Title: What Makes Partial-Label Learning Algorithms Effective?
Venue: NeurIPS 2024
Accepted: yes
Keywords: partial-label learning

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?

Abstract

A partial label (PL) specifies a set of candidate labels for an instance and partiallabel 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.

1 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 partiallabels (PLs)-a PL for an instance is a set of candidate labels, where a fixed but unknown candidate is the true label.

As benchmarking on simulated PLL versions of vision datasets becomes standard practice for evaluating PLL methods, new PLL approaches are emerging that integrate diverse advanced techniques to 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 1), making it challenging to choose the best direction for better algorithm design.

92

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Epoch

55

60

65

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iter=50944

iter=398

iter=199

iter=19

iter=3

iter=1

(a) Acc of IBS

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0.2

0.4

0.6

0.8

Margin

(b) Margin of IBS

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80

82

84

86

88

90

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maxi

CLPL

(c) Acc of ABS

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Epoch

0.800

0.825

0.850

0.875

0.900

0.925

0.950

0.975

Margin

(d) Margin of ABS

In this paper, we aim to summarize the success of PLL so far, and understand the indispensable elements in a well-performing PLL method, which can be condensed into minimal algorithm design principles . For this purpose, we think of the taxonomy of PLL 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-based 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 a 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 to prepare for true-label selection, and as training progresses, the optimization targets for candidate labels become distinct gradually, such that they exhibit IBS-like characteristics. 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 a 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 a loss function that does not differentiate candidate labels, e.g., enforcing the softmax outputs of them to sum to 1 [19]. However, stochastic optimization algorithms can implicitly lead to distinct outputs for each candidate label and show a progressive purification characteristic (Figure 1 and Lemma 3.1).

Execution matters. Whether a 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 a key insight: all successful PLL algorithms exhibit a common behavior characterized by a progressive transition from uniform to one-hot pseudo-labels , facilitated by the combination of PL purification and model updates in a mini-batch-wise manner . Building on this core strategy, modern methods also integrate various techniques from other domains, exemplified by Match from semi-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

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 PLL taxonomy and establish minimal algorithm design principles. At 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 a conclusive work to prevent redundant efforts in future research. (ii) We analyze the design philosophies and component frameworks of SOTA PLL methods, conducting comprehensive studies on benchmarksimulated datasets with PLs. Building on this, we highlight a minimal working algorithm that adheres to our design principles, and propose an enhancement strategy to mini-batch PL purification that have the potential to elevate performance across all existing SOTA methods.

2 Preliminaries

2.1 Notation

Consider a k -class classification problem. Let x ∈ X be features and y ∈ Y . = { 1 , 2 , . . . , k } be labels. Then one has ( x , y ) sampled from the ground-truth joint density p ( x , y ) over X × Y in supervised learning. PLL deals with PLL data ( x , S ) , which is independently drawn from a corrupted distribution p ( x , S ) of p ( x , y ) with p ( x ) unchanged. S ∈ { 2 [ k ] \∅\ [ k ] } denotes a PL, and D = ( x i , S i ) n i =1 is a 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 ∈ S | x , S ) = 1 . Let ∆ k -1 ⊂ [0 , 1] k denote the k -dimensional simplex. Let f : X → ∆ k -1 be a multi-label classifier to be trained, specifically, a composite of a backbone (e.g., ResNet [18]) and an inverse link function ψ -1 [27] (e.g., softmax ), so that f ( x ) can be interpreted as probabilities. Let ℓ : ∆ k -1 ×Y → R + be a surrogate loss function, e.g., cross-entropy loss. The classification risk of f is defined as R ( f ) = E p ( x ,y ) [ ℓ ( f ( x ) , y )] , which is the performance measure we would like to optimize.

2.2 Backgrounds

In this section, we review recent prominent PLL works. In PLL, a common practice is to adopt a weighted objective of the form

with the optimal weights w ( x , z ) = p ( z | x ) . If ℓ is the cross-entropy loss, the weight can be integrated directly into the loss function, acting as optimization target (pseudo-label) for x directly. In classical taxonomy for PLL [47], IBS trains predictive models based on fixed weights assigned to the training instances, i.e., ˆ w ( x , z ) = { 0 , 1 } k , while ABS sets uniform weights during training, i.e., ˆ w ( x , z ) = 1 / | S | .

Definition 2.1 (Mini-batch PL purification) . Mini-batch PL purification is a process where for each mini-batch B ⊂ D selected at iteration t , the weights are updated such that the distinction among candidate labels' contributions increases over iterations:

with g being a strictly increasing function that increases the weight for more likely candidate labels according to the model's confidence. The model's parameters θ t are updated by optimizing a weighted loss over B :

The standard practice is initializing the weights uniformly w 0 i = 1 / | S | if i ∈ S and w 0 i = 0 otherwise, and let f 0 be initialized randomly. The model f 0 is then updated for at least one epoch to perform a preliminary training phase. Then in each mini-batch of t -epoch, w ( x ) is computed where f is fixed, and then f is updated by the weighted objective where w keeps fixed in backpropagation. An instantiation of mini-batch PL purification was first introduced by [25]. They use a delayed mechanism, i.e., w ( x ) is computed by the output of historical model f t -1 on x , 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 to estimate w , which may rely on either Siamese networks [4] applied to two or more inputs (dual-augmentation match, i.e., DA), or co-teaching networks [16] where one network's outputs serve as targets for the other (dual-model match, i.e., DM). Furthermore, some methods advocate DA+DM framework; for example, PiCO [34] involves mutual guidance of two heterogeneous classifiers, with one built on top of a supervised contrastive learning architecture [20]. In addition techniques borrowed from various communities have propelled PLL methods to top performance, such as 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 PL 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 can enhance the performance by improving the model'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 consistency, a 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 dual-augmentation 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 of all augmentations in A ( x ) :

ˆ w is updated in a mini-batch-wise manner along with the model parameters and is initialized uniformly (mini-batch PL purification). In addition, the learning objective of DPLL includes another loss function as

where the vector subscript indicates the element is that position. It encourages the output of each non-candidate label to be zero.

Evaluation 1. Specific 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,

Instead of using a shared target for all views, we modifies the optimization target for each view separately based on the output of the other view:

where x 1 , x 2 ∈ A ( x ) , and

We combine two 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 in the contribution of these two components to learning. We found that Eq. 6 and Eq. 8 were comparable under the relatively simple settings, but Eq. 8 outperformed Eq. 4 in challenging scenarios (CIFAR-100 and mini-ImageNet). Note that Eq.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 over-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 to the original DPLL, but even showed some improvement, which is likely because Eq. 8 can model neighborhood consistency better than Eq. 4.

So far, we have extracted a core unit from DPLL, which takes the form of Siamese networks [4]: a weight-sharing network applied on two (or more) inputs for comparing, and PLs prevent the model from collapsing, i.e., outputting a 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 or neighborhood consistency.

Evaluation 3. Mini-batch PL purification does matter. Wemodify the learning strategy of 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 or epoch-wise iteration. Specifically, DASM-H uses hard labels as optimization targets for Eq. 8:

where e i denotes the i -th standard canonical vector, i.e., e i ∈ { 0 , 1 } k , 1 ⊤ e i = 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.e., 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 to 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-wise 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

and also improves computational efficiency. In addition, we change the dual feedforwarding to single. The optimization target of an input is modified in 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, as in DASM w/o.aug, causes a decrease in accuracy as 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 contrastive learning into PLL. It utilizes two heterogeneous classifiers sharing a backbone (one linear and one contrastive-based), guiding each other to instantiate Eq. 1. PaPi [40] investigates PiCO and identifies limitations in the contrastive learning module. Thus PaPi adopts a 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-normalized outputs of historical models to guide a prototypical classifier that shares the same backbone with the linear classifier. Both methods feed forward different views of 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 a 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 minibatch. We simplify this idea by removing the contrastive-based 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 a 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 a 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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labels with hard pseudo-labels, consistently leads to a 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 are 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 true 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 zero-and-normalized pseudo-labels generated from original x to supervise augmented x , and (ii) the reverse, using augmented x to supervise original x . The results are presented in Figure 2.

Switching from dual paths to a single path while retaining supervised learning on augmented instances with pseudo-labels from the original instances showed little change in accuracy. However, when using pseudo-labels from augmented instance to supervise original one, performance drops significantly. This suggests that data augmentation alone is 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 vs.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 1 and observed in Eq. 6 of Table 2, using stochastic algorithms to minimize loss functions, even ABS loss funtions that are traditionally considered to "treat all candidate labels equally", can also implicitly result in a 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?

We investigate several representative PLL losses, which are traditionally thought as ABS:

Modified negative log likelihood loss (Eq. 6) [38]: ℓ neg ( x , f ) = -∑ i/ ∈ S log(1 -f i ( x )) ;

APL loss [24]: ℓ APL ( x , f ) = 1 | S | ∑ i ∈ S ˜ ℓ ( f ( x ) , i ) , with GCE loss [49] as the component ˜ ℓ ;

Maximum likelihood loss [19]: ℓ maxi ( x , f ) = -log ∑ i ∈ S f i ( x ) .

Denote the scores of x outputted by the last layer before softmax as z , i.e., ψ -1 ( z ) = f ( x ) where f = ( ψ -1 ◦ f ( n ) ◦ · · · ◦ f (1) ) . Let us look at the gradients of ℓ neg and ℓ APL :

̸

̸

where q ∈ (0 , 1] is a tunable parameter of GCE. From a 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 all the probabilities, which implies that both loss functions 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 two losses. However, since the optimization targets for all candidate labels remain the same, minimizing these two losses does not align with our definition of mini-batch PL purification where the optimization targets are expected to diverge progressively.

Then we focus on the third loss ℓ maxi . We examine its gradients as

It is crucial to recognize two key points: (i) The philosophy of ℓ maxi is to ensure that the output of all candidate labels sums to 1, which is exactly the same as that of ℓ neg , which requires the output of all non-candidates to sum to 0. 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 ℓ maxi , the implicit optimization target of an instance is the zero-and-normalized outputs of current model on this instance itself, exhibiting consistent behavior with pseudo-label manipulation in SASM.

Lemma 3.1. Suppose using the same stochastic optimizer, then performing SASM is mathematically equivalent to minimizing ℓ maxi .

Empirical results in Table 5 also verified the theoretical findings. However, pseudo-label manipulation offers greater flexibility as it allows for more arbitrary modifications to the optimization targets, as DASM, SADM, etc. have done, and additional steps over generating soft pseudo-labels, 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: Q1. 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 a standard normal distribution with zero mean and variance σ 2 (as in normal initialization, Xavier initialization [1], He initialization [17]). For an instance x , the output z of a neuron after a ReLU activation is given by z = max(0 , wx + b ) , where w represents the

weight vector and b is a small constant bias. By the Central Limit Theorem, the mean of the weights ¯ w = 1 /n ∑ n i =1 w i for a sufficiently large number of neurons n approaches a normal distribution with mean zero and variance δ 2 /n . Applying Chebyshev's inequality, we have P ( | ¯ w | ≥ a ) ≤ δ 2 / ( na 2 ) . As n →∞ , ¯ w is close to zero with high probability. Then the output 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 N (0 , δ 2 ) , the initial outputs across classes approximate a uniform distribution as the number of neurons n →∞ .

̸

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 PLL hinges on a key assumption: the true label has a 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 ∈ S | x, S ) = 1 , p ( i ∈ S | x, S ) > 1 , ∀ i = y . This setup implies that, within any sufficiently small neighborhood in the data space, the true label will dominate. Consequently, when stochastic gradient-based 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-labels 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 a 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 a 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-Dependent 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 readiness. During the initial training phase, it selectively channels instances that have higher confidence in 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-labels 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.

StreamPurify is compatible to existing PLL 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 it 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-dependent warm-up, suggesting it as a promising direction for future improvements in PLL.

5 Discussion and Future Work

Wehave systematically delineated the core components underlying successful PLL methods, centering our insights around the pivotal effect of mini-batch 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 as IBS or ABS may 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 PLL methods to domains beyond vision tasks.

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Appendix

A Experiments Details

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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-ImageNet [32]. We generated PLs by the Flipping strategy [24] for FMNIST, CIFAR-10 and CIFAR-100. Each label i is added into PL with a flipping probability η y i = p ( i ∈ S | y ) independently and features are untouched: p ( s | x, y ) = M ∏ i ∈ S η y i ∏ i/ ∈ S (1 -η y i ) where M = 1 / ( 1 -∏ i = y η y i ) . We assumed η y i = η, ∀ i = y and η y y = 1 , and set η = { 0 . 3 , 0 . 7 } on FMNIST and CIFAR-10, η = { 0 . 05 , 0 . 1 } on CIFAR-100. For mini-ImageNet and ablation experiments (Figure 1, 2, 3, 4), we simulated the real scenario by setting the flipping probability for each incorrect label individually for each instance. We first trained a classifier with clean labels, and then for each instance, set the confidence prediction of the classifier as the flipping probability [42].

Our explorations used three backbones: 5-layer LeNet [22] on FMNIST, 18-layer ResNet [18] on CIFAR-10 and CIFAR-100, and 34-layer ResNet [18] on mini-ImageNet. All the methods were trained for 500 epochs with a standard SGD optimizer [9] with a 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 a random horizontal flips and crops [3]. For 'strong' augmentation on FMNIST and CIFAR-10, we added Cutout [8] to the weak augmentation, and on CIFAR-100 and mini-ImageNet, we additional leveraged AutoAugment [7]. We denote the augmentation by A ( · ) , with method clear from context. The implementation was based on PyTorch [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 in 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 1 (c-d), CLPL is a 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 4 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 ℓ 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.

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Peer reviews:
comments: 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.

STRENGTHS:
1. Through a comprehensive empirical analysis, the paper uncovers key factors that drive the effectiveness of partial-label learning algorithms.
2. This paper is well-written.
3. 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.
2. Given the empirical nature of the paper, it is crucial to include detailed implementation information to ensure reproducibility and transparency.
3. The contribution of the baseline methods need to be mentioned in the paper.

QUESTIONS:
1. In Table 3, it is better to provide the accuracy of the SOTA methods with/without the proposed StreamPurify method.
2. In Table 3, it seems the improvements can be marginal. The performance improvement of most methods is within 1%.
3. 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.
TITLE: Official Review
SOUNDNESS_CORRECTNESS: 3
DATE: 2024-06-20

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis 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.\n\nSTRENGTHS:\n1. 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.\n\nWEAKNESSES:\n1. 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.\n\nQUESTIONS:\n1. 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?\n\nLIMITATIONS:\nN/A.", "TITLE": "Official Review", "RECOMMENDATION": 6, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2024-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe 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​\n\nSTRENGTHS:\n1. 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.\n\nWEAKNESSES:\n1. 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\n\nQUESTIONS:\nPlease refer to the weaknesses section.\n\nLIMITATIONS:\nYes, the authors provided the discussion of the limitations.", "TITLE": "Official Review", "RECOMMENDATION": 6, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2024-07-11"}

comments: 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.

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.

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.

Theoretical results would provide a stronger validation of the proposed principles.

Comparisons on real-world datasets would be helpful.

QUESTIONS:
See above

LIMITATIONS:
N/A
TITLE: Official Review
SOUNDNESS_CORRECTNESS: 4
DATE: 2024-07-12

comments: 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.

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.

2. 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?

3. 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.

QUESTIONS:
1. The content of the paper is overly dense and requires further clarification, making it somewhat challenging to read and understand.

2. 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
TITLE: Official Review
SOUNDNESS_CORRECTNESS: 3
DATE: 2024-07-12