Organizations: The University of Tokyo, Japan · College of Computer Science and Technology, Jilin University, China · Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University, China · RIKEN Center for Advanced Intelligence Project, Japan
Learning from Label Proportions (LLP) is a weakly supervised problem in which the training data comprise bags, that is, groups of instances, each annotated only with bag-level class label proportions, and the objective is to learn a classifier that predicts instance-level labels. This setting is widely applicable when privacy constraints limit access to instance-level annotations or when fine-grained labeling is costly or impractical. In this work, we introduce a method that leverages Dual proportion Constraints (LLP-DC) during training, enforcing them at both the bag and instance levels. Specifically, the bag-level training aligns the mean prediction with the given proportion, and the instance-level training aligns hard pseudo-labels that satisfy the proportion constraint, where a minimum-cost maximum-flow algorithm is used to generate hard pseudo-labels. Extensive experimental results across various benchmark datasets empirically validate that LLP-DC consistently improves over previous LLP methods across datasets and bag sizes. The code is publicly available at https://github.com/TianhaoMa5/CV PR2026_Findings_LLP_DC.
Figures & tables
Figure 1: Training an instance-level classifier from a dataset with only bag-level class proportions.
Figure 2: A toy example of minimum-cost maximum-flow problem with 3 instances and 2 labels. Given a labeled bag {xi1,xi2,xi3,αi} and the current predicted outputs of instances {pi1,pi2,pi3} , we can form a corresponding directed multistage graph, and apply any off-the-shelf tool to solve for the optimal flow g∗ . It corresponds to the optimal candidate label assignment y^∗ with the highest probability, indicated by the bold amounts for the bold edges between instance and label nodes. Best viewed in color.
Figure 3: Overview of L lp-dc : the illustrated pipeline depicts the training process for a single bag. Given weakly augmented instances (x1w,…,xmw) and strongly augmented instances (x1s,…,xms) , the model g(⋅) predicts on the weak views g(x1w),…,g(xmw) ; their average is aligned with the label proportion α to compute the bag-level loss Lbag . Using these weak predictions and α , we build a graph and solve a minimum-cost maximum-flow problem to obtain pseudo-labels y∗ that satisfy the proportion constraints. Finally, we compute the instance-level loss Lins on the strong views g(x1s),…,g(xms) against y∗ .
Dataset
Model
Bag Size
Fully Supervised
16
32
64
128
CIFAR-10
DLLP
91.59 ± 1.52
88.61 ± 0.90
79.76 ± 1.45
64.95 ± 0.01
96.05 ± 0.33
LLP-VAT
91.80 ± 0.08
89.11 ± 0.22
78.75 ± 0.46
63.89 ± 0.19
ROT
94.86 ± 0.68
94.34 ± 0.65
93.97 ± 0.96
92.23 ± 0.81
SoftMatch
95.24 ± 0.12
95.25 ± 0.14
94.23 ± 0.18
93.87 ± 0.22
FLMm*
92.34
92.00
91.74
91.54
Table 1: Classification accuracy (mean ± std) on CIFAR-10, CIFAR-100, SVHN, Fashion-MNIST and MiniImageNet for different bag sizes. The highest accuracy is highlighted in bold. The symbol “*” indicates results for FLMm are reproduced directly from its original publication [ 55 ] , while the dash symbol “-” signifies the absence of reported results for SVHN, Fashion-MNIST, and MiniImageNet in FLMm’s experiments.
Figure 4: Pseudo-label accuracy (left) and pseudo-label ratio (right) during training on CIFAR-10 (left two panels) and CIFAR-100 (right two panels) under different bag sizes (16, 32, 64, 128).
Figure 5: Sensitivity analysis of the instance-level loss weight λ in Lins and the threshold τ parameter on CIFAR-10 and CIFAR-100. For λ∈{2,1,0.75,0.5,0.25,0} , performance remains stable over a moderate range, indicating robustness to the choice of λ . Similarly, for τ{0.95,0.8,0.6,0.3,0} , performance is consistent across a broad range, demonstrating robustness to threshold selection. Setting λ=0 or the τ to 1 reduces the method to DLLP.
CIFAR100
MiniImageNet
Method
16
32
64
128
16
32
64
128
DLLP
18.45
18.35
18.23
17.95
21.74
21.66
21.01
20.22
LLP-VAT
62.95
61.58
60.44
60.86
70.04
69.02
67.52
67.46
ROT (iter = 3 )
40.63
38.50
36.97
36.65
47.23
43.91
43.09
42.39
ROT (iter = 75 )
60.03
48.50
40.08
37.26
66.07
53.28
46.07
43.21
SoftMatch
39.45
38.70
36.45
36.40
46.03
42.95
42.23
41.73
Table 2: Execution time results on CIFAR100 and MiniImageNet (bag size ∈{16,32,64,128} ). Units are seconds per epoch. Reported numbers are the mean over 10 epochs under the same settings on a single NVIDIA A100 GPU. For ROT, iter denotes the number of Sinkhorn iterations.
Learning from label proportions (LLP) is a weakly supervised setting where training data are grouped into bags with only bag-level label proportions observed, and the goal is to learn a classifier that predicts labels for individual instances. Recently, a large body of methods has emerged; however, most of them rely on the assumption that instance-label pairs are sampled i.i.d. and randomly assembled into bags, an assumption often violated in real-world scenarios. Our experimental results indicate that these methods perform suboptimally under non-random settings. In this work, we adopt a more realistic assumption: bags are sampled i.i.d., and instance labels are conditionally independent given the instances. Under this setting, we show that the label counts follow a Poisson multinomial distribution. Motivated by this observation, we propose LLP via moment matching (LLP-MM), a simple yet effective approach which leverages multi-order factorial moments as training objectives, encouraging the classifier predictions to match these moments and thereby more fully exploit the underlying statistical structure of the data. Extensive experiments on benchmark datasets under various bag construction strategies demonstrate the effectiveness of our approach while maintaining high computational efficiency. Our code is available at https://github.com/TianhaoMa5/LLP-MM.
Semi-supervised learning (SSL) often suffers under class imbalance, where pseudo-labeling amplifies majority bias and suppresses minority performance. We address this issue with a lightweight framework that, to our knowledge, is the first to introduce Proportion Loss from learning from label proportions (LLP) into SSL as a regularization term. Proportion Loss aligns model predictions with the global class distribution, mitigating bias across both majority and minority classes. To further stabilize training, we formulate a stochastic variant that accounts for fluctuations in mini-batch composition. Experiments on the Long-tailed CIFAR-10 benchmark show that integrating Proportion Loss into FixMatch and ReMixMatch consistently improves performance over the baselines across imbalance severities and label ratios, and achieves competitive or superior results compared to existing CISSL methods, particularly under scarce-label conditions.
Prior work on partial labels learning (PLL) has shown that learning is possible even when each instance is associated with a bag of labels, rather than a single accurate but costly label. However, the necessary conditions for learning with partial labels remain unclear, and existing PLL methods are effective only in specific scenarios. In this work, we mathematically characterize the settings in which PLL is feasible. In addition, we present PL A-kNN, an adaptive nearest-neighbors algorithm for PLL that is effective in general scenarios and enjoys strong performance guarantees. Experimental results corroborate that PL A-kNN can outperform state-of-the-art methods in general PLL scenarios.
Nicolas A. Errandonea, Santiago Mazuelas, Jose A. Lozano +1
Basque Center for Applied Mathematics, Bilbao, Spain · Ikerbasque, Basque Foundation for Science · University of the Basque Country, Spain +1