What Makes Partial-Label Learning Algorithms Effective?
Authors: Jiaqi Lv
Yangfan Liu
Shiyu Xia
Ning Xu
Miao Xu
Gang Niu
Min-Ling Zhang
Masashi Sugiyama
Xin Geng
Venue: NeurIPS 2024 poster (2024)
Keywords: partial-label learning
algorithm design principles
Primary area: other
TL;DR: We summarize the success of PLL so far into some minimal algorithm design principles.

Abstract: A partial label (PL) specifies a set of candidate labels for an instance and partial-label learning (PLL) trains multi-class classifiers with PLs.
Recently, many methods that incorporate techniques from other domains have shown strong potential.
The expectation that stronger techniques would enhance performance has resulted in prominent PLL methods becoming not only highly complicated but also quite different from one another, making it challenging to choose the best direction for future algorithm design.
While it is exciting to see higher performance, this leaves open a fundamental question: what makes a PLL method effective?
We present a comprehensive empirical analysis of this question and summarize the success of PLL so far into some minimal algorithm design principles.
Our findings reveal that high accuracy on benchmark-simulated datasets with PLs can misleadingly amplify the perceived effectiveness of some general techniques, which may improve representation learning but have limited impact on addressing the inherent challenges of PLs. 
We further identify the common behavior among successful PLL methods as a progressive transition from uniform to one-hot pseudo-labels, highlighting the critical role of mini-batch PL purification in achieving top performance.
Based on our findings, we introduce a minimal working algorithm that is surprisingly simple yet effective, and propose an improved strategy to implement the design principles, suggesting a promising direction for improvements in PLL.

What Makes Partial-Label Learning Algorithms Effective?
Jiaqi L Yangfan Liu', Shiyu Xia', Ning Xu Miao Xu²,
Gang Niu 3.1 Min-Ling Zhang Masashi Sugiyama Xin Gengl.5+ 1.5*
Southeast University 'The University of Queensland
"RIKEN Center for Advanced Intelligence Project "The University of Tokyo
KKey Laboratory of New Generation Artificial Intelligence Technology and Its Interdisciplinary Applications (Southeast University), Ministry of Education, China {is. jisii. .l, gang niu. m1 mmlmmmmmmmm..mmmmmmmmmmmmmmmmmmm com,
miao miao.xu@ug xu@uq.uuuuuuoo edu. au, sugiēk. u u-tokyo. ac.
(liuyangfan, shiyu_xia, xning, zhangml, xgeng/@seu. edu,
Abstract
A partial label (PL) specifies set of candidate labels for an instance and partial- label learning (PLL) trains multi-class classifiers with PLs. Recently, many meth- ods that incorporate techniques from other domains have shown strong potential. The expectation that stronger techniques would enhance performance has resulted in prominent PLL methods becoming not only highly complicated but also quite different from one another, making it challenging to choose the best direction for future algorithm design. While it is exciting to see higher performance, this leaves open a fundamental question: what makes a PLL method effective? We present a comprehensive empirical analysis of this question and summarize the success of PLL so far into some minimal algorithm design principles. Our findings reveal that high accuracy benchmark -imullldee datasets with PLs can misleadingly amplify the perceived effectiveness some general techniques, which may improve repre- sentation learning but have limited impact addressing the inherent challenges of PLs. We further identify the common behavior among successful PLL methods as progressive transition from uniform one-hot pseudo-labels, highlighting the critical role of mini-batch Pl. purificattio in achieving top performance. Based on our findings, we introduce a minimal working algorithm that surprisingly simple yet effective, and propose an improved strategy to implement the design principles, suggesting promising direction for improvements in PLL.
Introduction
Partial-label learning (PLL) [14, 12, 42] has been an established discipline in the weakly supervised learning field [50, 51] for decades, It aims to train multi-class classifiers from instances with partial- labels (PLs) a PL for an instance is set of candidate labels, where a fixed but unknown candidate is the true label.
As benchmarking simulated PLL versions of vision datasets becomes standard practice for evalu- ating PLL methods, new PLL approaches are emerging that integrate diverse advanced techniques enhance the performance. While many methods show great promise and some headway has been made in understanding the methodology against ambiguous label assignments [24], we find that state-of-the-art (SOTA) approaches look quite complicated and differ significantly from each other (Table l), making it challenging to choose the best direction for better algorithm design.
*Corresponding author.
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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6005
lan Lp
Spech
(a) Acc of IBS
(b) Margin of IBS
(c) Acc ABS
(d) Margin of ABS
Figure 1: Training accuracy and confidence margin of predicted pseudo-labed labels for traditional IBS and ABS methods on FMNIST with PLs: (a-b) show the granularity EM execution in classical IBS methods is refined from single step to an entire epoch, facilitating a smoother transition from uniform to one-hot pseudo-labels; (c-d) demonstrate that when ABS methods are optimized using SGD, the optimization targets for candidate labels can gradually become distinct.
In this paper, we aim to summarize the success of PLL so far, and understand the indispensable elements in well- performing PLL method, which can be condensed into minimal algorithm design principles. For this purpose, we think of the taxonomy of PL.L approaches first, comb the evolution and trends in this field, thereby uncovering key factors that drive their effectiveness and motivating future research.
The widely accepted PLL taxonomy [47, 24] divides methods based on the treatment of PLs into identification- strategy (IBS) and average-based strategy (ABS):
IBS disambiguates each PL to select the most likely true label for training;
ABS treats all candidate labels equally for training.
However, the boundary between these two categories is vague, resulting in lack of consensus on the category of many recent approaches which purifies each PL on the fly during model training [25, 37, 39]. They initially look like ABS, since uniform targets are always used prepare for true-label selection, and as training progresses, the optimization targets for candidate labels become distinct gradually, such that they exhibit IBS-like characteristies. The tricky fact is that such approaches are classified as ABS or IBS hinging on which definition of category researchers are willing to relax (e.g., [45] versus [35])] In light of the evolving approaches within PLL., is there a need to establish a third category within the taxonomy to capture the "hybrid strategy", as attempted by recent work like [43, 5]?
We suggest that the answer is in the negative, since our analysis confirms the fluidity of method categorization within PLL, emphasizing that IBS, ABS, and so-called hybrid strategy often overlap due to the dynamic nature of their implementation:
Training manner of IBS. Typical IBS approaches [48, 13] perform one-step EM to identify the true label in each PL (E step) and then train supervised classifier (M step). To mitigate overfitting to wrongly identify labels, multi-step EM IBS [11, 10] are proposed. As iterations are executed more frequently, the identifocation of true labels becomes increasingly smooth (Figure 1).
Implicit differentiation in ABS. Typical ABS approaches [19, 6] design loss function that does differentiate candidate labels, e.g., enforeing the softmax outputs of them to sum to [19]. However, stochastic optimization algorithms can implicitly lead distinct outputs for each candidate label and show a progressive purification characteristic (Figure and Lemma 3.1).
Execution matters. Whether method truly exhibits progressive characteristics and the extent of progression also depend on the optimizers used and hyperparameters like the learning rate and batch size (Figure 4).
Therefore, predefining a method's category and then asserting its utility can limit our understanding of its true nature and effectiveness. Further, our empirical incestigations reveal key insight: all successful PLL algorithms exhibit common behavior characterized by progressive transition from uniform to one-hot pseudo-labele facilitated by the combination of PL purification and model updates in mini- manii-bach-wwee wise manner. Building on this core strategy. modern methods also integrate various techniques from other domains, exemplified by Match from coni-supervised learning [3, 29], aiming to further enhance model performance. While intuitively, better performance could be achieved if stronger techniques are employed, our findings indicate that these enhancements often yield marginal gains when compared to the primary benefits derived from mini-batch PL purification. Notably, even

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Table Comparison of techniques used in eight prominent PLL methods. v / indicates whether a technique is used, and an underline denotes the key components of the respective methods.
Mini-b. purif.
Data
Exp.Mov
Match
PL. methods
Mixup
Main assumption
augment. Average
DA DM
PRODEN [25]
DNNs learn pattern first
CC [12]
X
X
x
X PLs are generated uniformly
LWC [37]
X
x
Pl.s are class-dependent
PICO [34]
V
Same class representations cluster Input is invarient to the translations High-confid. sample is likely correct X
X
DPLL [38]
X
V
X
SoLar [33]
V
V
PaPi [40]
V
Same class representations cluster Stable high-confid. sample is correct
CroSel [30]
V
when these additional techniques result in significant improvements, they tend to boost the model's ability to learn representations rather than resolving the inherent ambiguities of PLs.
The main contributions of our paper can be summarized as follows: (i) We advance the understanding of PL.L taxonomy and establish minimal algorithm design principles. the core of these principles is mini-batch PL purification, a fundamental aspect that goes beyond using supervised information. These principles not only enhance the efficiency of algorithm development but also act as conclusive work to prevent redundant efforts in future research. (ii) We analyze the design philosophies and component frameworks SOTA PLL methods, conducting comprehensive studies on benchmark- simulated datasets with PLs. Building this, we highlight minimal working algorithm that adheres to our design principles, and propose an enhancement strategy to mini- batch PL purification that have the potential elevate performance across all existing SOTA methods.
Preliminaries
2.1 Notation
Consider a k-class classification problem. Let æ E X' be features and E y = (1,2,.... be labels. Then one has (x. y) sampled from the ground-truth joint density p(æ,3) 3) over X' x y in supervised learning. PLL deals with PLL data S), which is independently drawn from corrupted distribution p(x.S) of p(x, y) with p(z) unchanged. S E (21%) (X denotes PL. and D (x,, St) is PLL dataset. The key assumption of PLL is that the latent true label of an instance is always included in its PL., i.e., p(y E S(x, = Let A A C [0. 1] denote the k-dimensional simplex. Let ʃ X k be multi-label classifier to be trained, specifically, composite of a backbone (e.g., ResNet [18]) and an inverse link function 6- [27] (e.g., sof tmax), so that (x) can be interpreted as probabilities. A y - R4 be a surrogate loss function. e.g., cross- cross-entropy loss. The classification risk of f is defined as R(f) Ep(r,) the performance measure we would like to optimize.
[(( [((f()) v)]. which
2.2 Backgrounds
In this section, review recent prominent PLL works. In PLL, a common practice is adopt weighted objective of the form
R(f) = Ep(x,5) Σ sES w(x =))(f
(I)
with the optimal weights w (z =)= p(2(x). If E is the cross-entropy loss, the weight can be integrated directly into the loss function, acting as optimization target (pseudo-label) for æ directly. In classical taxonomy for PLL [47]. IBS trains predictive models based on fixed weights assigned to the training instances, i.e., (2, 2) = {0, 1}*, while ABS sets uniform weights during training, i.e.
((x 2) 1/|S|.
3

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Definition 2.1 Mini-batch PL purification). Mini-bated bati- PL purification is process where for each mini-batch B C selected iteration t, the weights are updated such that the distinction among candidate labels' contributions increases over iterations:
We++ 1 (m; J, 5) = g (model's confidence for æ based on current and previous iterations),
with y being strictly increasing function that increases the weight for more likely candidate labels according to the model's confidence. The model's parameters 0, are updated by optimizing weighted loss over B:
8i+1 = 8 - m7 Ve Σ ((,))) (f((x; 8c), (, (1+1()))
-
The standard practice is initializing the weights uniformly w 1/|s] if E and un otherwise, and let f be initialized randomly. The model fo is then updated for at least one epoch to perform a preliminary training phase. Then in each mini- batc- of t-epoch, w(x) is computed where f is fixed, and then f is updated by the weighted objective where keeps fixed in backpropagation. An instantiation of mini-batch PL purification was first introduced by [25]. They use delayed mechanism, i.e., w(xx) is computed by the output of historical model f on æ, implicitly assuming that DNNs learn pattern first [2], and the delayed mechanism mitigates the accumulation of errors. Then, some methods replace the delayed mechanism with Match techniques estimate w, which may rely on either Siamese networks [4] applied to two or more inputs augmenttgtntttiionn match, i.c., DA), or co-teaching networks [16] where one network's s outputs serve targets for the other (dual-model match, i.., DM). Furthermore, some methods advocate DA+DM framework; for example, PiCO [34] involves mutual guidance of two heterogeneous classifiers, with one built top of supervised contrastive learning architecture [20]. In addition techniques borrowed from various communities have propelled PLL methods to top performance, such mixup [46] and data augmentation like cropping and flipping [28], which have become mainstream.
As shown in Table 1, prominent methods in recent years rely on the mini-batch PI. purification strategy and specific enhanced tools. However, our research reveals a significant disparity in the impact of these components, at least on current benchmarks. Mini-batch PL purification is sufficient to provide a reliable guarantee of performance, while the additional tools contribute relatively little. Although techniques like data augmentation enhance the performance by improving the model's s robustness to input variations, they primarily boost representation learning, but not benefits the disambiguition for PLL.
3 Understanding Minimal Algorithm Design Principles
In this section, we inverstigate four SOTA PLL methods that have consistently demonstrated top accuracy across various benchmark tasks. By methodically dissecting these methods and analyzing the components credited for their robustness against PLs, we distill the essential elements contributing to their success. We defer the experiments details to Appendix.
3.1 PLL with DA Match
Algorithm details. The key contribution of DPLL [38] lies in incorporating neighborhood consis- tency, technique adapted from semi-supervised learning, into PLL. This technique maximizes the similarity among several perturbed views of the same instance, thereby inducing smoothness in the structure of learned representations, referred to as augll-aagmenttiion match (DA Match).
Specifically, DA Match instantiates Eq. 1 by specifying the loss function as the KL divergence and estimating the weights by a weighted sum of outputs all augmentations A(ær):
R(x, f) - A(re) ((x) log f ((A(z)))
(4)
Σ (TTEE (z(a)) fi(a)) APol E S,
0(x 2)
(5)
otherwise.
S is updated in a uniformly (mini-batch PL purification). In addition, the learning objective of DPLL includes another loss function as
manner along with the model parameters and is initialized
((x, = - ies log(1 - [((A()))),
(6)
4

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where the vector subseript indicates the element is that position. It encourages the output of each non-candidate label to be zero.
Evaluation 1. Specifie implementations do not matter. First, we replace the two terms in learning objective with alternative approaches. Eq. 6 is conceptually equivalent to encouraging the sum of the outputs for the candidate labels to be close to one, i.e,
[xx - log E ies f(((z))).
Instead of using shared target for all views, we modifies the optimization target for each view separately based on the output of the other view:
R(x, f) = - (2)2(x)) log f(x1) ) + uh (2) log f(x2))
(8)
where σ1, 22 E A(xx), and
w2(1) (ar 2) - L f
E S,
otherwise.
We combine DA Match terms and two loss functions in pairs, respectively. As can be seen from Table 2, there was no significant difference between the results of these four combinations. This indicates that the specific implementation methods of DA Match, including the exact form of the loss function, is not critical.
Evaluation 2. Additional losses do not matter. We then split the combined learning objectives into two separate objectives to examine the difference the contribution these two components to learning. We found that Eq. 6 and Eq. 8 were comparable under the relatively simple settings, but Eq. outperformed Eq. 4 in challenging scenarios (CIFAR-IO0 100 and mini- ImageNet). Note that 6 is a traditionally considered ABS loss, and Eq. 8 implements mini-batch PL purification. It is commonly believed that ABS does not require identifying the true labels during training. leading to weer-parameterized DNNs memorizing all candidate labels [44], which results in poor performance. However, as discussed in Section 1, ABS can still achieve acceptable performance because the optimization process may induce differentiated outputs. We will elaborate on this in more detail in Section 3.4. Another noteworthy observation is that Eq. 8 not only did not lead to a decrease in accuracy compared the original DPLL, but even showed some improvement, which is likely because Eq. 8 can model neighborhood consistency better than Eq. 4.
So far, have extracted core unit from DPLL, which takes the form of Siamese networks [4]: weight-sharing network applicd on two (or more) inputs for comparing, and PLs prevent the model from collapsing, i.e., outputting constant for all inputs. We call Eq. 8 dual augmentations single model (DASM), as depicted in Figure 5. However, it remains to be seen whether the effectiveness of DASM is due to mini-batch PL purification neighborhood consistency.
Evaluation 3. Mini-batch PL purification does matter. We modify the learning strategy DASM by either altering the mini-batch PL purification strategy or removing the consistency component. We compare them in Table 2, where the "-H", "-S" or "-E" suffix means using the hard pseudo-labels, one-step iteration epoch-wiee wise iteration. Specifically, DASM-H uses hard labels optimization targets for Eq. 8:
(x2( = e', (0) = where arg max f(1) and j = arg max f(22),
(10)
where e denotes the i-th standard canonical vector, i.e., e {0, 13*,, TTe 1. DASM-S simulates one-step EM methods by training the model with uniform targets for the first 50 epochs, and then transforming PLL into supervised learning by using one-hot pseudo-labels (i.c., the argmax of the model's output for each instance at the 50th epoch) for the next 450 epochs. The results indicated that the performance of DASM-H and DASM-S was inferior to DASM. This can be attributed the models' inability to adjust learning targets at the appropriate time based on the underlying learned patterns: Since DNNs tend to fit easy patterns first and gradually memorize harder ones, a phenomenon known as memorization effects [2], DASM-H may remember unreliable information due to random initialization, and DASM-S may lead remember too much undesired memorization [15]. DASM-E shifts from a mini-batch- manner to an epoch-wise manner, performing pseudo-label estimation and model updates at the epoch level, which resulted in decreased accuracy. Compared to DASM-E, mini-batch manner benefits from using the up-to-date model for generating optimization objectives
5

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Table 2: Conceptual and empirical comparisons (%) of various simplifications of DPLL. v /xx indicates whether technique is used.
Mini-b. purif.
ABS
Data
FMNIST
CIFAR-100
mini-I.Net ins.-dep.
Methods
DA
loss
augment.
0.3
0.7
0.05
0.1
Eq. 4+6 DPLL
93.82
92.68
76.81
75.93
52.22
Eq. 4+7
V
/
93.80
92.44
79.35
78.85
53.40
Eq. 8+6
V
J
93.49
92.19
79.75
78.87
53.78
Eq. 8+7
93.57
92.20
79.53
78.85
54.09
Eq. 6
X
X
93.58
92.12
76.96
75.94
44,69
Eq. 8 DASM
X
93.89
92.85
79.70
79.62
54.71
DASM-H
X
93.86
92.37
78.25
33.22
34.59
DASM-S
X
93.28
90.75
78.65
76.22
36.71
XXXX
DASM-E
93.80
92.35
79.30
79.11
53,44
SASM
X
x
93.83
92.18
79.38
78.19
55,45
DASM w/o.aug
X
X
90.86
89.60
60.18
56.39
30.85
and also improves computational efficiency. In addition, we change the dual feedforwarding to single. The optimization target of an input is modified place according to its own output, which we term single augmentations single model (SASM). It was somewhat surprising that this method does not require additional components, performed remarkably well, implying DA may not be necessary.
Evaluation 4. Does data augmentation matter? Additionally, removing data augmentation from DASM, in DASM w/o.aug, causes decrease in accuracy expected. We will discuss its impact further in Section 3.3.
3.2 PLL with DA+DM Match
Algorithm details. PiCO [34] enhances representation learning by incorporating supervised con- trastive learning into PL.. It utilizes two heterogeneous classifiers sharing backbone (one linear and one cittrasttve-basede guiding each other to instantiate Eq. 1. PaPi [40] investigates PiCO and identifies limitations the contrastive learning module. Thus PaPi adopts more efficient approach inspired by the delayed mechanism in PRODEN, instantiating Eq. 1 without the need to maintain two separate models. Besides, PaPi also uses the zero-and- and-annmal--zeed outputs of historical models to guide a prototypical classifier that shares the same backbone with the linear classifier. Both methods feed forward different views the same input. We refer to such franework as dual-augmentation and dual-model match (DA+DM Match). CroSel [30] is the latest PLL method that, in addition to using the DM framework to generate optimization targets for each other, also selects samples with more accurate pseudo-labels for the other model to compute supervised loss.
Evaluation. At high level, PiCO draws inspiration from co-teaching [16]: instead of training a single classifier, it trains two classifiers simultaneously and lets them teach each other in every mini- batch. We simplify this idea by removing the contrastive-baset classifier and using two networks with the same architecture but different initialization, which is also CroSel without its sample selection module. We call such method dual augmentations dual models (DADM). Taking it step further, single augmentation dual models (SADM) removes one data augmentation, feeding both networks the same view of an instance within the same epoch. Conversely, if we cancel DADM from CroSel, the remaining implementation is co-teaching adapted for PLL (Coteaching in Tabel 4). For PaPi, we strip away the prototypical classifier, resulting in a streamlined version akin to PRODEN with added data augmentation (PRODEN+), to explore whether the specific instantiation of DM makes difference. Figure 5 illustrates their basic workflow.
Our results are shown in Table 4. Both DADM and SADM outperformed PiCO and were comparable with CroSel, and PRODEN+ generally matches the performance of PaPi. Deleting the implementation of mini-batch PL purification, whether by altering the iteration frequency or replacing soft pseudo-

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A 24
stines
Opech
Egosch
Opech
(a) Acc of pseudo-labels
(b) Test Acc
(a) Train Acc
(b) Validation Acc
Figure 2: Comparative results of different training setups of DASM on FMNIST with PLs. (a) shows the pseudo-label accuracy,
Figure 3: Warm up different iterations on FM- NIST with PLs. Red lines mean terminating the warm-up phase a local maximum in val- idation accuracy.
while (b) presents the test accuracy.
labels with hard pseudo-labels, consistently leads decline in performance. The observations reaffirm that mini-batch PL purification is essential for achieving top performance. By comparing the performance of the DM framework with the SM framework, we discover that the DM framework's edge often comes from the diverse capabilities of the two networks, which help handle the noise introduced by PLs. On the other hand, the DA methods without any special design (DASM, DADM, PRODEN+) showed suboptimal performance than the SA methods, perhaps hinting at the importance of exploring different augmentation methods [31] to discover appropriate choices for class-invariant patterns, remaining for future research.
3.3 Does Data Augmentation Help Identification Better?
Our findings indicate that mini-batch PL purification and data augmentation pivotal for PLL, achieving competitive performance when both techniques are implemented. Data augmentation is a well-established regularization tool, enhancing model robustness to input variations. In the following, we explore whether its role in PLL extends beyond this conventional purpose, specifically whether it facilitates the crucial task of identifying the label among candidate labels. If data augmentation aids true-label identification, we would expect that augmented examples generate more accurate pseudo-labels, then enhancing the performance. Specifically, we experiment with DASM by setting one view as augmented and the other as non-augmented. We also use different training setups: (i) using
pseudo-labels generated from original æ to supervise augmented æ, and (ii) the reverse, using augmented æ to supervise original æ. The results are presented in Figure 2.
Switching from dual paths single path while retaining supervised learning on augmented instances with pseudo-label, from the original instances showed little change in accuracy. However, when using pseudo-labels from augmented instance supervise original one, performance drops significantly. This suggests that data augmentation alone insufficient to preserve the mutual information between examples and their true labels, as augmented views may discard task-relevant information, thereby degrading performance. Following this reasoning, our results suggest that data augmentation indirectly benefits the classifiers built upon representation learning rather than aiding in label disambiguation. Therefore, it should NOT be considered a design principle for PLL.
3.4 PLL through Pseudo-Label Manipulation vo.Loss Minimization
Mainstream methods mentioned above conduct mini-batch PL purification primarily by directly manipulating the optimization targets of candidate labels. However, as analyzed in Section I and observed in Eq. 6 of Table 2, using stochastic algorithms to minimize loss functions, even ABS loss funtions that traditionally considered to "treat all candidate labels equally", result in progressive effect of pseudo-labels. To our knowledge, no existing research has explored the relationship between pseudo-label manipulation and loss minimization. Our findings raise the question: how do these two methods compare in terms of their effectiveness and mechanisms in the context of PL identification?
also implicitly
We investigate several representative PLL losses, which are traditionally thought as ABS:
Modified negative log likelihood loss (Eq. 6) [38]: fneg (2, f) Eves log(1 - f((x));
APL loss [24]: (APL(E, f) = [TT Exe (() f), with GCE loss [49] as the component غ
7

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Maximum likelihood loss [19]: (mase((F.f - log Eies f((x))
Denote the scores outputted by the last layer before sof toft 2, i.e. 1/ (=)
f(x) where
/= (wi-l o ((a) o...o ). Let us look at the gradients of Eneg and AXPL
Hlneg
-kk Eigs EJey
k E
(11)
Ozk
[u(1 - E Eigs.itk Ejey
otherwise,
ØLAPL.
TST (frs Eies, St f2(1 (1(1-fo) fi)) [ST fk Ey
& E otherwise,
(12)
Ozk
where q E (0, 1] is tunable parameter of GCE. From gradient perspective, we observe that while the implicit optimization targets for all candidate labels are the same for each loss function, their optimization speeds differ. Specifically, the gradients of the candidate labels are consistently negative until one candidate label accumulates promote the output of each candidate label to converge to 1. As a result, the candidate labels compete for dominance. A label with a higher output probability experiences a larger gradient and thus becomes the winner. According to the memorization effects of DNNs, such a label is more likely to be the true label receiving a larger gradient at the beginning, which explains why the labels become distinguishable with these losses. However, since the optimization targets for all candidate labels remain the same, minimizing these two losses does not align with our definition mini-batch PL purification where the optimization targets are expected to diverge progressively.
the probabilities, which implies that both loss functions
Then we focus on the third loss lmaxi. We examine its gradients as
d6
[ Sn fi
A: E S,
Lieget
(13)
8zk
otherwise.
It is crucial to recognize two key points: (i) The philosophy of maxi is to ensure that the output of all candidate labels sums 1, which is exactly the same as that of Eeg. which requires the output of all non-candidates to sum to O. However, their gradients are completely different, indicating that they lead to different optimal empirical solutions even with identical initialization and stochastic optimizer. (ii) When learning with maxi, the implicit optimization target of an instance is the zero zero-and -ad--ndd-onn aad-normalized outputs of current model on this instance itself, exhibiting consistent behavior with pseudo-tabel manipulation in SASM.
Lemma 3.1. Suppose using the same stochastic oplimizer, then performing SASM is mathematically equivalent to minimizing Emaxi.
Empirical results in Table 5 also verified the theoretical findings. However, pseudo-label manipulation offers greater flexibility it allows for more arbitrary modifications the optimization targets, as DASM, SADM, etc. have done, and additional steps over generating soft pseudo-labely such as sharpening [29], but the targets of loss functions are fixed.
Now, our empirical investigations have firmly established the necessity of mini-batch PL purification along with using supervision. Supervision can be used in two ways: directly within the loss function as it in supervised learning, or to manipulate pseudo-labels on-the-fly. We identify SASM is the minimal working algorithm. It achieved superior or at least comparable performance compared with SOTA PLL methods in most cases, while not requiring multiple forward propagations or additional components.
3.5 Probing the Implementation of Mini-Batch PL Purification
Here, we examine the implementation of mini-batch PL purification, raising at least two questions: QI. Does different initialization methods impact the performance? Q2. Why does model confidence in PLs is effective to disambiguation?
In early training stages, our primary concern is if initialization methods might cause certain candidate labels to receive significantly higher confidence. Consider a neural network where weights are independently drawn from standard normal distribution with zero mean and variance o² (as in normal initialization, Xavier initialization [1], He initialization [17]) For an instance æ, the output of neuron after a ReLU activation is given by = max(0, wx + b), where represents the
8

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weight vector and b is small constant bias. By the Central Limit Theorem, the mean of the weights
= 1/n -i= w; for sufficiently large number of neurons n approaches normal distribution with mean zero and variance 82 /n. Applying Chebyshev's inequality, we have P([Ø) 2 a) S 80/ /(aa). As n + 00, w is close to zero with high probability. Then the oulput for each neuron z will be close to b. By a similar reasoning, this result generalizes to deeper layers, suggesting that the initial outputs across classes approximate a uniform distribution regardless of the number of layers.
Lemma 3.2. For a neural network initialized with weights w drawn from a normal distribution (O008%) 8²), the initial outputs across classes approximate uniform distribution as the number of neurons +
Then we explain why using model's output as a proxy for the probability that a candidate label is the true label works. This practice of using the high-confidence label as the true label, introduced to PLL by [25], has long been foundational in noisy-label learning (e.g., [16, 23)). Its success in PL. hinges on a key assumption: the true label has higher probability of appearing among the candidate labels than any incorrect label. In fact, the experimental setups employed across PLL methods impose a further restriction on this assumption, that is, p'y E S|z, S) = p( E S| > 1, Vi + y. This setup implies that, within any sufficiently small neighborhood in the data space, the true label will dominate. Consequently, when stochastic gradient- optimizers are used, the true label tends to contribute more frequently to the objective function, making it more likely to be learned first.
4
Improving Mini-Batch PL Purification
4.1 Motivation
The standard practice involves initiating the process with uniform pseudo-labels for one epoch to bootstrap the classifier's basic capabilities. Our first observation is that the effect of warming up for one epoch is nearly indistinguishable from not warming up at all, prompting further investigation into the actual efficacy of the warm-up phase. Suppose a neural network is initialized with weights drawn from a Gaussian distribution with mean zero and a sufficiently small variance. If the inputs are normalized, the pre-activation values across a neural network tend to be small and centered around zero. When these values are input to a softmax function, the resulting distribution across classes tends to uniformity.
Our second observation is that a prolonged warm-up using uniform pseudo-labela often leads to the network overfitting to candidate labels, as illustrated in Figure 3, evident around 50 epochs with a decline in validation accuracy. While overfitting to the training data becomes apparent about 120 epochs, marked by a drop in training accuracy after previously reaching peak.
We simply terminate the warm-up phase at a local maximum in validation accuracy, about 5 epoch, preventing excessive memorization while preserving more information beneficial for generalization. Then the results showed a little improvement. Several approaches [34, 24] have used multiple epochs for warm-up and treat the number of warm-up epochs as hyperparameter. However, due to the varying difficulty levels across samples, using a uniform duration for the warm-up phase could result in performance disparities among different subgroups within the dataset. This suggests the need for an adaptive warm-up strategy.
4.2 StreamPurify: An Instance- Warm-Up Strategy
Building upon the analysis and our established design principles, we propose StreamPurify, a novel instance-dependent warm-up strategy, which fine-tunes the entry into the mini-batch PL purification phase based on each instance's 's readiness. During the initial training phase, it selectively channels instances that have higher confidence the accuracy of their pseudo-labels into the PL purification phase, while others continue training with uniform targets until they meet the readiness criteria. This filtered progression helps prevent DNNs from harmfully memorizing incorrect pseudo-labes and mitigate the accumulation of errors from inadequately learned samples. Differing from sample selection techniques used in noisy-label learning [36] that reevaluated samples in every iteration, our filter approach is conducted without replacement. Once the training samples are transitioned to the purification phase, they do not revert to uniform targets, ensuring that the strategy remains in line with mini-batch PL purification.

---

Table 3: Classification accuracy (%) improvement of PLL methods with StreamPurify.
FMNIST
CIFAR-10
CIFAR-100
mini-I.Net
Methods
0.3
0.7
0.3
0.7
0.05
0.1
ins.-dep.
SASM
0.15
0.09
0.02
0.34
0.30
0.21
1.82
SADM
0.05
0.22
0.10
0.18
0.19
0.58
0.99
DADM
0.03
0.02
0.03
0.46
0.66
0.51
0.72
DASM
0.36
0.26
0.13
0.29
0.22
0,42
1.41
DPLL
0.11
0.00
0.06
0.40
0.85
0.47
0.95
PICO
0.29
0.43
0.60
0.49
0.35
0.62
1.03
PaPi
0.17
0.36
0.30
0.20
0.68
0.47
0.89
StreamPurify is compatible to existing PL.. methods and can absorb various sample selection criteria, such as small-loss trick. We adopt the sample selection method from CroSel [30] that chooses the samples with stable and high confidence as a filter criterion within StreamPurify. and combine with the mini-batch PL purification approaches discussed in our paper. Empirical evaluations indicate that methods augmented with StreamPurify generally exceed the performance of their conventional counterparts, validating the effectiveness of StreamPurify, especially in complicated learning scenarios. This substantiates the robustness and adaptability of instance- deeeede-deeendeen warm-up. suggesting it as a promising direction for future improvements in PLL.
5 Discussion and Future Work
We have systematically delineated the core components underlying successful PL. methods, centering our insights around the pivotal effect of mini-bater PL purification. We have proposed StreamPurify, an enhanced mini-batch PL. purification strategy that tailors the learning path for each sample based on its state of readiness. We reaffirm that strictly categorizing PLL methods oversimplify the dynamics of how these methods operate in practice. In the future, we wish to explore advanced PLL approaches guided by the minimal algorithm design principles. We also wish to extend the applicability and understanding of PL. methods to domains beyond vision tasks.
IBS or ABS may
Acknowledgements
This research was supported by the National Science Foundation of China (62406066, 62206050, 62125602, 62176055, 62076063), Jiangsu Province Science Foundation for Youths (BK2024122) BK20210220), China Postdoctoral Science Foundation (202 1700002)), Young Elite Scientists Sponsorship Program of Jiangsu Association for Science and Technology (TJ-2022-078), the Aus- tralian Research Council Discovery Early Career Research Award (DE230101116), the Fundamental Research Funds for the Central Universities (2242024k300335 the Big Data Computing Center of Southeast University, JST CREST Grant Number JPMJCR 18A2 and grant from Apple, Inc. Any views, opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and should not be interpreted as reflecting the views, policies or position, either expressed implied, of Apple Inc.
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Appendix
A Experiments Details
As benchmarking on partially labeled vision datasets has become standard practice in evaluating deep PLL methods, we conduct experiments on FMNIST [41], CIFAR- 100 [21] and mini-ImageNett [32]. We generated PLs by the Flipping strategy [24] for FMNIST, CIFAR- 10 and CIFAR-100. Each label is added into PL with a flipping probability ni. = p(i E Sly) independently and features are untouched: p(s|2, y) M Ihes nf 1l (1 n7.) where M 1/(1 b n²") We assumed {0.05, 0.1] on CIFAR-100 100. For Imag-emteeet and ablation experiments (Figure 1, 2, 4), we simulated the real scenario by setting the flipping probability for each incorrect label individually for each instance. We first trained classifier with clean labels, and then for each instance, set the confidence prediction of the classifier as the flipping probability [42].
T/"" = 7, o y and mi = 1, and set 1) = {0.3, 0.7) on FMNIST and CIFAR-10,
Our explorations used three backbones: 5-layer LeNet [22] on FMNIST, 18-layer ResNet [18] on CIFAR-10 10 and CIFAR-100, and 34-layer ResNet [18] on mini-ImageNet. All the methods were trained for 500 epochs with standard SGD optimizer [9] with momentum of 0.9 and the batch size was 256 (128 for mini-ImageNet). We left out 10% of the corrupted training samples as a validation set, and searched the initial learning rate from {0.1, 0.07, 0.05, 0.03} with cosine learning rate scheduling. We conducted 3 trials for each experiment, and recorded the mean test accuracy in percentage. There were two kinds of random augmentations involved. "Weak" augmentation was random horizontal flips and crops [3]. For "strong" augmentation on FMNIST and CIFAR- 10, we added Cutout [8] the weak augmentation, and CIFAR- 100 and mini-ImageNNet we additional leveraged Augment [7]. We denote the augmentation by A(-), with method clear from context. The implementation was based on PyTorcc [26] and experiments were carried out with GeForce RTX 4090 D.
Notably, we focused on the core components of the SOTA PLL methods mentioned in this paper, rather than strictly adhering to the settings detailed their original implementations. This approach was taken to ensure fair and meaningful comparisons. For instance, we did not include techniques such as mixup in PaPi or the triple augmentation used in DPLL. As a result, the reported performance metrics in our paper might be slightly lower than those presented in the original publications.
B Experimental Results
In Figure (c-d), CLPL is traditionally considered ABS loss from [6]. Figure 4 illustrates the dynamic changes in the same method under different hyperparameters and optimization methods. One can expect that with more extreme hyperparameters or optimization methods, the approach may degrade to one-step EM or persist with nearly uniform optimization targets. This indicates that method categorization must be assessed on a case-by-case basis post hoc. Figure 5 is the workflow of several key methods proposed in the paper. Table provides conceptual and empirical comparisons of various simplifications of PiCO, PaPi and CroSel. Consistent with Table 2, the results reiterate that mini-batch PL purification is pivotal to achieve top performance. Table 5 presents the results of minimizing three loss functions. It is evident that maxi yield similar results with SASM, and owing to the mini-batch PL purification, and due to the implementation of mini-batch PL purification, the accuracy is higher than the other two losses.
14

---

Table Conceptual and empirical comparisons (%) various simplifications of PiCO, PaPi and
CroSel.
Mini-b. purif.
Data
FMNIST
CIFAR- 100
mini-I.Net
Methods
DA
DM
augment.
0.3
0.7
0.05
0.1
ins.-dep.
PICO
93.40
91.64
76.11
75.65
48.36
DADM
V
93.59
92.40
80.28
79.13
53.69
DADM-H
X
V
V
92.60
85.13
79.99
35.72
36.30
DADM-S
X
V
V
92.12
87.81
78.16
74.66
36.42
DADM-E
X
V
V
93.66
92.22
80.08
78.49
52.18
SADM
V
X
94.02
92.36
80.11
79.65
54.64
SADM-E
X
93.72
92.51
89.85
78.66
53.08
PaPi
V
93.54
91.54
80.10
79.62
57.10
PRODEN+
/
93.70
92.52
79.85
79.51
52.39
PRODEN
x
91.61
90.45
62.47
59.10
29.21
CroSel
93.84
92.31
80.40
80.06
53.58
Coteaching
93.86
92.37
79.25
33.22
41.34
Table 5: Average training test accuracy (%) learning with three loss functions.
FMNIST
CIFAR-100
mini-I.Net
0.3
0.7
0.05
0.1
ins.-
training
test
training
test
training
test
training
test
training
test
lueg
94.98
92.28
92.05
91.29
89.66
74.91
86.35
74.20
30.40
28.04
(APL
93.53
93.01
88.10
89.09
87.15
72.68
78.31
68.10
45.92
43.01
Imaxi
95.39
93.77
93.01
92.17
93.45
78.91
90.56
78.20
55.39
54.72
11:10c
1.66
50
J/6
Spath
Figure 4: Training accuracy and confidence margin of predicted pseudo- for SASM with different learning rate or optimizer on FMNIST with Pl.s.
lass
sytn
Jone
fax
Modelf
Modelly
Model
Modelf,
Model
Model
Modal (1-11)
Modde
DASM
SADM
DADM
PRODEN+
Figure 5: Illustrations four effective units of SOTA PLL methods. We omit a symmetric loss from the other path, except PRODEN+ which can only compute mee-path losses. "//" means stop gradient.
15

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Reviews:
[{"review_id": "1dYO6g2Hvu", "reviewer": "Reviewer_PELT", "summary": "This paper simplifies the process of PLL by distilling critical success factors for high performance into a minimal algorithmic design through extensive empirical analysis. This work is a step forward in making PLL methods more accessible and efficient, offering substantial insights into traditional complex algorithms.", "questions": "1. The content of the paper is overly dense and requires further clarification, making it somewhat challenging to read and understand.\n\n2. In the proposed mini-batch PL purification, how sensitive is the performance to different batch sizes, and are there optimal batch size recommendations based on your experiments?", "limitations": "N/A", "rating": 7, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The paper is highly motivated, offering impressive reflections on the categorization and algorithm design principles in the PLL community. The paper's main contribution lies in enhancing understanding, and a simple improvement StreamPurify driven by this understanding, is commendable.", "weaknesses": "1. There are several simplified approaches that achieve comparable performance, which makes the conclusions less clear.\n\n2. While the design principles ensure comparable performance, it remains unclear what implications this has for future algorithms, for example, how can stronger components be integrated with these design principles?\n\n3. The effectiveness of the proposed mini-batch PL purification is supported only by some empirical results, and the significance of this change should be discussed in more detail.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We would like to thank the reviewer for taking the time to review our work and the positive comments regarding its significance. Below are our responses to the comments in Weaknesses and Questions.\n\n> C1. Q1. There are several simplified approaches achieve comparable performance, which makes the conclusions less clear. Q2. It remains unclear what implications this has for future algorithms, for example, how can stronger components be integrated with these design principles?\n\nOur main contributions are to abstract the consistent philosophy underlying SOTA PLL methods into minimal algorithm design principles, thus avoiding future algorithm designs based on trial and error. **Takeaway**: Designing well-performed PLL methods should purify PLs in a mini-batch-wise manner. \n\nThe simplified methods mainly **serve as demos to illustrate our findings**. Thank you for your insight that they can further serve as backbones for incorporating stronger components and provide important prototype for future exploration into PLL. The intuitive idea is that stronger components are expected to achieve better performance, and we believe it is also necessary to consider the coupling effects between different components. Consider SASM and SADM and combine them with consistency regularization. We conduct experiments on FMNIST with instance-independent and instance-dependent PLs. The results of test accuracy are as follows:\n\n| method\\flippingprobability | 0.3 | 0.7 | ins.-dep. |\n| --- | --- | --- | --- | \n| SASM | 93.83 | 92.18 | 90.64 |\n| + consistency regularization | 93.89 | **92.85** |  91.00 |\n| SADM | **94.02** | 92.36 | 90.65 |\n| + consistency regularization | 93.59 | 92.40 | **91.04** |\n\nWe observe that directly combining a generally useful method does not necessarily boost performance. The results are related to the generation process and instantiations details (e.g. what augmentation involved). The specific algorithm design is beyond the scope of this paper. We leave the exploration of different instantiations of design principles and their combinations with various components to future work.\n\n> C2. The effectiveness of the proposed mini-batch PL purification is supported only by some empirical results, and the significance of this change should be discussed in more detail. Q2. In the proposed mini-batch PL purification, how sensitive is the performance to different batch sizes, and are there optimal batch size recommendations based on your experiments?\n\nQ1. Thank you for the constructive comments. Mini-batch PL purification was first proposed in [1], and widely adopted in subsequent PLL methods. The key difference from previous PLL methods lies in the frequency of estimating pseudo-labels and updating the model iterations. It is worth mentioning that mini-batch-wise update has been used in many other fields such as noisy-label learning [2], distribution shift [3], etc. We will give a detailed analysis of its advantages, and the relevant discussions have been in [1,2]. Traditional EM-based PLL methods update the model based on the current pseudo-labels until convergence. To avoid overfitting to pseudo-labels, epoch-wise PL purification uses pseudo-labels for model updates in the whole next epoch. The confirmation bias caused by inaccurate pseudo-labels accumulates throughout the epoch. In contrast, batch-wise PL purification updates the model right after estimating pseudo-labels of each batch. The updated model can better estimate pseudo-labels of the next batch, alleviating the confirmation bias batch by batch.\n\nQ2. We conduct a sensitivity analysis on the batch size on FMNIST with instance-dependent PLs. The test accuracy are as follows:\n\n| method\\batchsize | 32 | 64 | 128 | 256 | 512 | #dataset |\n| --- | --- | --- | --- | --- | --- | --- |\n|SASM | 89.85 | 89.85 | 90.29 | **90.64** | 89.75 | 80.87 | \n|SADM | 89.86 | 89.91 | 90.14 | **90.65** | 89.56 | 78.02 |\n|DASM | 89.93 | 90.51 | 90.57 | **91.00** | 90.35 | 80.80 |\n|DADM | 90.16 | 90.01 | 90.46 | **91.04** | 89.99 | 78.53 |\n|PRODEN+ | 89.09 | 89.24 | **90.01** | 89.91 | 89.76 | 79.54 |\n\nWe can observe that very coarse execution granularity (large batch size) might result in the model trapped in local optimum, while very fine granularity (small batch size) might result in unstable estimation of the true labels, leading to degraded performance. We recommend treating batch size as a hyperparameter that requires tuning for optimal performance. The batch sizes used in our experiments are shown in Appendix A, and will add the analysis in the revised manuscript.\n\n[1] Progressive Identification of True Labels for Partial-Label Learning. ICML’20\n\n[2] SemiNLL: A Framework of Noisy-Label Learning by Semi-Supervised Learning. TMLR\n\n[3] Rethinking Importance Weighting for Deep Learning under Distribution Shift. NeurIPS’21", "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": "OAMY2uZ5JC", "reviewer": "Reviewer_ygK7", "summary": "The paper offers a comprehensive empirical analysis to understand what makes partial-label learning (PLL) methods effective, focusing on the transition from uniform to one-hot pseudo-labels in mini-batch PL purification. It analyzes the complexity and diversity of SOTA PLL methods, proposing simplified algorithm design principles that maintain high performance with less complexity. It introduces a minimal working algorithm that adheres to the principles and shows its effectiveness.", "questions": "See above", "limitations": "N/A", "rating": 7, "confidence": 5, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "The authors revisit PLL and provide a detailed empirical analysis that addresses its fundamental question—what contributes to the effectiveness of PLL methods. It might not only clarify the field but also guide future research directions. Writing is good quality.", "weaknesses": "The definition and implementation details of mini-batch PL purification are not sufficiently clear, particularly the impact of batch size on the effectiveness. It is unclear why this technique is the most effective points.\n\nThe limitations of the proposed principles do not be discussed, particularly in terms of the practical applicability of the introduced algorithms like SASM, SADM, DASM, and DADM. Future guidelines on how to effectively utilize these methods would be beneficial.\n\nTheoretical results would provide a stronger validation of the proposed principles.\n\nComparisons on real-world datasets would be helpful.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We would like to thank the reviewer for taking the time to review our work and the positive comments regarding its significance and writing quality. Below are our responses to the comments in Weaknesses and Questions.\n\n> C1. The definition and implementation details of mini-batch PL purification are not sufficiently clear, particularly the impact of batch size on the effectiveness. It is unclear why this technique is the most effective points.\n\nThank you for raising this point. We give a detailed analysis of the advantages mini-batch PL purification and also conduct a sensitivity analysis on the batch size. Please kindly refer to our response to Comment 2 of Reviewer PELT. \n\n> C2. The limitations of the proposed principles do not be discussed, particularly in terms of the practical applicability of the introduced algorithms like SASM, SADM, DASM, and DADM. Future guidelines on how to effectively utilize these methods would be beneficial.\n\nThank you for the comment. Firstly, we need to clarify that all the proposed methods in this paper serve more as demos to illustrate our findings. \n\n**Practical applicability** We compare these methods on different PL datasets. Specifically, we set the instance-independent flipping probability $\\eta={0.3,0.7,0.9}$, class-dependent flipping probability $\\eta={0.6}$, and also generate the instance-dependent PLs on FMNIST. The results of test accuracy are as follows:\n\n| method\\PLgeneration | ins.-indep0.3| ins.-indep0.7| ins.-indep0.9| class-dep0.6 | ins.-dep. |\t\n| --- | --- | --- | --- | --- |--- |\n| SASM\t| 93.83 | 92.18 | 90.12 | 94.12 | 90.64 |\n| SADM\t| **94.02** | 92.36 | 90.10 | 94.10 | 90.65 |\n| DASM\t| 93.89 | **92.85** | **90.97** | 94.15 | 91.00 |\n| DADM | 93.59 | 92.40 | 90.54 | **94.23** | **91.04** |\n| PRODEN+| 93.70 | 92.52 | 88.27 | 94.09 | 89.75 |\n\nWe can observe that different methods exhibit variations in performance under different scenarios, particularly the versions with multiple augmentations. It is important to note that we did not delve into many tuning details because outperforming SOTA methods is not our objective. Further, the simplified methods can also serve as backbones for incorporating stronger components and provide important prototype for future exploration into PLL. An intuitive idea is that stronger components are expected to achieve better performance, and we believe it is also necessary to consider the coupling effects between different components. The instantiation details are not within the scope of this paper and we leave the explorations to future work.\n\n**Limitations** As mentioned in our paper, using simulated PLL versions of vision datasets is currently the standard practice for evaluating PLL methods. Consequently, our work follows this established approach. The explorations on various types of real-world datasets may be a critical direction for future research in the PLL field. \n\n> C3. Theoretical results would provide a stronger validation of the proposed principles.\n\nThank you for your insightful comments. Since our goal is understanding effectiveness of SOTA PLL methods, which themselves always lack a solid mathematical foundation, extracting commonalities from these methods requires a high degree of abstraction **from a philosophical and conceptual perspective**, even necessitating the omission of detailed methodological and algorithmic specifics. Therefore, establishing a solid mathematical foundation becomes nearly impossible with the current mathematical tools. Additionally, it's important to note that the performance and runtime of mini-batch PL purification depend on certain hyperparameters, such as batch size. This dependency further reduces the applicability of a mathematical characterization.\n\n> C4. Comparisons on real-world datasets would be helpful.\n\nThanks for the valuable suggestion. Since these datasets are in tabular form, comparing methods should be compatible with scenarios that do not involve data augmentation. All the methods use MLP-3 and batch size is 256. IPAL [1] is a most advanced method without mini-batch PL purification. The results of test accuracy are as follow. The results on real-world datasets support our conclusion.\n\n| method\\dataset | Lost | BirdSong | MSRCv2 | Soccer Player | Yahoo! News |\n| --- | --- | --- | --- | --- |--- | \n| SASM | 69.84 | 69.38 | 53.84 | **54.55** | 64.99 |\n| SADM | 69.38 | **70.32** | **57.29** | 54.25 | 65.04 |\n| PRODEN | **73.60** | 70.12 | 56.60 | 54.33 | **67.23**|\n| IPAL | 65.75 | 70.30 | 53.47 | 53.36 | 65.55 |\n\n[1] Solving the Partial Label Learning Problem: An Instance-Based Approach. IJCAI’15", "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": "xP5tnAUMlX", "reviewer": "Reviewer_TEwD", "summary": "The paper presents a comprehensive empirical analysis of various Partial-Label Learning (PLL) methods. The authors identify that mini-batch Partial-Label (PL) purification is a key component for achieving top performance in PLL, as it progressively transitions from uniform to one-hot pseudo-labels. The study also introduces a minimal working algorithm that is simple yet effective, emphasizing the importance of mini-batch PL purification and suggesting improvements to enhance PLL methods​", "questions": "Please refer to the weaknesses section.", "limitations": "Yes, the authors provided the discussion of the limitations.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The paper provides a detailed analysis and summary of the development in the PLL field and the core contributions of various state-of-the-art methods. I believe this is highly insightful and educational for future work.\n\n2. The proposed StreamPurify is simple yet effective, achieving improvements over previous methods across different benchmarks.\n\n3. The overall writing of the paper is very coherent and logical, with a clear analysis of the field's development and issues.", "weaknesses": "1. The paper attempts to extract commonalities from numerous methods to identify the most critical elements for PLL. The authors introduce a descriptive concept/definition called Mini-batch PL purification to summarize the label disambiguation process. However, this definition is limited to a textual description and does not effectively use mathematical language to depict it. For example, I think entropy or relative entropy (or their variants) could be a worthwhile choice to describe the label disambiguation process. When model prediction confidence is evenly distributed among multiple label candidates, the entropy of the label confidence distribution is high. However, when a winner label emerges, taking most of the prediction confidence, the entropy decreases. [1] has already analyzed and explored this from the perspective of entropy. In summary, failing to systematically and scientifically construct a mathematical definition of Mini-batch PL purification is the main drawback of this paper.\n\n2. On the other hand, I believe many PLL works have realized that the key to label disambiguation is the process that is highly related to continuously increasing the max model prediction confidence. However, the main question is, during this process, how can we ensure that the model's high-confidence label is indeed the true label?\n\n3. The authors provide another insight, which is that a label with high confidence tends to receive a larger gradient, further enhancing its advantage, i.e., the winner-takes-all phenomenon [2]. So, during model initialization, if uniform labels are used for warm-up training, wouldn't the label confidence distribution of a data instance be heavily influenced by the initial parameters? If some labels happen to have higher confidence at initialization, wouldn't their advantage continue to grow?\n\n[1] Candidate-aware Selective Disambiguation Based On Normalized Entropy for Instance-dependent Partial-label Learning (ICCV 2023)\n\n[2] Towards Unbiased Exploration in Partial Label Learning", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We would like to thank the reviewer for taking the time to review our work and the positive comments regarding its significance and writing quality. Below are our responses to the comments in Weaknesses and Questions. \n\n> C1. The authors introduce a descriptive concept/definition called Mini-batch PL purification to summarize the label disambiguation process … failing to systematically and scientifically construct a mathematical definition of Mini-batch PL purification is the main drawback of this paper.\n\nThank you for your insightful comments! Since our contributions center on understanding existing SOTA PLL methods, which themselves always lack a solid mathematical foundation, extracting commonalities from these methods requires a high degree of abstraction **from a philosophical and conceptual perspective**, even necessitating the omission of detailed methodological and algorithmic specifics. Therefore, establishing a solid mathematical foundation becomes nearly impossible. Additionally, it's important to note that the performance and runtime of mini-batch PL purification depend on certain hyperparameters, such as batch size. This dependency further reduces the applicability of a mathematical characterization.\n\nThank you for your suggestion regarding entropy. As an alternative method to the widely used loss value [1], entropy is a heuristic technique for estimating the quality of pseudo-labels. To our knowledge, neither entropy nor loss allows for a strict mathematical definition of their mapping to label quality.\n\n> C2. On the other hand, I believe … high-confidence label is indeed the true label?  & The authors provide another insight … wouldn't their advantage continue to grow?\n\nThank you for your insights! These are very good questions which are **critical issues in the PLL research area**, and all previous PLL works ought to have answered but often have not. First, we must clarify that although these issues are indeed foundational, they **serve as prerequisites rather than the main focus** of our paper. However, we appreciate the opportunity to humbly offer analysis on these concerns below:\n\n> C2Q1. I believe many PLL works have realized that the key to label disambiguation is the process that is highly related to continuously increasing the max model prediction confidence … how can we ensure that the model's high-confidence label is indeed the true label?\n\nWe agree that the key to label disambiguation is continuously increasing the max confidence. This very process underscores the fact: we *cannot guarantee* that high-confidence label is indeed the true label, hence a progressive transition is essential. \n\nThen we would like to discuss why using the high-confidence label as the true label often works. This idea was first introduced by PRODEN [3] to the PLL community, and it has been extensively used in the noisy-label learning field (e.g. [1,4]). Its applicability in PLL due to the key assumption that the probability of a true label to be the candidate label is dominant. In fact, in the experimental setup of all PLL methods, it is assumed that $p(y \\in S|x,S)=1, p(i \\in S|x,S)<1, \\forall i\\neq y$. This implies that within any geometric neighborhood in the data space, the true label is dominant. Informally speaking, when stochastic gradient optimization is used, the true label contributes more frequent to the objective, making it more likely to be learned first. Then the PL purification process reinforces this knowledge. For more analysis related to this topic, we recommend reading [5].\n\n> C2Q2. The authors provide another insight, which is that a label with high confidence tends to receive a larger gradient, further enhancing its advantage, i.e., the winner-takes-all phenomenon [2].\n\nWe must clarify that we *have not claimed* that “a label with high confidence tends to receive a larger gradient”. This statement originates from [2]. With all due respect, we disagree with this statement. In fact, the opposite is typically true, a property determined by the link function and the proper loss [6]. Higher confidence corresponds to lower loss and consequently smaller gradients.\n\n> C2Q3. If uniform labels are used for warm-up training, wouldn't the label confidence distribution of a data instance be heavily influenced by the initial parameters? \n\nThank you for asking! Actually, label confidence distribution *will not* be heavily influenced by the initial parameters. Mathematically speaking, given any neural network, the parameters $w$ are typically initialized using a standard random normal distribution. According to the Chebyshev inequality and the Central Limit Theorem, we have: $P(|\\bar{w}|≥a)≤\\frac{\\sigma^2}{na^2}$. When the number of neurons $n$ is sufficiently large, the sampled values of $w$ are very close to zero. Consequently, the output for each dimension $z=\\max(0,wx+b)$ will be close to a small constant $b$. This means that during the initialization phase, no labels will receive significantly higher confidence. We conduct a toy experiment to demonstrate this point. We initialize different sizes of MLPs using various initialization methods and record their outputs for FMNIST after softmax (without training), specifically the margin between the highest and lowest outputs:\n\n| network\\initialization | normal | Xavier | He |\n| --- | --- | --- | --- |\n| mlp-3 | 2.4e-3 | 0.03 | 0.05 |\n| mlp-5 | 4.9e-5 | 0.004 | 7.9e-3 |\n| mlp-10 | 2.4e-5 | 2.4e-5 | 2.0e-4 |\n\nWe can observe the initial output distribution closely approximates a uniform distribution. Moreover, by using uniform targets to update for at least one epoch, we ensure that the model acquires a certain level of discriminative capability before relying on its outputs. Thank you for raising this point, we will add the discussion in the revised version.", "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": "OXH9fD9mlq", "reviewer": "Reviewer_RRwY", "summary": "This paper presents an interesting survey of current popular PLL methods. The survey examines various aspects such as training techniques, optimization processes, and loss functions to identify the key factors that make PLL methods effective. Ultimately, the authors attribute the main reason for PLL's success to the mini-batch PL purification, which aligns with our intuition. Based on this finding, the authors propose an instance-dependent warm-up strategy StreamPurify, pointing the way for future research in PLL.", "questions": "1. The biggest challenge in PLL is considered to be the elimination of label ambiguity, specifically identifying the true label from candidate labels. This seems to be strongly correlated with mini-batch PL purification. Would observing label changes during training, as done in CroSel, potentially be a better way to identify the factors that make PLL methods effective?\n2. For IBS and some compromise methods, is it true that once the model easily selects a label, it is less likely to change? Is this related to training settings such as the optimization method?\n3. Can the expansion of the sample space brought by data augmentation be considered as helping contrastive methods to disambiguate labels, even though experiments suggest that data augmentation is not a key factor?\n4. The focus of PLL work is on classification tasks. Are the observations in this paper still valid for regression tasks that have emerged recently?", "limitations": "N/A.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The analysis of the effectiveness of PLL methods is simple and clear.\n2. The analysis from various perspectives is thorough.\n3. The experiments are comprehensive.", "weaknesses": "1. The conclusion that \"mini-batch PL purification is an important factor in making PLL methods effective\" aligns with most current work and appears to be widely recognized.\n2. The authors propose a method, StreamPurify, which seems similar to CroSel. Although the authors indicate that StreamPurify can use the sample selection method from CroSel, I believe this approach lacks novelty, as such methods have been widely used in many weakly supervised learning scenarios.\n3. The paper seems to have not discussed different types of PL generation, which have been considered key assumptions in previous theoretical work, such as RC and CC. Different types of PL generation might lead to completely different results.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We would like to thank the reviewer for taking the time to review our work and the positive comments regarding its significance. Below are our responses to the comments in Weaknesses and Questions. \n\n> C1. The conclusion that \"mini-batch PL purification is an important factor in making PLL methods effective\" aligns with most current work and appears to be widely recognized.\n\nThank you for your insight. It is indeed a fact that mini-batch PL purification has become increasingly popular. A plausible explanation for this trend is that methods utilizing mini-batch PL purification yield better results, while traditional IBS and ABS are likely to perform poorly and thus were not be published in the literature. This observation just reaffirms the conclusion of our paper. However, it is important to highlight that existing studies **have not recognized** this factor as crucial to the effectiveness of PLL methods. Instead, they **typically focus on** adding more robust components, leading to SOTA methods quite complicated and different, and posing challenges in selecting the optimal direction for future algorithm design. Conclusive works like this paper should be vitally necessary.\n\n> C2. The authors propose a method, StreamPurify … I believe this approach lacks novelty, as such methods have been widely used in many weakly supervised learning scenarios.\n\nThank you for the comment. There may be a misunderstanding regarding the concept and significance of StreamPurify. The main contribution of this paper --- the minimal algorithm design principles in PLL --- motivates us to observe that existing SOTA often overlook the initialization phase and tend to uniformly end the warm-up process for all samples before starting the PL purification process. However, samples’ learning progress varies at the beginning of training [1,2,3]. Therefore, we propose **a general strategy**, StreamPurify, which adaptively adjusts the timing for different samples to enter the PL purification process based on their readiness. The innovation of our strategy lies more in its philosophy, making it flexible enough to be compatible with various sample selection criteria. In our experiments, we used the criteria in CroSel as a plug-in method and demonstrated the practical potential of StreamPurify. A subtle yet important distinction between StreamPurify and sample selection methods like CroSel is that our strategy is conducted without replacement. This approach, driven by our philosophical motivation and minimal algorithm design principles, **has never been studied** in PLL community. \n\nWe need to reiterate that all the proposed methods in this paper *primarily serve as demos* to illustrate our main understandings. We humbly believe that the significance and novelty of research should not be limited to algorithm design alone. Our findings and proposed strategy are expected to draw attention to the warm-up process, which can *push forward PLL as a whole*. \nThank you again and we will provide a clearer discussion in the revised version.\n\n> C3. The paper seems to have not discussed different types of PL generation … Different types of PL generation might lead to completely different results.\n\nWe have used different types of PL generation processes which are commonly used in the PLL community --- instance-independent PLLs and instance-dependent PLLs in our experiments. Furthermore, in our response to C2 of Reviewer ygK7, we added the class-dependent PL generation. Our findings are not influenced by different types of PL generation. \n\n> C4. Would observing label changes during training, as done in CroSel, potentially be a better way to identify the factors that make PLL methods effective?\n\nThank you for raising this point, while upon reviewing the CroSel work, we did not find the definition and application of “label changes”. If you could provide more specific details, we would greatly appreciate it and would be happy to address any further questions. By the way, CroSel owes its advancement to “a cross selection strategy” and “select confident pseudo labels” in the original paper, both of which are analyzed through ablation experiments in Table 4, and the conclusions also support our claims.\n\n> C5. For IBS and some compromise methods, is it true that once the model easily selects a label, it is less likely to change? Is this related to training settings such as the optimization method?\n\nThank you for asking. For IBS, as we mentioned in Section 1, traditional IBS methods have two stages: estimating pseudo-labels in the first stage and conducting supervised learning in the second stage. In this scenario, pseudo-labels are one-hot and remain fixed, and this is determined by the learning strategy and is not related to the optimization method. Sorry we are not clear on what is meant by “compromise methods”. \n\n> C6. Can the expansion of the sample space brought by data augmentation be considered as helping contrastive methods to disambiguate labels, even though experiments suggest that data augmentation is not a key factor?\n\nThank you for the summary. Data augmentation is an integral part of training deep learning models with image data, enhancing the size and quality of training datasets [4]. Therefore, although we emphasize a novel point that data augmentation is not a key factor for addressing the PLL problem itself, since current PLL methods are validated on image datasets, data augmentation is a necessary part to boost final accuracy.", "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": "y9zswr6SMe", "reviewer": "Reviewer_b5oN", "summary": "The paper examines the effectiveness of partial-label learning algorithms, identifying key factors contributing to their success. It discusses techniques from other fields that can enhance partial-label learning, such as the transition from uniform to one-hot pseudo-labels and the implementation of minimal algorithm design principles crucial for optimal performance. The document provides valuable insights into improving the performance of partial-label learning methods, making it a valuable resource for researchers in partial label learning.", "questions": "1. In Table 3, it is better to provide the accuracy of the SOTA methods with/without the proposed StreamPurify method.\n2. In Table 3, it seems the improvements can be marginal. The performance improvement of most methods is within 1%.\n3. More SOTA methods can be added to validate the effectiveness of the proposed method.", "limitations": "The paper lacks the discussion on the question of why this work has no societal impact or why the paper does not address societal impact.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. Through a comprehensive empirical analysis, the paper uncovers key factors that drive the effectiveness of partial-label learning algorithms.\n2. This paper is well-written.\n3. The proposed warm-up strategy improved the state-of-the-arts performance.", "weaknesses": "1. The paper would benefit from providing additional details about the proposed warm-up strategy to enhance clarity and understanding.\n2. Given the empirical nature of the paper, it is crucial to include detailed implementation information to ensure reproducibility and transparency.\n3. The contribution of the baseline methods need to be mentioned in the paper.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We would like to thank the reviewer for taking the time to review our work and the positive comments regarding its significance and writing quality. Below are our responses to the comments in Weaknesses and Questions.\n\n> C1. The paper would benefit from providing additional details about the proposed warm-up strategy to enhance clarity and understanding. \n\nThank you for your suggestion! Our proposed StreamPurify is an instance-dependent warm-up strategy that can be compatible with various sample selection criteria. In our experiments, the selection criteria were a) the confidence of the highest predicted label exceeded a threshold (0.75 in our experiments), b) the label was within the candidate label set, and c) the highest confidence label remained stable during the first three epochs. When these three conditions were simultaneously met, we considered the sample ready to enter the PL purification process. The warm-up phase was concluded for all samples by the 10th epoch. We will include these details in the revised manuscript.\n\n> C2. Given the empirical nature of the paper, it is crucial to include detailed implementation information to ensure reproducibility and transparency.\n\nWe have detailed all experimental setups in Appendix A. We will release the code and hyperparameters once the paper is accepted.\n\n> C3. The contributions of the baseline methods need to be mentioned in the paper.\n\nWe have listed the techniques and main contributions of the baseline methods in Table 1 and highlighted their philosophical underpinnings and algorithmic details in Section 3. We would provide a more detailed explanation in the revised manuscript.\n\n> C4. In Table 3, it is better to provide the accuracy of the SOTA methods with/without the proposed StreamPurify method.\n\nThank you for your suggestion. We will definitely include the detailed results in the revised version.\n\n> C5. Q1. In Table 3, it seems the improvements can be marginal. The performance improvement of most methods is within 1%. Q2. More SOTA methods can be added to validate the effectiveness of the proposed method.\n\nThank you for your comments. There may be a misunderstanding regarding the main focus of our paper. Our primary contribution is understanding and uncovering the underlying principles of PLL methods. We identify that all SOTA methods conduct mini-batch PL purification, exhibiting a common behavior characterized by progressive transition from uniform to one-hot pseudo-labels. \n\nBuilding on this core contribution, we additionally observed that existing SOTA often overlook the importance of the initialization phase and tend to uniformly end the warm-up process for all samples before starting the PL purification process. However, samples’ learning progress varies at the beginning of training. Therefore, we propose a strategy that adaptively adjusts the timing for different samples to enter the PL purification process based on their readiness. The significance of our strategy lies more in its philosophy and concept rather than in the specific details of its implementation, making it flexible enough to be compatible with various sample selection criteria. In our paper, we used an existing method as a plug-in criterion and demonstrated the practical potential of StreamPurify on multiple datasets with different PL generation processes. \n\nIn a word, **all the proposed methods in this paper primarily serve as demos to illustrate our findings rather than aiming to outperform SOTA methods**. Our strategy is expected to draw attention to the warm-up process, which can push forward PLL as a whole. We appreciate your suggestion and add two SOTA methods [1,2]. The test accuracy on FMNIST with instance-independent PLs is as follow:\n\n| method\\flippingprobability | 0.3 | 0.7 |\n| --- | --- | --- | \n| [1] | 93.12 | 92.84 |\n| + StreamPurify | 93.67 | 93.41 | \n| [2] | 95.62 | 93.49 | \n| + StreamPurify | 95.70 | 94.19 | \n\n[1] PiCO+: Contrastive Label Disambiguation for Robust Partial Label Learning. TPAMI’23\n\n[2] Candidate-Aware Selective Disambiguation Based on Normalized Entropy for Instance-Dependent Partial-Label Learning. ICCV’23", "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:

Meta-review: This is an interesting and solid contribution on partial-label learning (PLL), which investigates what makes a PLL method effective. All reviewers were positive about the paper and recommended accepting the submission.
Decision: Accept (poster)