regarding ABCD and xBD are presented in Appendix [D] Each dataset was partitioned into two non-overlapping subsets, denoted as positive and negative, according to their category labels. For the training process, 1000 positive samples were utilized from CIFAR-10, 10, CIFAR- 100, and STL-10, 300 from ABCD, and 500 from xBD, respectively. A comprehensive summary of the dataset statistics is presented in Appendix D
Baselines. To evaluate the effectiveness of NcPU, we compare it against eleven baseline methods: uPU (Du Plessis et al.,, (2015), nnPU (Kiryo et al. (017). vPU (Chen et al. 2020). ImbPU (Su et al.)
2021 J. TEDn (Garg et al. 2021). PUET (Wilton et al. 2022). HolisticPU (aan et al. (023a),
DistPU (Jang al. 2023), PICO (Wang al. 2024), La (Long et al. 2024), and (ZC al. 2025). In the CE method, unlabeled data are treated as negative samples. Representation learn- ing modules are also incorporated into PiCO, LaGAM, and WSC. Nevertheless, LaGAM requires auxiliary negative samples, whereas WSC relies on additional pre-estimated parameters. PiCO, originally designed for partial label learning, exhibits suboptimal performance when applied to PU learning tasks. For NePU, all momentum hyperparameters are set to 0.99, and the w. is set to 50 for all datasets. More detailed implementation settings are provided in Appendix F ResNet- 18 (He et al. 2016) is adopted as the backbone for all methods. For methods that require Tpp Tp is estimated using KM2 (Ramaswamy et al., 2016).
Metrics. Overall accuracy (OA) and F1 score are adopted as the primary metrics. Precision, recall, and area under receiver operating characteristic curve are provided in Appendix G are repeated three times, and both the mean and standard deviation are reported.
All experiments
5.2 MAIN RESULTS
NePU achieves the best performance. The results of all methods are presented in Table where the proposed NcPU achieves the best performance across all datasets. Notably, NePU does not re- quire additional negative samples or pre-estimated parameters. Compared with other methods that also do not rely on additional negative samples, NcPU achieves improvements in OA of 6.81%. 81,, 12.89%, 5.78%. 2.20%, and 0.78% CIFAR-10, CIFAR- STL-10, ABCD, and xBD, respec- tively. Although LaGAM achieves the second-best performance on three benchmark datasets, it requires additional negative samples as input. As algorithm originally designed for partial label
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Table 2: Ablation and comparative analyses on CIFAR-100 dataset. NCL: Non-contrastive Loss. LD: Label Disambiguation.
Table 3: Performance Analysis of &, under risk estimation with the real Hp and supervised methods.
NCL
LD
CIFAR
CIFAR 100
Method
61,54%7
40.58
84.36
30
OA
FI
OA
FI
&
$0,27801
1,09544
97,972la
0.55+12
uPU uPU+4 nnPtI 83,25
69.43
41,3241
61.68499
44,18
73.22417
72.75
74.10-2
71.47499
97.35
96.66442
83.71416
81.40
84.58"u
85,90als
79.1241a
93.96403
76.9449
71,22
68. 1241e
4
75,14
79.91-17
67.15:56
98.73495
mnPU+4 97.03al2
96.37482
87.81
87.23aM4
4, s'+SAT
50,25*00
1.01
97.85-10
0,51
Supervised+C.
98.53-90
98.17'81
94,45'0
94.52
&
88.28
88.14
89.12-10
87,27
Supervised+2,
98. 98.75
98.43401
94,56*0.
94.64
learning, PiCO exhibits inferior performance compared with NcPU. Finally, is observed that NePU achieves results comparable to, or even surpass, those of its supervised counterpart, demonstrating the effectiveness of noisy-pair robust representation alignment PU learning.
NePU learns more discriminative representations. The t-SNE visualization of representations on the training data demonstrates the learning ability of the PU learning methods under unreliable supervision (Figure 2) As shown in Figure 2 compared with other PU learning methods, NcPU produces more discriminative representations through noisy-pait robust intra-class representation alignment.
NePU has broad application potential in HADR. NePU achieved the best performance on both the ABCD and xBD datasets. Among them, the xBD dataset, which encompasses nineteen disaster events with global coverage, highlights the remarkable application potential of NcPU.
5.3 ABLATION STUDIES AND ANALYSES
f, and can benefit each other. Due the influence of non-discriminative features, alone is insufficient, as shown in Table whereas its integration with &, leads to notable improvements. Furthermore, this mutually beneficial effect can be theoretically justified from the perspective of the EM algorithm, as detailed in Section 4
Ê, demonstrates robustness against noisy pairs. The results in Table corroborate the theoretical analysis, demonstrating the robustness of L, to noisy pairs, with L, + s achieving 88.28% OA compared to 84.58% for L, + s. C, is robust to noisy pairs without losing performance in supervised learning tasks, achieving results similar to L, (Supervised+C. vs. Supervrrvs in Table
PhantomGate plays important role in label disam- biguation. As shown in Table 2, in the absence of unam- biguous negative supervision, class-conditional prototype la- bel disambiguation (s') tends to yield trivial solution, re- sulting in high recall but low precision for the positive class. When SAT is employed to introduce negative supervision, the inaccurate negative supervision improves the precision of the positive class but substantially reduces its recall. In contrast, PhantomGate enables the model to discard inaccu- rately selected negative samples, thereby achieving a better balance between precision and recall of the positive class.
Roslthee Magative
-30
Poelive haggative
100
0
100
100
L50
uPU features
uPU- L. features
50
i, significantly enhances PU learning methods. Risk es- timation methods, which have been validated both theoret- ically and empirically as the most simply and robust ap- proaches, are utilized as baselines to reduce the impact of hyperparameters and heuristic techniques. As shown Ta- ble 3 compared with uPU and nnPU, the methods employ- ing C, achieve superior results, highlighting the importance of learning discriminative representations. The t-SNE visu- alization of learned representations shown in Figure
-50
Poollive
-10
Mlggative
Kangative
100
unPU features
100
100
MPPU+
Gestures
100
Figure 4: t-SNE visualizations of the representations learned by risk esti- mation methods on CIFAR-10 train- ing dataset.
While nnPU serves the foundation of
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100
100
100
100
50
60
60
60
0.9
0.99
0.999
0.9999
8.9
0.99
0.999
0.9999
0.9
0.99
0.999
0.9999
10
30
50
70
(a) Analysis of a
(b) Analysis of
(c) Analysis of
(d) Analysis of wo
Figure 5: Analyses of hyperparameters on the CIFAR-I0 dataset.
deep PU learning by constraining the negative risk to be non-negative, we show that uPU+C, can achieve superior performance without this constraint. Remarkably, L, enables simple PU meth- ods to achieve highly competitive performance, this insight opens a promising direction for deep PU learning. More experiments are presented in Appendix
Analysis of hyperparameters. As shown in Figure 5 NcPU is insensitive to a and 7. A smaller accelerates the update of pseudo targets, whereas larger w, facilitates the learning of more discriminative representations, thereby enhancing label disambiguation. Additional experiments are provided in Appendix H Overall, NePU demonstrates robustness to hyperparameters, as the same parameters used across all five datasets:
7 0.99 and w, 50.
Analysis of training stability. While the gradients of Ê, do not vanish and include the term V they do not
100
lead to significant overfitting or training instability: (1) Ben- efiting from the asymmetric architecture and random data augmentation, qi * k, is ensured, which can enable the nu- merical stability of the gradient; (2) As q. ky approaches 1, the gradient magnitude becomes Te. instead of infinity,
within a finite number of training iterations, L, does not lead to notable overfitting or training instability; (3) The training stability can also be empirically verified (Figure 6 Taking the results on CIFAR-10 10 dataset as an example, NePU has achieved promising performance the 400th epoch. After extended training for a longer period, the results NePU does not exhibit overfitting instability; (4) The numerical stability can be improved by constraining the value of q, kj (e.g.. ..... [10-4, 4, - 11.
65
60
CIFAR-1U
CIFAR-100
55
200
400
600
800
1000
1200
Epoch
Figure 6: OA curve NePU during the training process. NePU exhibits stable training performance over a prolonged training process.
RELATED WORKS
Positive-Unlabeler Learning. A straightforward approach is identify reliable negatives from the unlabeled set and then train a supervised classifier on positives and these negatives (Gong et al.] Yu al. 2004). but its performance heavily depends the correctness of the selected sam- ples. Recent studies try to directly estimate supervision from all PU data, such as cost-sensitive based methods (Li al. 2022). label disambiguation based methods (Zhang al. 2019). risk es- timation based methods (Kiryo et al. [0117; Zhao et al.) 2022 (Su et al. 2021 Wilton et al. 2022
2018
methods (Kato al. 2019)). and variational prin- Zhao et al. 2023b), density ratio estimation-
ciple methods (Chen et al. [2200] Zhao et al. 2023a). Recent studies (Long et al. 2024 Yuan et al., 2025 leverage contrastive learning module obtain better representations, but still suffer from
noisy pairs and require either auxiliary negatives (Long et al. (024) or pre-estimated uр (Yuan et al.) In contrast, the proposed NePU robust to noisy pairs and free from such requirements.
2025
Contrastive and Non-contrastive Representation Learning. Self-supervised learning has re- cently made significant progress in acquiring high-quality representations. Depending on the use of negative pairs, self-supervised learning methods are broadly categorized into contrastive and non-contrastive learning: contrastive losses encourage embeddings similar images to aligned (alignment) while pushing apart those of different images (uniformity) (He et al., 2020; Wang & Isola 2020; Huang et al. 2023a Lu et al. 2023); non-contrastive losses only align embeddings of
similar images (Grill al. 2020 Chen & He 2021 Guo al. 2025). Beyond self-supervised set-

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Published as a conference paper at ICLR 2026
tings. SupCon was proposed to extend contrastive learning by incorporating full supervision (Khosla et al. 2020). Recent works actively explore the application of contrastive learning to weakly super-
vised
tasks Li et al. 2022 Huang et al. 2023b] Zhang et al. 2024] Wang al. 2022 2024 Yuan
et al. 2025). However, most of these methods rely on supervised contrastive learning with pseudo labels, which suffer from the problem of noisy pairs. 'he CoTAP Loss (Wen et al., 2025 is pro-
posed to align the representations of semantically similar objects in self-supervised dense represen- tation learning, and the negative effect of noises is alleviated by assigning higher weights to sample pairs with top scores. The WSC framework (Zhou et al., 2025). graph-theorett, weakly super- vised contrastive learning method, introduces continuous semantic similarity; however, it requires pre-estimated parameters as input. In contrast, NcPU, which builds non-contrastive learning, is robust to noisy pairs and does not rely on such requirements.
CONCLUSION
This paper identifies the challenge of learning discriminative representations as the key bottleneck in PU learning. Theoretical analysis demonstrates that noisy pairs dominate representation learning optimization, while the proposed NoiSNCI. and PL.D form an EM-inspired framework that itera- tively benefits each other. Extensive evaluations on both benchmark datasets and remote sensing building damage mapping tasks validate the effectiveness of the proposed NcPU. Applications of binary classification with only positive data annotated can benefit from this study, and we expect fu- ture research to extend this framework beyond image classification. Masked image modeling will be incorporated to harness more powerful backbone frameworks. Beyond PU learning, the framework holds promise for broader applications in more weakly supervised learning scenarios.
ETHICS STATEMENT
This study complies with the ICLR Code of Ethics. The study does not involve human subjects, and no personally identifiable information was collected or processed. All datasets used in this work publicly available and widely adopted in the research community. We have carefully considered potential risks of harm that may arise from our methodology or findings, and we believe the insights primarily benefit scientific and educational purposes. While our model may be applied in various domains, we encourage responsible usage and highlight that it should not be deployed in sensitive contexts without thorough evaluation of fairness, bias, privacy, and security concerns. We confirm that this work adheres to research integrity standards, including accurate reporting of methods and results, avoidance of conflicts of interest, and compliance with relevant legal and ethical guidelines.
REPRODUCIBILITY STATEMENT
is provided to facili- tate the reproduction of the experimental results. Theoretical results, including assumptions and complete proofs, are presented in detail in the main text and the appendix. All datasets used in this work are publicly available and have been widely adopted in the research community.
code repository
com cww.:Henggee-22aao5///eeee
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A MORE T-SNE VISUALIZATIONS OF LEARNED REPRESENTATIONS
CE denotes the training strategy that employs cross-entropy loss, where unlabeled data are assumed to negative samples. Compared to supervised features, positive and negative features from other methods (nnPU (Kiryo et al. 2017). DistPU (Jiang et al. 2023), HolisticPU (Wang et al., 2023a), TEDn (Gagg et al. 2021)) WSC (Zhou et al. (025g) exhibit significant overlap on the train- ing dataset (Figure
Positive Negalive
100
50
50
0-
-50
-50
550
-50
Negalivee
Negalive
200
Negative
(a) CE features
(b) nnPU features
(c) WSC features
(d) DistPU features
50
50
-50
Positive
-50
Positive
-30
Positive
-50
Pasitive Negative
Negative
Negative
Negative
(c) HolisticPU features
(f) TEDn features
(g) NePU features
(h) Supervised features
Figure 7: t-SNE visualizations of the representations learned by different PU learning meth- ods on CIFAR-10 training dataset. Compared with supervised features, the positive and negative features obtained from other methods (nnPU, DistPU, HolisticPU, TEDn, WSC) exhibit substantial overlap, indicating that the primary bottleneck in PU learning lies in acquiring discriminative repre- sentations. In contrast, the representations produced by NcPU demonstrate discriminative ability.
B THEORETICAL ANALYSIS
B. DERIVATION OF GRADIENTS AND GRADIENT MAGNITUDES
The supervised con-contraet loss (L,) and noisy-pair robust supervised non-contrastive loss (C.) are defined as follows:
Lx(2;, 2(1 1( 1 = =,,}.
E,(x;, = 2 (q.. 1 = vı
TAl Only the case 1/y, y3} is considered because the loss is not calculated when ( yj = 0. The prediction head is regarded as an identity function for simplicity.
where q q and k T
k
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The gradients of (z,; w.y can be obtained as follows:
(C,
0q, kj
dq:
0q:
aq: kj
2 Oq:
0q.
d 0v q: qi
22
qi
(20)
9; 9 dq.
9, 9
dq:
-2
q kk
9, 9: v 9, qi
2
(I q: hrg.
| l2
The gradients of (x,,, æzy) can be obtained as follows:
aC, (2,, xz))
0g, k
0q:
V1 9, k, 0q.
(21)
-1
(I - q:q. kjj
q: l12 V 1 q. Kj
Considering that the following equation holds:
II q:q.))
(q:q.
(q. qi
(22)
q.9. T
(I-Q:9.) ( q.9.
= (I 9.4.
(I 9.9.
q.9. T q.q. + q.q.
(23)
q:
The gradient magnitudes of Cr( R.)) can be obtained as follows:
(2,, x;)
OC, (x,, x3,)
OC, (x,, xz,)
0q:
Oq.
dq.
4
kj (I 1-::q7) T (I-q:q.) k3
q:q.
|/
kJ (I q:q. kk
|1qil12 2
(24)
(k] k; k3 q.q. kg))
1|q.ll2
11q.112 (1
(q. k)
4
(1
(q.. 4))
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The magnitudes of gradient of (z;, x,) can be obtained as follows:
(z, x;))
0C, (Z, z,) T (Zr ( xz))
3q:
Oq:
Oq:
1
k3 (I q.q.
(I- q.q. (I-q.q)) k3
|| 112 (1 7. ki))
(1- (ă, k)
11a:112 (1 0, kiz)
(25)
(1 q k2)) (1 + (q. k;))
11q:112 (1 -,1 k:z)
|| 12 (1 + (q) kj))
(1 + (ā. dj)).
| 1
B.2 DETAILED DERIVATION OF NePU IN EM FRAMEWORK
At the E-step, each unlabeled example is assigned to specific cluster. At the M-step, minimiz- ing (x) encourages the embeddings to concentrate around their respective cluster centers. The detailed theoretical interpretation is provided below.
E-Step. Given network g(-) parameterized by 0, the objective is to find 0* that maximizes the log-likelihood function:
0 arg max
log p( p(x(0) arg max
log Σ p(xx210)
O
2EZ
{0, }} denotes the latent variable associated with data. Since this function is difficult to optimize directly, surrogate function is used to lower-bound it:
where =
p(a, x 00) Q(2)
Σ log Σ pax = Σ log Σ Q(2) BEL
sEZ
sE2
(26)
p(x, 200)
2 Σ Σ (()) log
(2)
øEU =EZ
where Q(z) denotes distribution over z's (E Q(2) = 1). To ensure that the equality holds, p(w.= must be constant. Then, have:
(())
p(u, 2 p(æ, z|0)
Q(=) Σxez 2)) p(x(0) = p(z|æ, 0),
(27)
which corresponds the posterior class probability: p(z|ær 0) = plyla 0). At this step, the classi- fier predictions are injected into the EM framework, linking the latent variables with the supervision from PU data. Considered the predicted label ÿ arg max f fæx ), and considering that the label of each sample is deterministic, we have p(y xz, 0) = 1 = y). Then, 0" can be obtained as:
0 arg max
Σ RELd
Σ
1 v) loo.poo..... v)
(28)
0
M-Step. At the M-step, the goal is to maximize the likelihood presented in Eq. 28). We will demonstrate that under some mild assumptions, minimizing (x) is equivalent to maximizing a lower bound of (q. For analytical convenience, all unlabeled data are considered in each iteration:
(1 (1- q [Ta.)
Rx( = nu well
Σ
(29)
O
k,E0
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RT(x))
1
Σ DEUl R.E
V q k.
(30)
where Q corresponds to the positive peer set of the example æ. Since the positive peer set of æ is constructed based on the supervised model predictions arg max (z), the unlabeled data can be divided into two subsets S. C U (c E {0, 1}), where Se = {ar arg max f(z) = c, a E UJ. Then the (ax) can be reformulated as follows:
2
(x)
q
k+
Thu
aell
k EQ
2
Σ
llā(x) 3(x')1?
11u
S
S.Ell
ES,
2
Σ
[1((=)112 -2)(x) g(x0) + (1 )1())
Thu
2
S.EM
BES, x'ES.
2
(E
Σ 3(ar))
SSo - -
Tu S.EM
#ES.
Eo
2
(|Sel g(x)) ((tc)((()ve))
Thu S.EM
Sel
#ES
(31)
2
Σ
[Sc
Σ ((zz)
Vc
Th S.EMl
LEES
2
[8al (1 (1-1|eal1*
Thu S.Eu
T
2
|Sel -2 Σ g(x)
vc + 11 |1
Thu S.ell
LEE..
2
[1ā( 20(x)) T Ve [kel1²)
nu B.ElwEE.
2
l0(xx) vel2
nu S.EM DES.
where ve represents the mean center of S.. For simplicity, the augmentation operation is omitted and q = (xx). Since n, is usually large, we approximate [S.] [@l
Assume the distribution of each class in the representation space is a d-variate von Mises-Fisher (vMF) distribution, which leads to: h( x) c=( ālm), where D. ve/ |lelll is the uni-
concentration parameter, and ca(x) the normalization constant. Under the assumption form class prior, optimizing (31 and (2)) is equivalent to maximizing L, and L, below, respectively.
Sa
Sc
L1
||lll
voll
L2.
(32)
The
nu
S,ell
S.eul
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arg min Published as a conference paper at ICLR 2026
Figure 8: Examples from the ABCD dataset: the first row shows pre-disaster imagery, and the second row shows post-disaster imagery.
The lower bound becomes tight when ||ell is close to 1, which implies that the data with the same label are concentrated in the representation space. More detailed proofs are as follows:
arg min (x) = arg min
Σ
llØ(x) - well
e
S.EM mES.
Σ [10(())11 - -2](x) 'vc + 11be
0
S.EM mES.
(33)
(1Sal - 1cll-Sallleedl (lec1)
arg min 0
S.Eld
|Scl |//|
arg
nu
S.ell
arg max
ΣΣ
1( = u) logglll 0) = arg max
ΣΣ Σ
1 = y) log logp(æyy. 0)
wELl DEZ
DEUl DEZ
arg max
Σ
logp(zly= c,
S.Eu weS.
(34)
arg max
KD ((x)
S.Eul seS.
Saa
arg max
||elll
nhe
S.Ell
Given that
C, 0z)) S C, xz),
(35)
we can obtain
R₂(x) S (z)
(36)
In other words, minimizing (x) is also equivalent to maximizing a lower bound of Eq. 28 Given
that NcPU can be interpreted from the perspective of the EM framework, its non-contrastive learning module and classification module can mutually enhance each other during the iterative process, allowing NePU converge (local) optimum.
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Algorithm 1: Pseudocode of NePU (one epoch).
Input:
Training dataset D, classifier f, online network 9, target network g', initialized pscudo targets as initialized class prototypes momentum hyperparamcters a, 3,
for iler = ..2..... .......d. do sample mini-batch B from D
// classifier prediction {ut arg max fa(x:) e B}
// online embeddings generation
B2 = (q: = g(Aug (a:))læ; (
B)
// class-cenditions
prototype updating
for æ; E B do
p. = Normaizeeaau: + a)
end
update the target network
momentum update g' by using g
target embeddings generation
10
B& = (k; = (Aug, (m; E B)
// self threshold updating 0(1)
max{p[0).6(1)) 7
// phant.c pscudo target updating for æ. do
12
13
= OneHot(arg max q. 14;))
$ = Bat + (1 B)r:
[0, 1JT
f1( 2 7
15
fi(x:) <T
16
// netwerk updating minimize loss L
17
18
end
C PSEUDOCODE OF NcPU
The pseudocode of NePU summarized in Algorithm
D DETAILED DESCRIPTION OF DATASETS
To demonstrate the promising applicability the proposed NcPU in the field of HADR, two remote sensing building damage mapping datasets utilized: ABCD (Fujita al.) 2017) and xBD (Cupta jet al. 2019). The ABCD dataset
single-hazard dataset annotated to determine whether build- ings were washed away by a tsunami. It comprises both pre-disaster and post-disaster imagery, as illustrated in Figure g The spatial resolution of the ABCD dataset is 40 cm. The xBD dataset large-scale scale.
dataset encompassing building damages caused by six different dis- aster types worldwide (carthquake, wildfire, volcano, storm, flooding, and tsunami). It contains both pre-disaster and post-disaster imagery; however, to ensure distinction from ABCD, only the post-disaster imagery from xBD is employed in this study. Specifically, in processing xBD, each building is buffered by a distance equal 0.5 times its size, and the minimum bounding rectangle of each buffer is cropped and used as training data. For classification, the categories "Destroyed" and "Major Damage" are regarded as the positive class. More detailed dataset statistics are presented in Table 4
E
IMPLEMENTATION DETAILS OF PICO AND WSC
For PiCO Wang et al. 2202 2024), this paper treats unlabeled data as data associated with coarse candidate label set. During training only the pseudo labels of the unlabeled data are updated, while positive samples consistently trained with their ground-truth labels. At the beginning of training.
19

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Published as a conference paper at ICLR 2026
Table 4: Summary of datasets.
Dainset
Paa
* F'Tesring Data
9p-
Positive Class
Inpar Size
CIBAR-10
1000
40000
10000
0,1.8,9
3 32
CIFAR-100
1000
40000
10000
Animal
52
STL-10
1030
90000
8000
0,2.3,8.9
3xx 96 96
ABCD
300
4000
3377
0.5
washed-oway
6 122 x 128
xBD
500
20000
37682
0.4
2,3
3 x 64 64
Table 5: Results CIFAR-10 and CIFAR-100 datasets (meantstd).
Additional N Data
CIFAR- 10
CIFAR-100
Method
OA
Fl
P
AUC
QA
F1
R
AUC
CE
60,45201
2.42a014
92.62455
1.22222
59,16219
50,36mic
1.86.12
80,92844
0.94911
62.36434
uPU
65,52492
26.82440
88,73407
15.80403
50.43420
61 4445
43.12421
82,0941
29. 29,25413
11.19437
unPU
87,29-0
71 t0
85,897
81.65116
89,77193
72
74.93*11
67,85
83
78.61
vPU
85,94a8
82,90 9g.9g
80 $0,42429
85,7442
92. 92,95338
69.0 69,01412
70.78422
67,1042
75.07=3s
75.5
ImbPU
87.29-0
83.80 1
85.53+1
82, 13
89,76-91
72,07
75.05
67.82
84,02
78.30*9
TEDi
86.29'2
70
91.63*1
72.47%
94.53+92
00.55* "
61,73*1
84 4
48.67
81,83*
PUET
78.51 40
73.85
71.94
75.86
62.8 62.81
71.09401
58.14
91,45022
HolisticPU
84,20-21
78. 10
87,31-74
70.96
93.08-11
64.01
51,94-151
75,71
41.40-144
73.89-16
DisPU
85,29*76
83,96 *h
74,77
95. 25.86.1m
95.8 95.80
67 67.63
73.6 73.68**
62,07"95
90.64*1
77.53*
PICO
89,72"1
87.40
85
89. 19.13"
95.61
69 10.
72.71
66.66
79.97
76,47
LiGAM
95,78405
94, 9gans
92,03a15
97. 97.96ans
1981
84,82s01
84,42402
86,7330
82,23405
92,33485
WSC
90.55a03
87,9 87.92443
89,99425
86.0855
96.23302
75.39421
73,7644
78.7942
69.76441
83.35418
NePUrours)
97.36-
96,67"0
97,53*14
95 m2
99,30*91
88, 88.28
88.14
89.12"!
87,27
94, 94,99*91
Supervised
96, 969r
96, 2g
95,438ta
97. 07.06a11
99.5g440
89,65903
89.7ga14
88.6 88.63905
90.97413
95, 95.99422
Table 6: Results on STL- and ABCD datasets (tea
Method
Additional N Data
STL-10
ABCD
OA
AUC
R
AUC
CE
50.30-00
L11982
98.48425
0.60a11
75,38
55.70422
20,93424
95.65-83
11,75403
1841
uPU
57.08-84
25 88-13
94.67405
14,9941
72.84417
83.76424
81.47429
94.27484
71,83466
92.67435
unPU
80.624
79.28482
85,14
74,19413
87,96
87.73424
88, 88,36403
83,93410
93,2940
94,0g420
75.76445
70.524004
87,93425
60.1 60.134147
81885411
84.06430
13.1444
84.16491
85 50-1D
93. 19410
ImbPU
80.68-84
79.1 1-:1
85.0040
74.524t
87,89
88. 1442
88, 6940
$1.56404
93,25444
94,33423
TEDs:
66.26449
19, 19.9044177
95.00415
34 34,354102
86,77418
88, 90:39
89, 19.0
87,35414
90,9641a
94,93003
PUET
75.36
73.50 1
79,35
68,56443
78.0 78.0942.
66.52424
61,97425
71.9
HolisticUU
72.81444
66.064143
85.954006
58,264555
86.74414
65 65.49a11
51.604
87.69411s
36,97439
$2.874ms
DisPUU
85.62-15
85 $5.11=99
$7.13450
84.00
12,19
86.25 86.25
87.36*
80.84=2.8
95.11
95.30
PICO
60.71494
71.04-33
56,264M
96.36'13
78.80414
74.07+3
79,27413
66.00
99,254m3
83.65
LaGAM
88.6 $8.62480
88 $8.50=41
89,60
87.43
95,25
75, 25.90+34
75.38446
76.85+9a
73,994t
83,87414
WSC
79.06+15
74.16-7
95,40447
61.11
92.89MM3
80.10=>x
16.12
94.33-94
63,98
94.07=91
NcPU(our))
91.40=b
90.82-46
97.38
15.1
96.52-11
91.10=>
91
89,89-12
92.58
96.01
Supervised
92. 02
91
42.22404
91, 11
97, 18
the pscudo labels of the unlabeled data are initialized as negative. For WSC Zhou et al.] (2025), unlabeled data are initialized as negative samples, thereby reformulating the PU learning task problem of learning with noisy labels. The classification model is subsequently trained using the Learning with Noisy Labels method proposed in WSC.
F IMPLEMENTATION DETAILS OF NcPU
All momentum-related hyperparameters (o,, B, and 7) in NcPU are fixed at 0.99 across all datasets. The model is trained for 1300 epochs for all datasets. Optimization is performed using SGD with a momentum coefficient of 0.9, combined with cosine annealing learning rate scheduler. The initial learning rate is set to 0.01 for the STL-10 dataset, 0.0001 for the xBD dataset, and 0.001 for all other datasets. The w, is set to 50 for all datasets, while the Wen is assigned value of 0.5 for CIFAR-100
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Published as a conference paper at ICLR 2026
Table 7: More ablation analysis between 2, and
CIFAR-IO
CIFAR-
&
OA
FI
OA
FI
75.61"1
56.48
61.54*14
40.58
6166045
7,72-24
50.27am
1.09a4
97.36
96,67
88.28
88,14
Table 8: More ablation analysis on label disambiguation.
CIFAR-10
CIFAR: 100
Label Disembigattonn
OA
R
OA
F1
97.41
96.79m1
95.88
97.72
75.14"
7991"11
67.15
98.73"5
6 SAT
60.15400
2,24
98,00412
1,3463
50.25400
1011
97,85
0,51
97.3640
96.67922
97,5344
95
88.2900
89.12477
87,27322
and 5 for the remaining datasets, A warm-up phase is applied at the beginning of training, during which pseudo targets are kept fixed for the first 30 epochs.
G MORE EXPERIMENTAL RESULTS
The results of precision (P), recall (R), and area under receiver operating characteristic curve (AUC) presented in Table T NePU achieves better trade-off between P and R.
H MORE ABLATION ANALYSES
Ê, and can benefit each other. Experiments on the CIFAR-10 dataset (Table (7 further validate the theoretical analysis in Section demonstrating that Ê, and s can benefit each other, thereby enabling NcPU achieve superior performance.
PhantomGate plays an important role in label disambigua- tion. More detailed results on label disambiguation are pre- sented in Table 8 While class- conditional prototype-based la- bel disambiguation (s') performs well on the CIFAR-10 10 dataset, it fails to achieve satisfactory results on the CIFAR- 100 dataset. Specifically, this approach achieves relatively high recall for the positive class but suffers from low precision, indicating ten- dency to over-identify samples as positive. Therefore, incorpo- rating negative supervision through SAT and PhantomGate is es- sential, even if it slightly degrades performance on CIFAR-10. 10.
80
25
04 Treining
70
65
55
i, significatly enhances the performance of PU learning methods. Apart from Table also conducted another of experiments to analyze the contribution of representation quality on PU learning and test the robustness of É, with respect to fewer training data and higher Tp. CIFAR-100 is used the experi- mental dataset, with the division of positive and negative classes consistent with the main experiments, and ResNet-18 18 serves the backbone. To highlight the effectiveness of Ê. the Tp is set to 0.6, with 1000 positive training samples and 20000 unlabeled training samples. Optimization
50
1.00
150 Epoch
200
250
300
Figure 9: 4 will accelerate the model's correct fitting to the training dataset.
Table 9: Non-contrastive loss analysis on CIFAR- dataset.
DA
F1
performed using SGD with a momentum coefficient of 0.9 and a cosine annealing learning rate scheduler. The initial learning rate is set to 0.001. The u, is set to 100. The pair-construction strategy is generalized by in- troducing a similarity threshold (7), which enables more flexible construction of pairs:
uPU
66,844431
60.1241.5
unPU
69.51-416
69.524
72.71
76.29-51
78.4742
uPU+
80.06a0
79.6744.22
81,55
$1.59mis
S1 (mx)) + fi (1x))) (x
(37)
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Published as a conference paper at ICLR 2026
View (Sinilaity 0.5)
0.2
03
05
2.1
1200
Tay View (Sintartt 2 9.7)
Sucface Pist of Pain Sanikaitys F:00fedte 16000 fekel
64
02
02
154)
1,00
Figure 10: An illustration of pairs selection based on similarity. In the top-view representation, the colored regions indicate the pairs involved in training. It can be observed that smaller r leads to a larger number of pairs being included. In particular, when T = 0.5, the selection becomes equivalent to pairs selection using pseudo labels.
100
100
80
CA
60
0A
F2
0.9
0.99
0.999
0.9999
0.5
3.0
5.0
(a) Analysis m
(b) Analysis Went
Figure 11: Analyses of and Went-
For example, lower threshold allows more pairs to participate in training, but also introduces higher proportion of noisy pairs. As illustrated in the Figure [0] when т 0.5, the strategy is equivalent to selecting samples with j, Új as pairs. In this experiment, is set to 0.2 to ensure the inclusion of sufficient number of pairs during training. As shown in Table g Ê, significantly improves the classification performance of the baseline model and accelerates the model's is correct fitting of the training data, which may in turn facilitate label disambiguation (Figure D)
Analysis on Imbalanced Datasets. NcPU has been validated under more challenging conditions: class imbalance IO) and distribution imbalance (Su a 2021 Zhao al. (023b) (Table [I] WSC was selected as the comparison method due to its best performance without any auxiliary information. In class imbalance scenarios, the number of positive samples is significantly smaller than that of unlabeled samples. The imbalance ratio (IR) is used to quantify the degree of class imbalance, defined as the ratio of the number of unlabeled samples to positive samples. IR can be increased by reducing the number of positive samples (all other settings remain consistent with the main experiments). Results Table demonstratee that NePU robust to class imbalance. Recent studies (Su et a 1 Zhao et al. 2023b) have indicated that distribution imbalance is another critical challenge for PU learning tasks: a low मp exerts adverse effects on classifier training. In the experiments of Table TI 20000 unlabeled samples were used, and distribution imbalance was simulated by decreasing the up (all other settings are consistent with the main experiments). Results in Table show that NePU is robust to distribution imbalance.
Analysis of hyperparameters. 1) denotes the momentum hyperparameter for updating the target network. As shown in Figure a]),,, NcPU is robust 1). In practice, observe that NcPU may
22

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Published as a conference paper at ICLR 2026
Table 10: Class imbalance results on CIFAR-10 dataset.
Table 11: Distribution imbalance results on CIFAR-10 10 dataset.
IR: 80
IR:
53.33
Tpi 0.05
Tp. 0.1
Method
Method
QA
OA
OA
OA
81.46450
71.31264
19-70--0
86.59114
900 00,97703
88.48a04
90.72403
88.36404
NcPU(ours)
93,70440
91.34511
96.44-00
95,42414
NcPU(ourS)
93.57a03
91.36402
93.88464
91.81 91.81400 406
Table 12: Computational overhead of different methods on CIFAR-10 dataset.
Trainnn Phase
Inference Phase
Task Performance
Method
Training Time//poch (s)
Batch Inference (ms/256 samples)
GFLOPs
87.29
83,71
LaGAM
14.79
95. 95.78465
94,90elss
12.92
0,56
WSC
16.00
90.55
87,92sls
NePU
97.36%0.
96.67402
occasionally exhibit instability during training with a very small probability, but this issue can be effectively mitigated by the entropy regularization term. Furthermore, the model is also robust to the weighting of the entropy regularization Went (Figure IT).
I ANALYSIS ON COMPUTATIONAL OVERHEAD
The comparison computational overhead between NcPU and other existing PU learning methods in both training and inference phases is presented in Table 12 Among these methods, nnPU is classic PU learning algorithm without a representation learning module, while LaGAM, WSC, and NePU all incorporate representation learning modules: (1) In the training phase, compared with nnPU, the PU learning algorithms with representation learning modules exhibit increased training time per epoch, but there is significant difference in the per-epoch training time between NePU and the other algorithms with representation learning modules; (2) In the inference phase, NePU and other methods only utilize single classification network for inference, thus NePU achieves the same inference speed and computational complexity to the other methods; (3) Compared with other methods with representation learning modules, NePU does not show significant increase in per-epoch training time, yet it delivers a substantial improvement in OA and Fl.
J THE USE OF LARGE LANGUAGE MODELS
Large Language Models (LLMs) were employed exclusively for the purpose of correcting grammat- ical errors and enhancing the clarity of expression.
23


Reviews:
[{"review_id": "fiDLqiPsSi", "reviewer": "Reviewer_PR5m", "summary": "This paper introduces NcPU, a non-contrastive PU learning framework that addresses the representation separability in PU learning. The proposed method integrates a noisy-pair robust non-contrastive loss (NoiSNCL) and a phantom label disambiguation (PLD) module. NoiSNCL enhances intra-class representation alignment under noisy supervision, while PLD refines pseudo labels through prototype-based, regret-aware updates. Theoretically, the framework is grounded in an EM-based interpretation, and empirically, NcPU achieves substantial gains across multiple datasets, even surpassing supervised baselines.", "questions": "Please see the weaknesses.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "1. The paper clearly identifies the representation separability issue as the bottleneck in PU learning, and the motivation is well justified and convincing.\n2. The proposed noisy-pair robust loss effectively mitigates the influence of false labels, a common problem in PU learning under weak supervision.\n3. The proposed method achieves significant and consistent improvements, even outperforming supervised models on several benchmarks.\n4. The paper is well-organized and clearly written, making the technical ideas easy to follow.", "weaknesses": "1. The loss function  $\\tilde{\\mathcal{L}}_r = 2\\sqrt{1 - \\langle q, k \\rangle}$may cause numerical instability when $\\langle q, k \\rangle \\approx 0$, since the gradient involves a term  $\\frac{1}{\\sqrt{1 - \\langle q, k \\rangle}} \\to \\infty$. Although the composed gradient may remain finite, the authors should discuss the numerical stability and possible mitigation strategies.  \n\n2. The idea of introducing robust non-contrastive alignment has conceptual overlap with prior work such as the CoTAP loss proposed in “Semantic Concentration for Self-Supervised Dense Representations Learning” (TPAMI 2025).  \n   While the problem settings differ, it would strengthen the contribution to discuss distinctions or novel theoretical insights explicitly.  \n\n3. A naïve self-supervised baseline (e.g., BYOL or DINO pretrained representations combined with standard PU learning) is missing, which would help isolate the contribution of NoiSNCL and PLD from pretrained feature quality.  \n\n4. The paper still uses BYOL as its base self-supervised method, which has been surpassed by recent approaches like iBOT (ICLR 2022) and DINO v1/v2.  Future work could benefit from integrating NcPU with stronger backbone frameworks to further validate its robustness.  \n\n5. The proposed framework involves multi-view alignment and prototype-based refinement, which may increase training time and computational cost.  A runtime comparison with existing PU learning or non-contrastive baselines would clarify efficiency and practical feasibility.\n\nOverall, this paper is worthy of acceptance. Once the above issues are adequately addressed, I would be inclined to raise my score.", "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": "P2idYdzozo", "reviewer": "Reviewer_5HgC", "summary": "This paper identifies an insight that noisy pairs tend to dominate the representation learning process, as their gradient magnitudes overwhelm those from the clean pairs. To address this, it proposes a PU learning framework called NcPU. The method introduces two key components: 1) a noisy-pair robust supervised non-contrastive loss (NoiSNCL) that aligns intra-class representations while tolerating noisy pairs through gradient analysis, and 2) a phantom label disambiguation (PLD) module that refines supervision through regret-based label updating. Experimental results demonstrate the framework's effectiveness, with additional results showing its applicability in post-disaster building damage mapping tasks.", "questions": "Please refer to the weaknesses.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- This paper provides an insight by identifying and formally analyzing the \"noisy-pair gradient dominance\" problem in traditional contrastive learning. \n- Building on this insight, the proposed method is well-designed. The experimental evaluation is comprehensive, demonstrating state-of-the-art performance across multiple benchmark datasets.\n- The paper is generally well-written, explaining the proposed method, with detailed descriptions.", "weaknesses": "- The dual-network architecture inevitably increases training cost compared to simpler PU methods. A quantitative comparison of computational overhead would help practitioners evaluate the trade-offs.\n- While performance on standard benchmarks is strong, validation under more challenging conditions (e.g., extreme class imbalance, very limited positive samples) would better demonstrate the method's robustness.", "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": "hZSGCGjd1W", "reviewer": "Reviewer_TpVx", "summary": "This paper addresses Positive-Unlabeled (PU) learning on complex datasets, where existing methods struggle to learn discriminative representations under unreliable supervision. The authors propose NcPU, which combines a noisy-pair robust non-contrastive loss (NoiSNCL) with a phantom label disambiguation (PLD) scheme for conservative negative supervision. The method is theoretically analyzed under the EM framework and empirically validated on complex datasets, showing promising results.", "questions": "1. As shown in Equation (7), the authors adopt a square-root loss in the proposed NoiSNCL objective. Consequently, the gradient does not vanish even when the two features of $x_i$ and $x_j$ are identical. Specifically, when $\\\\tilde{q}_i^\\\\top \\\\tilde{q}_j = 1$, the gradient magnitude becomes $\\\\frac{2}{\\\\| q_i \\\\|_2^2}$. Would this non-vanishing gradient potentially lead to overfitting or training instability?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1. The t-SNE visualization clearly demonstrates that the proposed method enables the model to learn more discriminative and meaningful features than previous approaches.\n2. The authors provide a theoretical analysis to show the effectiveness of their proposed method based on EM framework. \n3. Experimental results show that the proposed method surpasses previous methods by a considerable margin.", "weaknesses": "1. The novelty of the proposed method is relatively limited. Specifically, it is constructed by incorporating existing techniques such as BYOL, class prototypes, and SAT. The main contribution of the method lies in the introduction of the modified loss term, $\\\\tilde{\\\\mathcal{L}}$. \n2. The proposed method requires substantially longer training time compared to previous approaches. Specifically, the authors train for 1500 epochs to achieve the best performance, whereas competing methods, such as WSC, are trained for only 250 epochs in their original paper, requiring roughly one-sixth of the training time.", "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)