Reduction-based Pseudo-label Generation for Instance-dependent Partial Label Learning
Authors: Congyu Qiao
Ning Xu
Yihao Hu
Xin Geng
Venue: NeurIPS 2025 poster ()
Keywords: instance-dependent
partial label learning
pseudo-label
Primary area: general_machine_learning
TL;DR: We propose to leverage reduction-based pseudo-labels to alleviate the influence of incorrect labels and train our predictive model.

Abstract: Instance-dependent Partial Label Learning (ID-PLL) aims to learn a multi-class predictive model given training instances annotated with candidate labels related to features, among which correct labels are hidden fixed but unknown. The previous works involve leveraging the identification capability of the training model itself to iteratively refine supervision information. However, these methods overlook a critical aspect of ID-PLL: within the original label space, the model may fail to distinguish some incorrect candidate labels that are strongly correlated with features from correct labels. This leads to poor-quality supervision signals and creates a bottleneck in the training process. In this paper, we propose to leverage reduction-based pseudo-labels to alleviate the influence of incorrect candidate labels and train our predictive model to overcome this bottleneck. Specifically, reduction-based pseudo-labels are generated by performing weighted aggregation on the outputs of a multi-branch auxiliary model, with each branch trained in a label subspace that excludes certain labels. This approach ensures that each branch explicitly avoids the disturbance of the excluded labels, allowing the pseudo-labels provided for instances troubled by these excluded labels to benefit from the unaffected branches. Theoretically, we demonstrate that reduction-based pseudo-labels exhibit greater consistency with the Bayes optimal classifier compared to pseudo-labels directly generated from the training predictive model.

Reduction-based Pseudo-label Generation for Instance-dependent Partial Label Learning
Congyu Qiao! Ning Xu 1.2, Yihao Hu and Xin Geng 1.2
School of Computer Science and Engineering, Southeast University, Nanjing 210096, China 2 Key Laboratory of New Generation Artificial Intelligence Technology and Its Interdisciplinary Applications (Southeast University), Ministry of Education, China { (qiaocy, xning, yhhu, xgeng @seu. edu.cr
Abstract
Instance-dependent Partial Label Learning (ID-PLL) aims to learn a multi-class predictive model given training instances annotated with candidate labels related to features, among which correct labels are hidden fixed but unknown. The pre- vious works involve leveraging the identification capability of the training model itself to iteratively refine supervision information. However, these methods over- look critical aspect ID-PLL: within the original label space, the model may fail to distinguish some incorrect candidate labels that strongly correlated with features from correct labels. This leads to poor-quality supervision signals and creates bottleneck in the training process. In this paper, we propose to lever- age reduction- based pseudo-labels to alleviate the influence of incorrect candidate labels and train our predictive model overcome this bottleneck. Specifically, reduction-basee pseudo-labels are generated by performing weighted aggregation the outputs of multi-branch auxiliary model, with each branch trained in la- bel subspace that excludes certain labels. This approach ensures that each branch explicitly avoids the disturbance of the excluded labels, allowing the pseudo-labels provided for instances troubled by these excluded labels to benefit from the un- affected branches. Theoretically, we demonstrate that reduction-based pseudo- labels exhibit greater consistency with the Bayes optimal classifier compared to pseudo-labels directly generated from the training predictive model.
Introduction
Partial Label Learning (PLL), a typical weakly supervised learning paradigm, aims build a pre- dictive model that assigns the correct label to unseen instances by learning from training instances annotated with a candidate label set that obscures the exact correct label [5], B, [e] The necessity to learn from such weak supervision naturally arises in ecoinformatics [211. 32], web mining [22]], mul- timedia content analysis [50,, 2], and other domains, owing to the difficulty in collecting large-scale high-quality datasets.
PLL has been studied along two different routes: the identification-based route[[33, 2G. 24, I1 51, BR B2], which treats correct labels as the latent variable and tries to identifies them, and the average-basee route 5 52 23], which treats all candidate labels equally. To facilitate practical PLL algorithms, some researchers have focused on instance-dependen
PLL (ID-PLL), where incorrect labels related to features are likely to be selected as candidate labels, and tackled this challenge by following the dentiifcationn-assee route. [А-]] explicitly estimate the label distribution aligned with the model output on candidate labels through variational inference.
[39] induce
Corresponning author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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contrastive learning framework from ambiguity to refine the representation of the model. [28]] model the generation process of instance-dependent candidate labels by leveraging prior knowledge in the model output [ propose candidate labels by leveraging the margin between the model output values on candidate labels.
method that progressively identifies incorrect
These previous approaches involve leveraging the identification capability of the training model itself to iteratively refine supervision information. They exereise this capability through the outputs [94, 28, I.I. [8] or representations [39] from the training model. However, these methods overlook a critical issue in ID-PLL: some incorret candidate labels strongly related to features may not be distinguished with correct labels by the model within the original label spaces. As a result, the model generates increasing amounts of incorrect identification information, further leading to the training bottleneck. Unlike previous approaches that iteratively train the predictive model under the influence of misleading supervision before performing identification, we prioritize eliminating the influence of misleading candidate labels within label subspaces, and then train an auxiliary model free from this influence to provide accurate identification information.
In this paper, we propose to utilize reduction-based pseudo-labels to mitigate the influence of incor- rect labels and train our predictive model. Specifically, reduction-based pseudo-labels are generated by aggregating the outputs of a multi-branch auxiliary model, with each branch trained in a label subspace that excludes certain labels. This approach allows each branch to explicitly avoid the inter- ference of the excluded labels. Consequently, instances affected by these excluded labels can benefit from the pseudo-labele provided by the corresponding branch. Note that the auxiliary model will not be involved in the testing time, which is similar to [44] 28]. Moreover, given mild assumptions, we demonstrate that pseudo-labels generated from the model trained in the label subspace could exhibit greater consistency with the Bayes optimal classifier compared to those from the predictive model
itself. Our contributions can be summarized as follows:
Theoretically, we prove that reduction-based pseudo-labels generated from the model trained in label subspace could be more consistent with the Bayes optimal classifier than that from the predictive model itself.
Practically, we propose novel pseudo-label generation approach named RPLG to deal with the ID-PLL problem, which utilizes the multi-branch auxiliary model with each branch trained in a label subspace to alleviate the impact of incorrect candidate labels strongly related to the instances and disturbing the training process.
2 Related Work
PLL has been studied along two different routes: the identification-based route and the average- based route. Identification-based approaches [[33, 226, 211, B, 4Р] are intuitional since they aim to gradually identify latent correct labels from candidate labels or eliminate incorrect labels out of candidate labels, which is also commonly referred to as disambiguating. In recent years, most researchers have attempted to tackle the problem of PLL along the identification-base
route and achieved tremendous improvements. Average-based approaches [I2,. S. 522 tend to deal with a learning objective where all candidate labels are treated equally. A typical average-based approach is based on distance between instances and predict the label of unseen instance by voting among the candidate labels of its nearest neighbors the feature space. Very recently. [23] theoretically and empirically demonstrate their proposed approach along the average-based route have an advantage in robustness. In this paper, we still choose to follow the route of identification-based routes to handle ID-PLI..
Identification in PLL are performed by various means. In traditional PLL, to which deep neural networks (DNN) have not been applied, [2G] maximize the margin between the maximum model- ing output from candidate labels and that from non-candidate labels implicitly identify correct labels, while [ further try to directly maximum the margin between the correct label and all la- Conditional Multinomial Model to maximum the
bels. [2T]]] propose the Logistic
likelihood of candidate label, marginalizing away the latent correct labels. [53] R. F2, [3] leverage the topological information in the feature space to iteratively update the confidence of each can- didate label or the label distribution, from which we could determine correct and incorrect labels.
In deep PLI., [+ enhance the identification ability of the model by designing an entropy-based regularization term and temporally assembling predictions of the model as the guidance of train-

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ing. [22|] propose progressive identification method that normalizes the output of the model on candidate labels in each epoch as the weight in the cross-entropy loss. [+7]]] reduce identification envor by introducing a network-cooperation mechanism. [ build a risk-consistent estimator and a dlassifier-consiiter tion with parameter weighting losses on candidate and non-candidate labels, implicitly enhancing idetification. [[5T, Mi. [ improve identification through class activation value, semantic label repre- sentation and structured representation provided by deep graph neural networks, respectively. [CS]] propose a contrastive learning framework that could adapt to PLL and leverage the class prototypes in the framework for identification. [ل>]]] augment the data to obtain conformed label distributions ca- pable of identification to perform manifold regularization. However, these works have been actually considering PLL by unrealistically assuming that incorrect candidate labels are uniformly sampled while the phenomenon of instance dependence is widely observed in various fields [40] including PI.I..
estimator relying on the process of identidication. [[66] propose loss func-
L5
From [ identification in ID-PLL, which is more practical, begins to be noticed. [+ explicitly
estimate the label distribution [& SS. IG. [E]] for each instance, which reflect possibility that la-
bel selected into candidate sets through variational inference. [[9] induce a contrastive learning
framework from ambiguity and obtain identifiable representation in ID-PLL. [28] model the gen-
eration process of instance- dependdnt candidate labels to perform maximum-a-postene
implicitly
identifying the latent correct labels with prior information. [[ propose
method leveraging the margin between the model output values on candidate labels to progressively identify incorrect candidate labels. [[[]] perform identification with selection of vell-disambiguated samples. [G8] build a aelf-distillation framework rectifying the identification results of the teacher model enhance the reliability of distilled knowledge. In this paper, we propose to explicitly allevi- ate the influence of some incorrect candidate labels hard to be distinguished on the models through pseudo-labels generated in specified label subspace, further enhancing the identification process.
3 Proposed Method
3.1 Preliminaries
First of all, we briefly introduce some necessary notations. Let X' = R.9 be the g-dimensional instance space and y {1, 2, ..., c} be the label space with class labels. Given the PLL training dataset D = (x,, S.) S i S n} where æ; E X denotes the g-dimensional instance and S; C y denotes the candidate label set associated with æ;. In PLL, the correct label Mas, of the instance 2; must be the candidate label set, i.e., ya, E Sy. and each candidate label set S, should not be the empty set nor the whole label set, i.e., S, & {0. )). Besides, we do not consider the case that the candidate label set S; only has the correct label yz, in this paper, namely, S, * 1. For each candidate label set S; in the training dataset, we also use the logical label vector 4; [7,, 12, (2,...,1? 19] E (0, to represent whether the label j is one of the annotated labels, i.e., P 1 if j E S., otherwise I/ =0.
Let the posterior probability vector 77xx) = lnp ()")),,))))),........)..))) (x)) with ry' = p(y= joæ) denot- ing the posterior probability of the label j given the instance æ. A Bayes optimal classifier 1y* can be calculated using 17, i.e., 17" (x:) arg maxjey 77 (x)).
Moreover, let 5 y be the labels excluded from the label space y and r7(xx) (nft (xe), (F)),...., be the posterior probability in a label subspace without 5i The j-th element of r/ (x) denotes the posterior probability of the label j given the instance x and y & y.ic..
(x)
if $
(²())) = pp = =|x $ 5) =
(x)
0.
otherwise.
We consider the task of PLL is to learn a score function ʃ X - A where A denotes the e-dimension simplex, as our classifier with its prediction 1((x)) = arg maxjey [a())) consistent with that of the Bayes optimal classifier 17" (æ)). During the training process, the classifier f could be
3

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considered to be optimized by the following objective:
[(f(X - ) - 1 Σ (,;;;;;;;
(2)
where the classifier f is parameterized by O, l denotes the cross-entropy function, Q qq:, 92...., qn] is the pseudo-label matrix with each element qi = 4 ............ denoting the pseudo-label of the instance I,, satisfying Ej=1 o' = 1 and qf = 0 if & S, Since our target is to make the prediction of the classifier f consistent with that of the Bayes optimal classifier 17", the pseudo-label qi should put the most mass on the label predicted by the Bayes optimal classifier nf", i... arg maxjey qf 17" (z), which is a very challenging task under instance-dependent PLL.
3.2 Overview
To begin with, we provide a formal definition of disturbing incorrect labels, which are labels that the predictive model finds challenging identify as incorrect. We prove that model trained in label subspace excluding these disturbing incorrect labels can produce pseudo-labels more consistent with the Bayes optimal classifier for instances whose candidate label sets include these disturbing incorrect labels. Moreover, we establish a boundary for the conditional probability that the pseudo- labels of these instances consistent with the Bayes optimal classifier.
Motivated by these theoretical results, we propose RPLG, which leverages pseudo-labehs generated in label subspaces, i.e., reduction-based pscudo-labels, to train our predictive model. Reduction- based pseudo-labels are derived from the outputs of an auxiliary multi-branch model. Each branch is trained within distinct label subspace that explicitly excludes specific labels. To generate reduction- based pseudo-labels, we employ a meta-learned weight vector to fuse the outputs of all branches.
3.3 The RPI.G Approach
We first introduce the disturbing incorrect labels, which are hard to be distinguished as incorrect labels according to the output of the predictive model during training. These labels pose great challenge to generate pseudo-labels consistent with the Bayes optimal classifier (xx:).
Definition 1. ( incorrect label) An incorrect label j is said to be (T) disturbing for the predictor f on some instance æ with (x) * if 3e E (0, 1), Vj ), max (x) np' (æ)) S and 3r E (0, min 2,)], the posterior 17" (a) (x) 1y' (x) ST.
Here, T indicates the degree that the posterior (x) approaches 17" (z). The smaller its value, the easier the label j is selected into the candidate label set. e indicates the degree that the predictive model approximates the posterior 77. According to [B2], if ry" (x) (a) (xx) 2e, could distinguish label j as incorrect labels according to the output of the predictive model. Naturally, problem arises: how should we handle those samples with disturbing incorrect candidate labels
which satisfly vy" (a) (x)))
2e.
Then we start with analyzing the pseudo-labels of the instances, whose disturbing labels is denoted by Di. An auxiliary model &o considered to train without the influence of disturbing labels. On mild assumptions, we prove that the pseudo-label provided by the auxiliary model &p in a specific label subspace has more chance to be consistent with the Bayes optimal classifier than the predictive model. The proof can be found in Appendix I.
Theorem 1. Let I())
( VVj E V.jis is (T, J, -diistuuringg incorrect label for x with y + and Vj & V.j is not (T, J, e) distturri incorrect label for x²). Suppose that model yp trained
without the label space ÿ satisfies 7e' (0, min min min (2)) (n (m))))n (x) (m) (m)())) })
de(l de(1-E, Exer T (z))
with a =arg max JE5 (x) and b arg max max Je(o)u (z), (xd) (x)) I é', we could obtain:
((1"(x) arg max 9² I()) < p() (w) arg g' x E J J())). jey
(3)
JEY
Theorem 11 inspires us that we can decouple the training of the model from the generation model of pseudo-labels. By introducing some auxiliary model trained in the absence of the label subspace y

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we can generate pseudo-labels with better Bayesian consistency on the samples in J()). Here, D is not a point-wise concept. In fact, given V we could obtain set consisting of instances whose (r, f. +)disturbing incorrect labels exactly constitute the label set )
Additionally, we further analyze the chance that the pseudo-label provided by the auxiliary model is consistent with the Bayes optimal classifier. We assume the Tsybakov condition [63, 54l] holds around the margin of the decision boundary of the true posterior in the multi-class scenario.
Assumption 1. (multi-class Tsybakov condition) 3C2 0 and 3o (0, such that for all
t c to-
p(1p" (x) (xx) - 1 (())(()) S 5t) CrA
where s(x) arg maxje)ljzt 17 (x) denotes the second best prediction of n(x).
Under Assumption MI we could prove the pseudo-label provided by the auxiliary model yp has good chance to be consistent with the Bayes optimal classifier. The proof can be found in Appendix A
Theorem 2. Suppose that for E I()), its posterior 17(z)) fulfills Assumption B for constants C,A > 0 and to E (0, 1]. Suppose that model yp trained without the label space ý satisfies Bd' (0, min min (x)) (x)))))))))) }) with a = arg 5 np (ax) and 4r(1 4r(1-E,es (m))
b = arg max jи()) vp' (x)) (x) - 17 (x)) S S'', we could obtain:
(x) = arg max o'' J(T) 2 C(O(ce')]
max jey
(5)
Our theoretical insight inspires new algorithm for the generation of the pseudo-label qi in the optimization objective Eq. (2). To begin with, we decompose the pseudo-label qi into the basic pseudo-label μi and the reduction-based pseudo-label v;, i.c.,
oop + (1 aa)u.
(6)
where a trade-off hyper-parameter parameter to decide the influence the introduced reduction basse pseudo-labels. The basic pseudo-label μe; is initialized with uniform weights candidate labels and then could be calculated by using the outputs of the predictive model f:
(x 4
if E S.,
Exes, (I !
0.
otherwise,
which puts more weights on more possible candidate labels [24]] The reduction-based pseudo-label o; be obtained by the output of the model trained without the influence of the label from 1 to formulated as U, and a vector w; to weight these output:
U; w. U
(8)
Here, U [u], ......, u E cxe is reduction- -based matrix, which is an intermediate vari- able combined with the vector w; generate the reduction-basse based pseudo-label v, in Eq. (8). The j-th row of U, is initialized with uniform weights on candidate labels without label j and then calculated by:
(z(zi: ERESAND E (Z
ifr e S; (D).
(9)
otherwise,
where yo is an auxiliary model parameterized by {1, 10 to form c branches, and ø; is the extracted features given the instance æ,, The j-th branch (p=; 52,) is trained without j in the label space V and the loss function for the auxiliary model could be formulated by:
n
aux (Z:
ΣΣ
E(p((z; S2y), u!).
(10)
n
The j-th branch uses its previous outputs normalized on candidate labels without j as its supervision in the next epoch, which is similar to the initialization and training mode in PRODEN [[4]]. In this
5

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Table 1: Classification accuracy (mean:-std) of each comparing approach benchmark datasets for instance- dependent PI...
Dataset
FMNIST
KMNIST
CIFARIO
CIFARI00
TinylmageNet
RPLG
91.41-10.1%%
96.85:10.11% %
87.53:10.21 %
65.03=:.211
40.74:10.64%
DIRK
91.02=0.23%% 84.63 96.21=0049%%
25.77= 58.17:0.20%%
SDCT
90.98=0.45%
9..01 e
86.50=10.134
60.95:10.35%
36.50=10.35%
POP
0.312=0..5%%
95.03-10.83%
86.23+0.36%%
60.71+0.166 1
39.27:10.86%
IDGP
90.87=0.411 %
95.9810.51%
86.43=0.23%%
64.38-0.27%%
32.21#1.14%%
ABLE
90.43-0.09% 95.37+0.07%
85.11+0.244%
61.21+0.37%
23.60++0.77%
VALEN
90.36=0.1559
95.37+0.97%
85.48=0.62%%
62.9611.96%
37.14 %
PLCR
90.01=0.59% 95.25+00.33% .
86.37=t0.88%
64.12%t..3%%
24.59 1.68% +
PICO
88.24=0.3659 94.89+0.46%
86.16+0.21%
62.98:1.38%%
29.95::0.48%
CAVL.
87.81 1.27%
93.44+1.45%
59.67+3.30%
52.59+1.011%
28. 18.0070.777
LWS
88.79=0.3497
92.67+1..6%
37.49+2.82%
53.98+0..9%%
27.37+0..22%
RC
8..52.0.65%% 93.88+0..44%
85.95=10.40%
35.74 63.411
%
CC
99.78=0.4887
93.83++0.22%
79.96-t0.99%
62.40+10.84%
31.46:11.244 1.24%
PRODEN
0.55%
93.60+0.61%
86.0440.211%
62.56
33.37:10.77%
way, the j-th branch cp:;; could be considered as an approximation of 1/ (z) with 5 {i}-- Note that the multi- multi-branchhhe technique in our approach, as well as in [[0O] and earlier work [18], is merely training technique to save space and time via sharing the feature extraction layer.
And w; = [w/. wf...., w1l] E given the instance æ; i.e.,
IR lx a weight vector output by a model 9 parameterized by
w. = [0;;;; T).
(11)
Since it is unknown which label in the candidate set S; of the instance is the label interfering the correct label ya., we formulate the model g as a meta-learner and learn-to-learn a weight vector to eliminate the disturbance of incorrect candidate labels and obtain the reduction-based pseudo- label v, for training. We employ the reduction based pseudo-labes labels V = [11, U2,..., Un] with each element vs calculated from w, to update the predictive model f(; O)
1 Σ l(f(2; ; θ), vt), ginner (f(X: O) V)
(12)
n
Then, we assess the updated predictive model on the validation dataset Dval {(x)) y: yal) } to update the meta-learner g(:;
s
1
Couter (f(X θ), Y
(fx )),
(13)
72 val
Overall, the meta-leariing objective can be formulated as a bi-level optimization problem as follows:
I arg min Couter (f(X (* (T))), Y
F
(14)
C arg argmin Cianer CimeeT (f(X: V),
To solve the optimization of Eq. (14), an online strategy inspired by [+II] is employed update ② and I through single optimization loop, respectively, which guarantees the efficiency of the algorithm. Specifically, we shuffle the training set D into K mini-batches. Each mini-batch contains examples, i.e., ((t,, S.)]1 S S m). ). In the step A of training, we employ stochastic gradient descent (SGD) to optimize the meta-learning objective Linner and Lowter with the loss functions for the classifier and auxiliary model L and L the k-th mini-batch
First, as for the auxiliary model we update the parameter of each branch 52/ to 52 as follows:
m al(yp22;; S4 u²)
2 1111-52 22
(15)
m71
02

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Table 2: Classification accuracy (mean-tstd) of comparing algorithms the real-world datasets.
Dataset
Lost
BirdSong
MSRCv2
Soccer Player
Yahoo!News
RPLG
8.707%
75.27:10.23%
51.65.10.65%
56.94:10.34% %
68.01:00.1%
DIRK
79.24:10.33% 74.32:10.23%
48.59:10.88%
55.83:10.35%
67.65:10.32%
POP
78.57=0.45% 74.47:10.66%
45.86:10.28%
54,48:0. 10%%
66.38110.07%
IDGP
77.02 74.23
50,45=00.47%
55.99:10.28%
66.62:10.11
VALEN
76.87=0.86%
0..39%
49.97+
55.81 10%
66.26:t:0113%
CAVL
73.4710.13%
44.73:10.66%
54.06:10.67%
65.44.10..3%%
LWS
03.13% 51.45
49.85:10.49%
50.2410.45%
48.21
RC
76.26=+0.46% 69.33++0.32%
49.47+0.433%
56.02+00559%
63.51++0.20%
CC
63.54+0.255%
69.90++..8%%
41.50+0.44%
49.07+0036%%
54.86+-0.48%%
PRODEN
76.47 0.22%
13.4410.112%
45.10-10.16%
54.05 151%%
66.14410.100
where 31 the step size. Then, after updating 2 to 52
we could obtain the reduction-based
pseudo-label v; by Eq. (8) and optimize the inner objective of the bi-level optimization Eq. (14):
32
[l(s(x;; O²),
+ k+1 O
(16)
where B2 the step size. Note that after updating @* to @h+1 with the reduction-based pseudo- label U, O is dependent the parameters I of the meta-learner g. i.e., (T*), which allows the updation of D through the loss function Louter as follows:
83
(E(f(x: val @k+)),)s y:
p+++ = P
(17)
or
where we also randomly sample m examples from D and 33 the step size. Finally, we rollback the parameters of our classifier to O and employ the pscudo-label qi generated by Eq. (() to optimize with the same step size with Eq. (IG6):
B2
m
alss(;;; O*),
+ b 6
(18)
00
m
Note that we need to rollback to 0/. making it return to the appropriate optimization path. The goal of Eq. (IG) is optimize by further building the dependency between * and the meta-learner parameters T, while that of Eq. (IX) is to pursue @' for better prediction on unobserved instances, which is also the ultimate goal of the whole algorithm.
As the auxiliary model parameters { and meta-learner parameters I are updated iteratively, the pseudo-label q; is also refined contribute to the optimization of the classifier f(: ①) step by step. In this way, the performance of the predictive model continues to be improved our approach RPLG. The algorithmic description of RPLG is presented in Algorithm II in Appendix B.3. In framework RPL.G, the influence of label j is eliminated with the highest priority at the j-th branch (2) of the auxiliary model, whose label subspace does not include label j. Hence, instances whose disturbing incorrect labels include label j could obtain more correct reduction- based pseudo- labels by assigning more weight the j-th branch when performing aggregation through the weight vector w, which is learned by the meta-learner g(:; I').
4 Experiments
In this section, we validate the effectiveness of our proposed RPLG by conducting it on manually corrupted benchmark datasets and real-world datasets and comparing results against DNN-based PLL algorithms. Also, we explore RPL.G through ablation study, sensitivity analysis, convergence analysis, and time consumption. The implementation based on Pytorch [[7]] with the GPU model
NVIDIA RTX 3090. The source code is available at https: /ttt:///tttiii weitthubb... com/ 1m mi/rola
7

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89-
Table Classification accuracy (meandistd) for com-
parison against RPLG-NM.
87
Dataset
RPLG
RPLG-NN
FMNIST
91.41
89.68:10.34% 93.73:10.85%
Test Accuracy
86
KMNIST
96.85.10.11 %
CIFAR-10
87.53:10.21 %
85,43++..22%
85
CIFAR-100 100
65.03:10.21 %
61.1810.34%
TinyImageNe
40.74=0.64 %
35.35+ 1.01%
84
Lost
81.07+0..44% %
77.14+1.62%
BirdSong
73.1810..1%% 75.27-0.23% %
MSRCv2
51.6510.65%
46.62.1: 1.54%
Soccer Player
05.48++0.65% 0.344%
82
0.1
0.3
0.5
0.7
Yahoo!News
68.01-10.19%
06.3%
a
Figure I: Sensitivity analysis a.
4.1 Datasets
RPLG and compared DNN-based PLL algorithms are implemented on three widely used bench-
mark datasets in deep learning: [MNIS,[[]]], KMNIST [[]] CIFAR-10, 0, CIFAR-100 00 [α7]] and
Tiny Imyameeee [TS]]. For these datasets, we generate instance-dependent candidate labels through the same strategy as [BE]], which considers instance-dependent PLL for the first time, create man-
ually corrupted benchmark datasets.
Besides. since data augmentation cannot be performed on extracted features from audio and video data, our approach and auttentggmettiionn-- free PLL methods are also performed on five frequently used roaldworld datasets, which come from different practical application domains, including Lost [S]. Ri rdSong [II], MSRCv2 [21]]. Soccer Player [50] and Yahoo News [*]
As for benchmark datasets, we split 10% samples from the training datasets to form the val- idating datasets. As for real-world datasets, we conduct the algorithms with 80%/10%/10% train/validation// split. Then run five trials on each datasets with different random seeds and report the mean accuracy and standard deviation of comparing algorithms.
4.2 Baselines
We compare RPLG with six methods, which are designed for the challenge of ID-PLL: 1) DIRK [B7]], self-distillation framework which rectifies the label confidences the distilled knowledge to guide the training of the predictive model. 2) SDCT [35]], a sample selection framework which selects cell-disambiguated samples based on normalized entropy in two stages for the training of the predictive model with data augmentation. 3) PoP [Р4]] label purification framework which pro- gressively purifies each candidate labels as the performance of the trained predictive model improves. 4) IDGP [E77], a maximum-a taaximum-a-posterior approach which decomposes candidate labels into the results sampled from two different distributions to form a optimization objective for training. 5) ABLE [35], contrastive learning framework which is based on data augmentation and pulls ambiguity- induced positives closer and the remaining instances further in the representation space. 6) VALEN
[14], an encoder-decoder framework which leverages variational inference to recover latent label distributions for the guidance training the model.
Besides, we also compare our method with another seven classical DNN-hased PL. methods: 1)
PLCR [87]] manifold regularization approach which is based on data augmentation and proposes a consistency regularization objective to preserve manifold structure in feature and label space.
2) Pico [BS]], contrastive learning framework that relies on data augmentation and achieves la-
bel disambiguation through contrastive prototypes. 3) CAVL [5]]] dlentification-basee approach which identifies correct labels from candidate labels by class activation value. 4) Lws [G6], an identification-bar based approach which introduces leverage parameter as the trade-off between losses on candidate and non-candidate labels. 5) RC [0], a risk-consistent approach which utilizes the loss correction strategy to estimate the true risk by only using data with candidate labels. 6) CC [[]], classifeer-oonsiseett approach which leverages the transition matrix to learn predictive model that could approximate the optimal one. 7) PRODEN [[2]] a self-training algorithm which normalizes the

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output of the model on candidate labels and utilizes it as a weight on the cross- cross-entropy function for training.
To ensure fairness, we utilize the same network backbone, optimizer, and data augmentation strategy across all compared methods. We take the same backbone as [42, [8] CIFAR-100 CIFAR- 00 and all realworld datasets, and [20, B8] on TinyImageNet. The optimizer is stochastic gradient descent (SGD) [ with momentum 0.9, batch size 256, and epoch 250.
Besides, line with the approach presented in [|Z]]] we meticulously apply the data augmentation strategy. For hyper- papee-parametes, carefully select the most uppropriate ones for each algorithm to va ensure optimal model parameters based on their performances on the validation datasets. To mitigate overfitting, the training procedure of model will be halted prematurely if its performance on the validation dataset fails to improve over 50 epochs.
4.3 Experimental Results
The performance of each DNN-based method on each corrupted benchmark dataset is summarized in Table II where the best results are highlighted in bold and //o indicates whether RPLG statistically wins/loses the comparing method on each dataset additionally (pairwise t-test at 0.05 significance level). Overall, we observe that RPI.G significantly outperforms all comparative methods, whether ID-PLL or classic DNN-based PL.L approaches, across all benchmark datasets. The improvements are especially pronounced on the complex Tiny Innyeeaeeeet dataset.
Table 2 demonstrates the ability of RPLG solve the ID-PLL problem in real-world datasets. Note that data-augmeenttiion based algorithms, including SDCT, ABLE, PLCR and PICO, are not com- pared the real-world PLL datasets due to the inability of data augmentation to be employed on the extracted features from various domains. We can find that our method still has signifi- cantly stronger competence than others all datasets, even the large dataset Soccer Player and Tahoo News, against all other comparing algorithms.
4.4 Further Analysis
To demonstrate the effectiveness of the meta-learned weight w introduced by RPLG, explore vanilla variant, RPLG-NM, where a uniform weight is applied to the candidate labels of the instance instead of the weight output by parameterized model learned through meta-learning. The per- formance of RPLG compared to RPLG-NM is assessed using classification accuracy, with pairwise 1-tests conducted at significance level of 0.05. As shown in Table by leveraging the meta-learned weight's ability to select branches without being influenced by strongly associated incorrect labels, RPLG consistently outperforms RPLG-NM across all datasets, achieving superior performance.
Also, we conduct a parameter sensitivity analysis on a in our algorithm, which determines the influence of pseudo-labels from the multi-branch auxiliary model. Figure M iillustrates the sensitivity of RPLG on CIFAR-10 as a increases from 0.1 to 0.9. yields superior performance for RPLG. Besides, investigate the consistency and convergence of pseudo-labels generated by RPLG on CIFAR-10, as shown in Figures 2a and 2(6) in Appendix A.4 due to the space limit. It is clear that the generated pseudo-labels become consistent with the Bayes optimal classifier and converge as the number of epochs increases.
evident that an a value around 0.3
Furthermore, report the training time (in hours) in Table EL which is presented in Appendix A. due to the space limit. All methods were run for 250 epochs with a batch size of 256 on a single NVIDIA RTX 3090. Compared to some baselines, training time linearly due to meta-learning optimization and the multi-branch model. This efficiency achieved through the online strategy employed in meta-learning optimization and shared common lower layers in the multi-branch model.
approach RPLG only marginally increases the
5 Conclusion
In this paper, we proposed a novel method of utilizing reduction-based pseudo-labels to train our predictive model by mitigating the impact of incorrect candidate labels hard to be distinguished. Reduction-based pseudo-labels are produced through weighted aggregation on the outputs of multi- branch auxiliary model, where each branch of the model is trained within specified label subspace.

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This training strategy ensures that every branch can explicitly evade the interference from the ex- cluded labels. Theoretically, we prove that reduction-basee pseudo-labels display a higher degree of consistency with the Bayes optimal classifier.
Acknowledgements
This research was supported by the Jiangsu Science Foundation (BG2024036, BK20243012), the National Science Foundation of China (624B2040, 62576093, 62206050. 62125602, U24A20324, and 92464301), the Fundamental Research Funds for the Central Universities (2242025K30024), and the Big Data Computing Center of Southeast University.
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A Technical Appendices and Supplementary Material
A.1 Proofs of Theorem MI
Proof. For the conditional probability px)"(x)) = arg maxjey g21 E I())), we have:
p(n" (x) arg max o² J(Y))
jey
p(n" (a) arg jax q¹, a E (('))
p(æ E T('))
pp(n (x) arg 9¹, 17" (z) - 5T =T
(19)
p J(V))
+ (x) arg e 9¹, r7" (m) (x) 1, J())
p(a E I(Y))
Since, for E I()). Vj E 5. (x) 1 (x)
we could obtain:
p(n" (z) arg max o¹ I())) jey
_ (m) arg max p,, n7" (x) =T
p E I()))
+ pl(1(()) (x)) arg jay p,, 17" (a)) - (f) 7. T
(20)
p( I(Y))
p()"(x)) arg maxjey 9¹, n7" (m) (x) < T E I()))
p( E J(V))
Recall that 8 = arg max (w) 1/ (a). since Vj E y with j * 11" (a)). We have
(<) (z) S r²" (a) (x)).
(21)
Recall from Theorem I that arg max jax np (x), E y by definition. Additionally, since J()) consists inputs where all j E 5 are "incorrect labels" (i.e., y # with 1)" (x)).. fol- arg maxjey. (a) (a:). meaning is the index of the maximum of (xx among labels except the true label 17 (zz). Now, consider the structure of J()): all j (v) U y are not disturbing incorrect labels, which implies their corresponding r (ax) values are sufficiently small (otherwise, they would qualify as disturbing). Since ) is the maximum of n (æ)) over V and all other labels outside 5 (but in ) \ (x))) have smaller ry (x), a must be the maximum of o (x) over the entire set y \ {17 (x: Hence, s a.
lows that & 1y* (a). Thus, y {1) (a:)). Then, by definition,
Then we could obtain:
(x) arg max q' x E J())) jey
(x) arg max g¹, 17" (2) -x) ST T(1))
pl E J()))
p(nn (x: arg max q², 77"d (m)
(x) S T e I())) p( E I(Y))
(22)
p(n (w) arg max /2, 17" (w)
(xr S T, n1 (2) - (1) S 2e, (())
plæ E I('))
(x) arg magmaayyy 9e 1/ (w) (x) S <T, 17(2)) > 2e, I()))
p(x E I ()))
21

---

Since T S 2e, we could obtain:
p(n)" (x) = arg max o' x E J()))
jEy
p(n" (x:) arg ja g¹, (7))(()) ()) S T, (2) - 1)0 - S 2e, x E (())) plæ= E (('))
(w)
+ (()) arg max p, 17"h - 11" (x) S T, (x) (m) > 2e, x E I()))
pl E I('))
p(n) (a: arg maxxey q', (0) (x) S T, "T,n" (x0)(()) (7(x)) I 2c, x E I())
(23)
p(a: E I())))
p(nn (x) arg maxjey 9¹, n7" (w) 17 (x) S 2e, x (()))
p(x I())))
p(nn (m) (x)) S 22, I(Y))
p(æ= E I(V))
Recall that é' E (0, (1, min (D()) (n" (00 (a) (m)) (0a)
with
1e(1 Eser (2))
arg ja (x) and b = arg max max jE( 17 (x:). We have
(170 (m) x 17 (x) (17 (m) (x) - 17 (x))
2 2
2e(1 ΣjEr 1 ((=)
(1)² (1²) (x) 1/" (x) (17 (1z) (x) 77((x)
> 2
2e EjEÿ 1/ (xx)
(24)
(177 (m)) (x) - (z)
2 26
2c(1 Ejer (x))
1/" (2)) (x²)
(x) - 1/¹ (x)
2 26'
1 ΣjEド 171 (z)
Here, according to Eq. (W) we have n7" (a) - (x) > 26', and obtain:
(())((x) = arg max r² x E J())) jEY
p(17" (w) 1) < 2e, x E [
p(æ E I()))
(25)
p(a//r/ (a) 1/' (z) > 2c', x E I()))
pl E I()))
Recall that Vj E 1 1 (x) - - s.. We have
(m) (x) ()((x) > 2
(((((()) (w) - ( (z) + ''
(26)
n > (x) ".j.
6" (z) ل (z), vj V.j # (x)
Take arg maxjey  = arg maxjey اي (z), could obtain 7/ (z) arg maxjey d5.
22

---

Finally, we have
p(oi"(a) = arg max JEY
|/| E ((D))
(x)) arg jax 9², x E (}])
p(æ E (()))
p(n" (x) = arg max q¹, n7" (z) - (2) TT E J(0)) pa E J(D))
+ p()n(() = arg max p. n7" (x) 17 (x) > 1, - (())
p( E J(V))
p(nn (2) arg max q¹, 17" (a) (2) S <, I())
p( E [(V))
_p(n((=) arg maxjey ,¹, (2)) (x)
(x)) S T E I()) p(n E [()))
_p(nn (x) arg max 9¹ 77" (z)
17" (xx S T, n, (x) (x)xx) S 22, I(0))
pl E I())))
(27)
(x) arg max q', n"" (m) - - (x) S ST. (m) -z((x) > 22, I(D))
p( E [()))
(xx) arg maxjey ,², 17" (w) (x)) S T,, (w) - (2)) S 2e, x E I(D))
p( E I()))
p(nn (x) arg jay ,¹, 17" (w) (2)) S 2e, x E (()))
p( E T(²))
(())"((0) (0t) (xx) S 2c, x E T()))
p( E I()))
<p(nn' (m) (x) > 26', (()))
p(æ E I()))
<p(nn((>) (x:) arg maxjey g²
x I())
p(æ E I (V))
(x))"(x)) arg max E (())
jey'
The proof has been completed.
A.2 Proofs of Theorem
p(n"(x) arg max 8 x I(D)) jey
"0( (o) (x) 2 lo E J(D))
-#) ded
(x))
(28)
x (()))
()00 - (z)
=1 (1- 1) < 4ec 17t (x))
E T()))
(p) (x)
Since for æ E I(D), its posterior 7/xx) fulfills Assumption 11 for constants C, >>>00 and to E (0, 1]. we have
x 2 1 - C( (1-c(11177 17 (x))) -
(x)) arg max
= 1- -(0(e''') (29)
JEY
((rr (x)
The proof has been completed.
23

---

Algorithm RPLG Algorithm
Input: PLL training dataset D {(ar; S 2 i I n), validating dataset DDvll {artaa y 1
i S n Epoch I, Iteration K;
1: Initialize the parameters of the predictive model, the auxiliary model and meta-learner, i.e., Oo
(82)) and ro
2: i
do 3: Randomly shuffle the training dataset D and divide it into K mini-batches;
4: for k == 1,..... K
do 5: Calculate U, for the instance a; according Eq. (+);
6:
Update S to 52 according to Eq. (I5);
7:
Calculate v, for the instance æ; according to Eq. (N):
8:
Save O and update Ø to 0 according to Eq. (IG);
9:
Randomly sample mini-batch from D and update D r according to Eq. (ILI);
10: Calculate q: for the instance æ; according to Eq. Eq. (αI))
11: Rollback to O and update O to @ according to Eq. (03);
12: end for
13:
end for
Output: The predictive model f(; ().
A.3 Algorithm Table
The algorithmic description of RPLG is presented in Algorithm MI The reduction-based pseudo- labels are aggregated from the outputs of an auxiliary multi-branch model. Specifically, each branch of this auxiliary model is trained within a distinct label subspace that explicitly excludes set of specific labels. To generate the final reduction-bart based pseudo-label, we leverage meta-learned weight vector to fuse the output results of all these branches. Trained with the reduction based pseudo-labels, the predictive performance of the model consistently enhanced in our proposed approach RPI.G.
A.4 Further Analysis
Consistency and Convergence. We investigate the consistency and convergence pseudo-labels generated by our method RPLG the CIFAR-10 dataset, with results presented in Figures ya and L(b), As evident from these figures, the generated pseudo-labels gradually align with the Bayes optimal classifier and exhibit convergence the number of training epochs increases.
Time Consumption Analysis. Table presents training time measured in hours. All the methods were executed for 250 epochs with batch size of 256 on a single NVIDIA RTX 3090 with AMD EPYC 7453 28-Core Processor. In contrast to recent baseline methods, our proposed approach, RPLG experiences only linear increase in training time. The efficiency is attained by virtue of the online strategy used in meta-learning optimization and shared lower layers in the multi-branch model.
Trade-off between Effectiveness and Efficiency. One-branch-per-label is universal and conser- vative scheme to deal with ID-PI.I,, since each class may act as a disturbing class for other classes. In practice, when efficiency is preferred, using fewer branches via label clustering or dimensionality reduction is a good idea. Here, we formulate two variants of RPLG with fewer branches: RPLG-W W and RPLG-R. RPLG-W employs Word2Vee for label clustering to group labels into cluster with similar textual semantics (e.g., "dog" and "cat"). It retains only those branches where the excluded label belongs to the clusterthis is because labels with similar semantics are more likely to interfere with each other, so training series of subspaces that mutually exclude semantically similar labels helpful. In contrast, RPLG-R retains branches randomly. Table presents the performance of these two variants on TinylmageNet. From Table E we can observe that compared with randomly retaining branches, preserving branches that exclude semantically similar labels achieves, to some extent, favorable trade-off between performance and computational overhead.

---

Table 4: Comparison of the training time consumed by all approaches CIFARIO, CIFAR-100 and Tnngeett
Method
CIFARIO
CIFARI00
TinylmageNet
RPLG
2.32
3.01
6.38
DIRK
1,50
2.11
3.23
SDCT
1.86
1.93
6.15
POP
1.48
1.51
5.84
IDGP
2.91
2.90
6.34
ABLE
3,03
3.06
6,49
VALEN
1.18
1.37
5.63
PL.CR
1.38
1.44
5.27
PICO
3.12
3.15
5.96
CAVL
1.51
1.53
5.53
LWS
1.66
1.67
5.88
RC
1,47
1.50
5.55
CC
1,41
1.43
5.16
PRODEN
1.42
1.43
5.14
90-
Pscudo- Jabel Accuracy (%)
32-
70
24-
110
16
50
Epoch
Epoch
(a) Consistency
(b) Convergence
Figure 2: Further analysis of RPLG CIFAR-10
A.5 Limitations and Future Work
This is the first work introduce the concept of reduction-based pseudo-labels. This pseudo-label generation approach is motivated by derived theorems and is appropriate for addressing the chal- lenge of instance-dependent partial label learning and the limitations of previous works in this area. However, training the pseudo-label generation model in the label subspace does not necessarily re- quire all training samples, as some samples outside the subspace may noise for model training within the subspace. In future work, we will introduce a sample selection mechanism for training the subspace pseudo-label generation model, which is expected improve the model's training accuracy and efficiency.
A.6 Impact Statement
The aim of this study is advance the techniques and methodologies in the field of Machine Leam- ing. The approach we propose to deal with ID-PLL, typically weakly supervised learning, may bring about situation where data annotators other personnel involved in data-related occupations could potentially be replaced. We are acutely conscious of the importance of addressing the impacts of automation on employment and vigilant about its societal ramifications.
25

---

Table 5: Classification accuracy and time consumption of approach RPLG and its variants RPLG- W and RPLG-R with various branch retaining rates on Tiny ImageNet.
Method
Retaining Rate
Accuracy(%)
Time(h)
RPLG
100%
40.74
6.38
RPLG-W
80%
40.63
6.30
60%
40.27
6.23
40%
39.89
6.09
20%
39.53
5.97
RPLG-R
80%
39.65
6.30
60%
39.05
6.23
40%
38.78
6.09
20%
38.84
5.97
POP (ranked second)
39.27
5.84
26


Reviews:
[{"review_id": "SBHkpURaFw", "reviewer": "Reviewer_GUqm", "summary": "This paper addresses a key challenge in Instance-dependent Partial Label Learning (ID-PLL). The authors identify that existing methods, which rely on the model's self-identification capability, often encounter a training bottleneck because they struggle to distinguish the true label from incorrect candidate labels that are strongly correlated with instance features. To overcome this, the paper proposes a novel method, RPLG (Reduction-based Pseudo-label Generation). The core idea is to train the predictive model using \"reduction-based pseudo-labels\". These are generated by a multi-branch auxiliary model where each branch is trained in a \"label subspace\" that explicitly excludes one specific label, thereby avoiding its interference. The framework further incorporates a meta-learner to perform a weighted aggregation of the outputs from all branches to produce the final pseudo-label. Theoretically, the authors prove that their proposed pseudo-labels exhibit greater consistency with the Bayes optimal classifier.", "questions": "1. Must the number of branches equal the number of labels? Have you considered using fewer branches, such as via label clustering or dimensionality reduction, to reduce computation?\n2. How does the method handle labels that are both correct and disturbing in different samples?", "limitations": "1. The method trains one branch per label. As the number of classes increases (e.g., 200 in TinyImageNet), the computation and memory cost grows rapidly.\n2. The theoretical guarantees rely on ideal assumptions, such as the model closely approximating the posterior distribution and satisfying the Tsybakov condition.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. The concept of \"reduction-based pseudo-labels\" and the use of label subspaces to mitigate interference  is a highly novel contribution. The approach directly targets a well-articulated shortcoming in prior work, namely the model's inability to handle \"disturbing incorrect labels\", rather than offering a mere incremental improvement.\n2. The method is not just heuristic but is supported by a solid theoretical analysis. The authors provide theorems (Theorem 1 and 2) to formally justify the approach, demonstrating that the generated pseudo-labels are more consistent with the Bayes optimal classifier compared to those from the predictive model itself.\n3.The paper presents comprehensive and convincing experimental results. RPLG is shown to significantly outperform a wide range of baselines, including recent state-of-the-art methods, across various benchmark and real-world datasets. The ablation study comparing RPLG with RPLG-NM effectively validates the contribution of the meta-learning component.\n\nWeaknesses:\n1. The multi-branch model design incurs significant overhead when the number of classes is large. For example, TinyImageNet training time is substantially higher.\n2. While the paper uses a weight vector to fuse predictions from each branch, it does not analyze how the branches interact or whether some are redundant.\n3. While a variant without meta-learning (RPLG-NM) is compared, the necessity of using one branch per label is not ablated or justified. Could fewer branches suffice?\n4. All baselines use the same backbone and data augmentation, but many of them are not designed for ID-PLL. It would strengthen the case to compare against ensemble-based or meta-learning based approaches beyond the PLL field.", "was_revised": true, "final_justification": "The authors have successfully adressed the majority of my concerns as mentioned in the rebuttal.", "rebuttal": "We sincerely appreciate your meticulous review and professional feedback on our paper. Your recognition of **the novelty of the \"reduction-based pseudo-labels\" concept, the use of label subspaces to mitigate interference, and the solid theoretical analysis** is highly encouraging. In response to Weaknesses (W), Questions (Q) and Limitations (L), we would like to provide the following Explanations (E).\n\n---\n\n**W1/L1**: Linear growth of branches with classes leading to high computational overhead  \n\n**E1**:  As highlighted in Section 4.4 and Appendix A.4, our framework mitigates this through two key designs: (1) **shared feature extractors with parallel training of branches**, which reduces redundant parameter storage and computation; (2) **online meta-learning optimization**, which avoids exhaustive bi-level optimization. Experimental results in Table 4 show that RPLG incurs only a marginal linear increase in training time (e.g., 6.38 hours on TinyImageNet vs. 5.84 hours for the second-ranked algorithm baseline POP), which is manageable given the significant performance gains (40.74% vs. 39.27% accuracy on TinyImageNet). \n\nAdditionally, as noted earlier, we formulate variants of RPLG with fewer branches, considering the trade-off between performance and computational cost, which will be elaborated on in the subsequent section **E3**.\n\n---\n\n**W2**: Branch interaction and redundancy  \n\n**E2**: Branch interaction is implicitly realized through a reduction-based pseudo-label in an iterative process: the outputs of all branches for instance $ x_i $ are integrated into the reduction-based pseudo-label $ v_i $ via meta-learned weights $ w_i $ in Eq. (8), and in the next epoch, the pseudo-label is normalized into $ U_i $ in Eq. (9) for training the branches.\n\nBranch redundancy is addressed by the **meta-learned weight vector** in Eq. (11-17). The meta-learner $ g(\\cdot; \\Gamma) $ adaptively assigns weights to branches based on instance features, effectively suppressing redundant branches. For example, if a branch trained by excluding label $ j $ is irrelevant to instance $ x_i $ (i.e., $ j $ is not a disturbing label for $ x_i $), its weight $ w_i^j $ becomes negligible. This is validated by Table 3 in the submission, where RPLG (with meta-weights) outperforms RPLG-NM (uniform weights) across all datasets, demonstrating that learned weights eliminate redundancy. \n\n---\n\n**W3/Q1**: Necessity of one-branch-per-label \n\n**E3**: This is an insightful point. One-branch-per-label is a universal and conservative scheme to deal with Instance-Dependent Partial Label Learning (ID-PLL), since each class may act as a disturbing class for other classes. \n\nIn practice, when efficiency is preferred, using fewer branches via label clustering or dimensionality reduction is a good idea. Here, we formulate two variants of RPLG with fewer branches: RPLG-W and RPLG-R. RPLG-W employs Word2Vec for label clustering to group labels into a cluster with similar textual semantics (e.g., \"dog\" and \"cat\"). It retains only those branches where the excluded label belongs to the cluster—this is because labels with similar semantics are more likely to interfere with each other, so training a series of subspaces that mutually exclude semantically similar labels is helpful. In contrast, RPLG-R retains branches randomly. Table 1 presents the performance of these two variants on TinyImageNet. From Table 1, we can observe that compared with randomly retaining branches, preserving branches that exclude semantically similar labels achieves, to some extent, a favorable trade-off between performance and computational overhead.\n\n**Table 1.** _Classification accuracy and time consuming of our approach RPLG and variants with fewer branches on TinyImageNet._\n\n|Method|Retaining Rate|Average Accuracy(%)|Time(h)|\n|---|---|---|---|\n|RPLG|100%|40.74|6.38|\n|RPLG-W|80%|40.63|6.30|\n||60%|40.27|6.23|\n||40%|39.89|6.09|\n||20%|39.53|5.97|\n|RPLG-R|80%|39.65|6.30|\n||60%|39.05|6.23|\n||40%|38.78|6.09|\n||20%|38.84|5.97|\n|POP (ranked second)| - |39.27|5.84|\n\n\n---\n\n**W4**: Comparison against ensemble-based or meta-learning-based approaches beyond the PLL field\n\n**E4**: We have adapted MeanTeacher (a classic ensemble-based method for semi-supervised learning) [1] and Meta-Weight-Net (a classic meta-learning-based method for noisy label learning) [2]into versions for PLL learning by replacing the corresponding loss with the representative Proden Loss [3]. Table 2 presents the performance comparison between these two methods and our algorithm on CIFAR-100 and TinyImageNet. [1] Antti Tarvainen et al. Mean teachers are better role models: Weight-averaged consistency targets improve semi-supervised deep learning results. NIPS. [2] Shu et al. Meta-Weight-Net: Learning an Explicit Mapping For Sample Weighting. NIPS. [3] Lv et al. Progressive Identification of True Labels for Partial-Label Learning.ICML\n\n**Table 2.** _Classification accuracy of RPLG and methods beyond the PLL field on CIFAR-100 and TinyImageNet._\n\n|Method|CIFAR-100|TinyImageNet|\n|------|---------|------------|\n|RPLG|**65.03**|**40.74**|\n|MeanTeacher|62.73|34.86|\n|MetaWeightNet|62.64|33.91|\n\n---\n\n**Q2**: Handling labels that are both correct and disturbing across different samples  \n\n**E5**: Our approach RPLG addresses this through two core designs: multiple branches for label subspace training and a meta-learner for aggregation weights. For instance, if label $ j $ is disturbing for $ x_1 $ but correct for $ x_2 $, the meta-learner will learn to assign a larger weight $ w_1^j $ to branch $ j $ (trained in the label subspace excluding label $j$) during aggregation—this avoids the interference of label $ j $ on $ x_1 $. Conversely, for $ x_2 $, it will learn to assign a smaller $ w_2^j $ while increasing weights $ w_2^{k \\neq j} $, thereby preserving the signal from label $ j $.\n\n---\n\n**L2**: Assumptions in the theorems  \n\n**E6**: In our work, all assumptions are either restrictive or empirically grounded, and thus are acceptable considering that it is necessary to ensure tractable analysis. For instance, while we assume the model can approximate the posterior distribution, the extent of this approximation is controlled by $\\epsilon$, which is also an extension or relaxation of the assumption used in the earlier PLL work [1]. Additionally, the Tsybakov condition, which pertains to the dataset distribution, has been experimentally validated in the prior study [2]. [1] Feng et al. Provably Consistent Partial-Label Learning. NIPS. [2] Zheng et al. Error-Bounded Correction of Noisy Labels. ICML."}, {"review_id": "o9wkxCgODR", "reviewer": "Reviewer_LSa6", "summary": "This paper proposed to leverage reduction-based pseudo-labels to alleviate the influence of incorrect candidate labels and train the predictive model to overcome current training for Instance-dependent Partial Label Learning. The proposed method directly tackles an important gap in existing PLL research, offering a compelling motivation. In addition, the theoretical analysis is rigorous and well-integrated with the proposed methodology.", "questions": "Please see the weaknesses which need for more evidences and explanations.\n\nAdditionally, please answer the following questions:\n1. While the method is applicable to general PLL settings, the authors should evaluate and report its performance under uniformly random candidate label selection (i.e., uniform PLL) to demonstrate broader applicability.", "limitations": "The proposed method uses a meta-learner to optimize the sample-wise weight w, but only compares it against a uniform weighting strategy (RPLG-NM). Incorporating comparisons with alternative weight learning or fusion strategies (e.g., self-training, attention mechanisms, or ensemble-based reweighting) would further substantiate the claimed advantages.", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 4, "originality": 3, "strengths_and_weaknesses": "**Strengths:**\n1. This paper demonstrates a high standard of scholarly presentation, with clear organization and a coherent logical structure that aligns well with the expectations of top-tier conferences in the field.\n2. This paper addresses a critical challenge in Instance-Dependent Partial Label Learning (ID-PLL) — distinguishing the ground-truth label from misleading candidate labels — through a novel multi-branch auxiliary model architecture. This design directly tackles an important gap in existing PLL research, offering a compelling motivation.\n3. The theoretical analysis is rigorous and well-integrated with the proposed methodology. The mathematical derivations are sound and effectively support the algorithmic design.\n4. The experimental evaluation is thorough and well-executed, showcasing strong empirical performance across multiple benchmark datasets. The results clearly demonstrate the effectiveness of the proposed approach.\n\n**Weaknesses:**\n1. The paper would benefit from a more in-depth discussion of the theoretical component’s significance, particularly how the theory provides insights into or strengthens the proposed method.\n2. Since the multi-branch architecture employed is not entirely novel, this part of the contribution may be perceived as incremental. The authors should clarify what specific innovations differentiate their approach from prior multi-branch frameworks.\n3. The hyperparameter $\\alpha$ plays an important role in the proposed method. A more detailed ablation study focusing on its impact would provide deeper insight into the model's robustness and sensitivity.\n4. The proposed method uses a meta-learner to optimize the sample-wise weight $w$, but only compares it against a uniform weighting strategy (RPLG-NM). Incorporating comparisons with alternative weight learning or fusion strategies (e.g., self-training, attention mechanisms, or ensemble-based reweighting) would further substantiate the claimed advantages.", "was_revised": true, "final_justification": "The positive (motivation, theoritical analysis, and experiments) outweights the negative (novelty). I keep positive to the paper.", "rebuttal": "Thank you very much for your thorough review of our paper. We are grateful for your affirmation of **the high-standard scholarly presentation, the novel architecture for addressing the key challenge in ID-PLL, the rigorous theoretical analysis, and the well-executed experimental evaluation**. In response to Weaknesses (W), Questions (Q) and Limitations (L), we would like to provide the following Explanations (E).\n\n---\n\n**W1**: Need for a deeper discussion of the theory’s significance and insight into the proposed method\n\n**E1**: Thank you for pointing this out. To underscore the theory's significance and insight into the proposed method, we will add a discussion in the Appendix:\n\n> **Theorem 1** formally establishes that pseudo-labels produced by a model trained in a *label subspace*—one that deliberately excludes specific disturbing labels—are provably closer, in Bayes-optimal sense, to the ground-truth than labels generated in the full space. This result reframes the denoising challenge from “identifying correct labels within a noisy full space” to the more tractable task of “reducing the label space to eliminate interference.” It directly motivates RPLG’s **multi-branch auxiliary model**, where each branch deliberately trains in a subspace that omits a single candidate disturbing label.\n\n> **Theorem 1** also reveals that **no single subspace** can neutralize every possible type of label disturbance, because different instances are affected by different distractors. Consequently, an ensemble of subspace-trained branches is necessary to cover the full spectrum of disturbances. RPLG’s **meta-learned weight vector** in Eq. (11) operationalizes this insight: for every instance $x_i$, the weights $w_i$ are learned on-the-fly to emphasize branches whose excluded label is indeed the current instance’s primary distractor, thereby overcoming the limitation of single-subspace models.\n\n> **Theorem 2** further quantifies this consistency under the multi-class Tsybakov condition [29, 48], providing a lower bound on the probability that the subspace-trained model’s pseudo-labels align with the Bayes optimal classifier. This bound guarantees that, under mild statistical assumptions, the method’s pseudo-labels are reliably close to the optimal solution.  \n\n---\n\n**W2**: Novelty compared to prior multi-branch works \n\n**E2**: Thank you for helping us further enhance novelty. Although multi-branch architectures have been explored, our key contribution is the **principled exclusion of disturbing labels** within each branch—an approach grounded in a formal theoretical objective, rather than a mere engineering heuristic. Prior multi-branch studies such as [1,2,3] primarily pursue ensemble robustness and neither leverage label-subspace theory nor adopt posterior-shift reasoning. We will explicitly highlight this distinction in the Related Work section. [1] Lan et al. Knowledge Distillation by On-the-Fly Native Ensemble. NIPS. [2] Chen et al. Semi-supervised Learning with Multi-Head Co-Training. AAAI. [3] Wu et al. Multi-head mixture-of-experts. NIPS.\n\n---\n\n**W3**: More detailed study on α  \n\n**E3**: Figure 1 (Page 8) provides a sensitivity analysis of $ \\alpha $ on CIFAR-10, but we agree that a more detailed investigation would be valuable. Accordingly, we have additionally conducted sensitivity analyses of $ \\alpha $ on CIFAR-100 and TinyImageNet, with the results presented in Table 1. As shown, $ \\alpha $ values around 0.3 yield superior performance for RPLG, and its performance remains relatively stable within the interval [0.1, 0.7]—this demonstrates the robustness of RPLG.\n\n**Table 1.** _Classification accuracy of RPLG when $\\alpha$ varies on CIFAR-100 and TinyImageNet._\n\n|$\\alpha$|0.1|0.3|0.5|0.7|0.9|\n|--------|----|----|----|----|----|\n|CIFAR-100|63.21|**65.03**|64.45|64.03|60.31|\n|TinyImageNet|36.97|**40.74**|39.34|38.95|33.34|\n\n\n---\n\n**W4/L1**: Comparison of meta-weighting to alternative fusion methods  \n\n**E4**: We appreciate your further assistance in helping us highlight the advantages of introducing the meta-learner. As suggested, we formulate three variants of RPLG: \n\n> (1) RPLG-S (self-training): The weight of each branch for sample $x_i$ is determined by the confidence of the branch's output on $x_i$ in the previous epoch, i.e., $w_i^j=\\frac{\\varphi^{j}(z_i;\\Omega_j^{(t-1)})}{\\sum_{k=1}^c\\varphi^{k}(z_i;\\Omega_k^{(t-1)})}$, where $\\varphi^{j}(z_i;\\Omega_j^{(t-1)})$ is the output of the $j$-th branch at epoch $t-1$.\n\n> (2) RPLG-A (attention): A lightweight attention module (2-layer fully connected network + Softmax) is introduced to generate weights based on sample features $z_i$, i.e., $w_i=\\text{Attention}(z_i;\\Theta_{\\text{att}})$, where $\\Theta_{\\text{att}}$ is optimized jointly with the main model and auxiliary model.\n\n> (3) RPLG-E (ensemble-based reweighting): Weights are assigned based on the overall performance of branches on the validation set. Here, $ w^j = \\frac{Acc_{j}}{\\sum_{k=1}^{c} Acc_{k}}$, where $ Acc_{j} $ is the validation accuracy of the j-th branch, and the same weights are shared across all samples.\n\nTable 2 presents the performance of RPLG and its variants with alternative fusion, which demonstrates that the meta-learning-based weight strategy in RPLG has advantages over alternative weight learning or fusion methods in adapting to instance-dependent partial label scenarios, further substantiating the superiority of our meta-learner.\n\n**Table 2.** _Classification accuracy of RPLG and variants with alternative fusion on CIFAR-100 and TinyImageNet._\n\n|Method|CIFAR-100|TinyImageNet|\n|------|---------|------------|\n|RPLG|**65.03**|**40.74**|\n|RPLG-S|61.34|36.43|\n|RPLG-A|61.21|36.28|\n|RPLG-E|63.28|38.25|\n\n\n---\n\n**Q1**: Evaluation on Uniform-PLL  \n\n**E5**: As suggested, we conducted an experiment on uniform PLL settings follow [1,2] (uniformly sampling a candidate label set from the whole label space). Table 3 presents the performance of RPLG and uniform PLL baselines on KMNIST, FMNIST and CIFAR-10 in Table 3. We could observe that RPLG achieves superior or at least comparable performance to other approaches, confirming broader applicability of our approach. [1] Feng et al. Provably Consistent Partial-Label Learning. NIPS. [2] Zhang et al. Exploit Class Activation Value for Partial-Label Learning. ICLR.\n\n**Table 3.** _Classification accuracy of RPLG and compared methods on KMNIST, FMNIST and CIFAR-10 for uniform PLL._\n\n|Dataset(Backbone)|Method|Accuracy|\n|-|-|-|\n|KMNIST(LeNet)|CC|93.83±0.20%|\n||RC|94.01±0.15%|\n||LW|91.52±0.65%|\n||PRODEN|93.94±0.18%|\n||CAVL|**93.25±0.21%**|\n||RPLG|93.12±0.10%|\n|FMNIST(LeNet)|CC|88.96±0.14%|\n||RC|89.51±0.11%|\n||LW|88.28±0.33%|\n||PRODEN|89.23±0.12%|\n||CAVL|89.99±0.10%|\n||RPLG|**90.10±0.19%**|\n|CIFAR-10(ResNet)|CC|76.78±0.33%|\n||RC|78.56±0.37%|\n||LW|78.08±0.66%|\n||PRODEN|78.72±0.48%|\n||CAVL|79.10±0.25%|\n||RPLG|**79.38±0.19%**|"}, {"review_id": "CtOpTSSZj1", "reviewer": "Reviewer_S4hy", "summary": "This paper addresses instance-dependent partial label learning (ID-PLL), where training instances are annotated with candidate labels that may include feature-correlated incorrect labels. Existing approaches leveraging the training model's identification capability often encounter a bottleneck: within the originally given label space, the model struggles to distinguish strongly feature-correlated incorrect labels from true labels, leading to poor-quality supervision signals. To tackle this, this paper proposes reduction-based pseudo-labels generated via a multi-branch auxiliary model, each branch trained in a label subspace excluding specific labels. This design explicitly mitigates interference from hard-to-identify incorrect labels. Theoretically, it proves that reduction-based pseudo-labels exhibit higher consistency with the Bayes optimal classifier than pseudo-labels directly derived from the predictive model, validated through rigorous analysis on benchmark and real-world datasets.", "questions": "Please refer to the weaknesses.", "limitations": "Yes. The authors have adequately addressed the limitations and potential negative societal impact of their work in Appendix A.5 and A.6.", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 3, "originality": 4, "strengths_and_weaknesses": "Strengths:\n\n1. **Strong Novelty** \n   - The focus on the ID-PLL learning paradigm is novel. The paper emphasizes candidate labels that are difficult to identify in the original label space, which are clearly defined as ($\\tau$, $f$, $\\epsilon$)-disturbing incorrect labels in the paper.\n   - The paper presents novel theories by being the first to explore the posterior probability related to the Bayes classifier in label subspaces for partial label learning.\n   - The algorithm designed based on this theory is novel. The core idea of leveraging a multi-branch auxiliary model—where each branch is trained in a label subspace excluding specific labels—provides an insightful solution to mitigate interference from feature-correlated incorrect labels. This design explicitly addresses the limitation of prior methods.  \n\n2. **Theoretical Rigor**  \n   The paper makes significant theoretical contributions by proving that reduction-based pseudo-labels generated in label subspaces exhibit stronger consistency with the Bayes optimal classifier than those derived directly from the predictive model. The theorems (Theorem 1 and 2) and their proofs (Appendix A.1–A.2) are meticulously structured, establishing a rigorous theoretical foundation for the method. This theoretical insight validates the algorithm’s superiority in handling label ambiguity.  \n\n3. **Comprehensive Empirical Validation**  \n   The experimental design is robust, spanning diverse benchmark datasets (e.g., FMNIST, CIFAR-100, TinyImageNet) and real-world applications (e.g., Lost, Yahoo!News). RPLG demonstrates significant performance advantages, particularly on complex datasets like TinyImageNet, highlighting its generalizability. The time complexity analysis shows that RPLG achieves state-of-the-art results with only a marginal linear increase in training time, balancing efficiency and accuracy.  \n\n4. **Clarity in Presentation**  \n   The paper is meticulously written and well-structured, with clear notations and detailed algorithm descriptions (e.g., Algorithm 1 in Appendix A.3). Tables and figures (e.g., Tables 1–4, Figure 2) effectively visualize results, while the ablation studies and sensitivity analysis (e.g., on $\\alpha$ and meta-learned weights) enhance reproducibility. \n\nWeaknesses:\n\n1. It is better to further explain the objective optimization function of meta-learning in Eq. (14).\n\n2. It is better to further highlight the advantages of the algorithm in the interpretation of the experimental results section.", "was_revised": true, "final_justification": "I have read all the reviews and the authors' response. All my questions have been addressed. I keep the ratings unchanged.", "rebuttal": "We would like to express our heartfelt gratitude for your high-level evaluation of our paper. Your recognition of **the strong novelty in the ID-PLL learning paradigm, theoretical rigor, and comprehensive empirical validation** is a great encouragement. In response to Weaknesses (W), we would like to provide the following Explanations (E).\n\n---\n\n**W1**: Clarify meta-learning optimization\n\n**E1**: We provide the following explanation for Eq. (14):  \n\n> Eq. (14) implements a bi-level optimization framework where the meta-learner optimizes weights to minimize the predictive model’s validation loss after inner-loop updates. The outer optimization updates the meta-learner parameter $\\Gamma$ (which generates weight vector $w_i$) by minimizing $\\mathcal{L}^{\\text{outer}}$, evaluating the inner-optimized predictive model on the validation set $D^{\\text{val}}$. The inner optimization updates the predictive model parameter $\\Theta$ using $\\mathcal{L}^{\\text{inner}}$, leveraging reduction-based pseudo-labels $V$ (derived from the multi-branch auxiliary model) for training. The inner-optimized $\\Theta^{\\star}$ depends on the outer $\\Gamma$ (as $V$ relies on $w_i$), while the outer optimization’s objective depends on the inner $\\Theta^{\\star}$.\n\n---\n\n**W2**: Better highlight experimental advantages  \n\n**E2**: We will revise the experimental section to emphasize key findings with enhanced statistical evidence:  \n\n(1) **Superior performance on complex datasets** (TinyImageNet, Soccer Player, Yahoo!News):  \n> Our algorithm outperforms the second-best baseline algorithms on large, complex datasets, achieving a 1.47% improvement on TinyImageNet compared to POP and a 0.95% improvement on Soccer Player compared to IDGP.  \n\n(2) **Impact of meta-learning**:  \n> By leveraging meta-learned weights to select branches while mitigating the influence of strongly associated incorrect labels, RPLG consistently outperforms RPLG-NM across all datasets, with a notable 5.39% improvement on TinyImageNet.\n\nThese results will be highlighted more prominently in Section 4.3."}, {"review_id": "DafPLidwc1", "reviewer": "Reviewer_dbq6", "summary": "This paper addresses instance-dependent partial label learning (ID-PLL) by proposing RPLG, a method that generates reduction-based pseudo-labels using a multi-branch auxiliary model. The key insight is that some incorrect candidate labels strongly correlated with features are difficult to distinguish from correct labels, creating a bottleneck in training. To address this, each branch of the auxiliary model is trained in a label subspace excluding certain labels, allowing instances affected by excluded labels to benefit from unaffected branches. The authors provide theoretical analysis showing that reduction-based pseudo-labels can achieve better consistency with the Bayes optimal classifier, and demonstrate consistent improvements across multiple benchmark and real-world datasets.", "questions": "1. Beyond α, how sensitive is the method to other hyperparameters in the bi-level optimization? The paper mentions \"carefully selected\" parameters but provides limited guidance.\n2. How do you handle cases where auxiliary branches produce worse pseudo-labels than the original candidate sets? Is there any mechanism to detect and mitigate such degradation? What's the failure rate of pseudo-label generation across different datasets?\n3. Since branches share feature extraction layers to save computation, how do you ensure that the learned representations don't carry interference from excluded labels? Wouldn't this shared representation potentially undermine the core premise of label subspace training?", "limitations": "The requirement for training c auxiliary branches makes the approach prohibitively expensive for datasets with hundreds or thousands of classes, limiting its applicability to large-scale modern applications. Besides, I don't believe that the paper has a potential negative social impact.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths：\n1. The identification of \"disturbing incorrect labels\" that are strongly correlated with features represents a genuine challenge in ID-PLL that existing methods overlook. \n2. The reduction-based pseudo-label generation using multi-branch auxiliary models is creative and theoretically motivated, offering a principled way to handle label interference.\n3. Theorems 1 and 2 provide theoretical justification showing that reduction-based pseudo-labels can achieve better consistency with the Bayes optimal classifier under certain conditions.\n\nWeaknesses：\n1. The method directly uses generated pseudo-labels without any confidence estimation or quality control mechanism. Poor-quality pseudo-labels from unreliable branches could introduce more noise than the original candidate labels, but there's no safeguard against this degradation.\n2. Defining subspaces by simply excluding individual labels ignores semantic relationships between labels. Labels with similar meanings or hierarchical relationships should be considered together when defining exclusion sets. The current approach treats all labels as independent, which may not reflect real-world label structures.\n3. The relationship between the \"disturbing incorrect labels\" concept and the practical multi-branch implementation could be clearer", "was_revised": true, "final_justification": "I have reviewed the authors' rebuttal and discussions with other reviewers. The main concerns have been adequately addressed, and the authors provided convincing responses to the technical questions raised. I maintain my borderline accept recommendation.", "rebuttal": "We sincerely thank you for your careful review and constructive feedback. We are delighted by your recognition of **our identification of \"disturbing incorrect labels,\" the creativity of reduction-based pseudo-label generation, and the robust theoretical justification**. Below, we address your Weaknesses (W), Questions (Q), and Limitations (L) with detailed Explanations (E).\n\n---\n\n**W1/Q2**: Quality control on pseudo-labels\n\n**E1**:  While our method does not explicitly use traditional confidence scores (e.g., entropy-based thresholds), it incorporates adaptive weighting via meta-learning and hybrid pseudo-label fusion to control quality. \n\n(1) Adaptive weighting via meta-learning:\n\n> The core of our reduction-based pseudo-label generation (RPLG) lies in the **meta-learned weight vector $w_i$** in Eq. (11), which serves as a dynamic quality-control mechanism. Unlike uniform aggregation (as in our ablation RPLG-NM), $w_i$ is learned via a meta-learner $g$ to prioritize outputs from branches that are **least affected by the instance’s specific disturbing labels**. \n\n(2) Hybrid pseudo-label fusion:\n\n> The final pseudo-label $q_i$ in Eq. (6) is a weighted combination of two components: \n> - $v_i$: the reduction-based pseudo-label from the multi-branch auxiliary model, filtered via meta-learned weights.\n> - $\\mu_i$: a basic pseudo-label derived from the predictive model’s outputs in the full label space, serving as **an implicit quality-control buffer**.\n\nThese mechanisms collectively prevent low-quality pseudo-labels from degrading performance, as validated by consistent outperformance over baselines and ablations. As suggested, we additionally report the final failure rates of pseudo-label generation across datasets, compared with PRODEN [1], in Table 1. [1] Lv et al. Progressive Identification of True Labels for Partial-Label Learning. ICML.\n\n**Table 1.** _Failure Rate of our approach RPLG and PRODEN on benchmark datasets._\n\n|Method|FMNIST|KMNIST|CIFAR-10|CIFAR-100|TinyImageNet|\n|-|-|-|-|-|-|\n|RPLG|11.21|5.34|13.56|36.87|62.45|\n|PRODEN|14.55|6.87|14.66|39.25|67.88|\n\n\n\n---\n\n**W2**: Ignoring semantic label relations  \n\n**E2**: Please allow us to further clarify that \"Individual Label Exclusion\" serves as a flexible and general foundation, rather than a rigid constraint.\n\nOn one hand, through adaptive weight aggregation, the current design of excluding individual labels implicitly handles semantic/hierarchical relationships. For labels with strong semantic correlations (e.g., \"cat\" and \"kitten\" in an image dataset), their disturbing effects on a given instance often overlap: if an instance is troubled by \"cat,\" it is likely also affected by \"kitten.\" In such cases, the meta-learner $ g $ (which outputs weight vector $ w_i $) will automatically assign higher weights to branches excluding both labels. \n\nOn the other hand, when efficiency is preferred, we could retain less branches by considering semantic relationships between labels. Here, we formulate a variant RPLG-W of our approach. RPLG-W employs the Word2Vec technique for label clustering to group labels into a cluster with similar textual semantics (e.g., \"dog\" and \"cat\"). Then, it retains only those branches where the excluded label belongs to the cluster—this is because labels with similar semantics are more likely to interfere with each other, so training a series of subspaces that mutually exclude semantically similar labels is helpful. \n\nTable 2 presents the performance of RPLG and RPLG-W with fewer branches. From Table 2, we can observe that preserving branches that exclude semantically similar labels achieves a favorable trade-off between performance and computational overhead to some extent.\n\n**Table 2.** _Classification accuracy and time consuming of our approach RPLG and variants with fewer branches on TinyImageNet._\n\n|Method|Branches Retaining Rate|Average Accuracy(%)|Time(h)|\n|---|---|---|---|\n|RPLG|100%|40.74|6.38|\n|RPLG-W|80%|40.63|6.30|\n||60%|40.27|6.23|\n||40%|39.89|6.09|\n||20%|39.53|5.97|\n|POP (ranked second)| - |39.27|5.84|\n\n---\n\n**W3**: The relationship between disturbing incorrect labels and multi-branch implementation  \n\n**E3**: Thank you for helping us further improve the clarity of the paper. We will add the following paragraph after Eq. (10) to strengthen the relationship between disturbing incorrect labels and multi-branch implementation.\n\n> The multi-branch implementation is a practical instantiation of the strategy to counteract disturbing incorrect labels:  \n> - **Disturbing labels** define the set of problematic labels that must be excluded to reduce ambiguity;  \n> - **Each branch** is a specialized module trained to avoid one such label, eliminating its interference for instances troubled by it;  \n> - **Meta-learned aggregation** ensures instances rely on the branches most effective at mitigating their specific disturbing labels.  \n\nThis tight coupling between theory (disturbing labels) and implementation (multi-branch design) is what enables RPLG to outperform methods that ignore this targeted exclusion logic.\n\n---\n\n**Q1**: Sensitivity of other hyperparameters in the bi-level optimization  \n\n**E4**: Beyond $\\alpha$, the bi-level optimization in RPLG involves Step sizes ($\\beta_1, \\beta_2, \\beta_3$), which control the update rates for the auxiliary model. In practice, ($\\beta_1, \\beta_2, \\beta_3$) is set to be equal to the learning rate. Hence, they are selected within the range of [1e-4, 1e-1], consistent with the learning rate. We will further clarify this point in the last paragraph of Section 4.2. Here, we also provide their individual performance on CIFAR-10 for reference in Table 3. \n\n**Table 3.** _Classification accuracy of RPLG when $\\beta_1, \\beta_2, \\beta_3$ varies on CIFAR-10._\n\n|Hyper-parameters|1e-4|1e-3|1e-2|1e-1|\n|-|-|-|-|-|\n|$\\beta_1$|82.54|83.68|**87.53**|73.24|\n|$\\beta_2$|81.63|84.29|**87.53**|75.35|\n|$\\beta_3$|79.46|83.97|**87.53**|77.88|\n\n\n---\n\n**Q3**: Shared feature extractor undermining label subspace training  \n\n**E5**:  Shared feature extraction layers do not carry label-specific interference because: (1) they encode generic patterns; (2) branch-specific heads and losses enforce subspace isolation. This design balances computational efficiency with the integrity of label subspace training. The shared feature layer operates similarly to pre-trained backbones in transfer learning: generic features provide a strong foundation, while task-specific heads adapt them to new objectives. In our case, \"tasks\" are the label subspaces, and the branch heads adapt shared features to avoid excluded labels.\n\nAdditionally, we provide a variant RPLG-MLP, where the linear layer branches are replaced with MLP layers for further verification. Table 4 presents the performance of this variant and RPLG on FMNIST and CIFAR-10. From this, we could infer that the design of shared representation does not undermine the core premise of label subspace training.\n\n**Table 4.** _Classification accuracy (mean±std) of RPLG and variants with MLP branches on FMNIST and CIFAR-10._\n\n|Method|FMNIST|CIFAR-10|\n|-|-|-|\n|RPLG|91.41±0.13|87.53±0.21|\n|RPLG-MLP|91.32±0.11|87.46±0.23|\n\n---\n\n**L1**: Large-scale application  \n\n**E6**: We appreciate the reviewer’s concern about the scalability of the multi-branch design for large-scale datasets with hundreds or thousands of classes. We have already clarified this limitation and the directions for future work to improve upon it in Appendix A.5. In **E2**, we have provided a more efficient variant along with preliminary experimental results, which will be supplemented in the revised version. We believe this will further enhance its applicability in large-scale scenarios."}]

Author rebuttal:

Meta-review: Following the final round of reviews, the paper received one "Accept" rating and three "Borderline Accept" ratings. The reviewers recognized the technical novelty of the proposed approach and acknowledged the strength of both the theoretical analysis and the empirical results. Additionally, the rebuttal played a constructive role in the evaluation process, as it effectively addressed most of the reviewers' concerns and clarified several key points raised during the initial review phase.
Decision: Accept (poster)