Learning from Majority Label (LML)

• LML is a multi-class MIL framework where each bag is labeled by its majority instance, requiring recovery of latent instance labels from weak supervision.
• It addresses challenges of solution ambiguity and misalignment with standard MIL by enforcing count consistency through temperature-controlled softmax and specialized aggregation.
• Extensions like the Majority Proportion Enhancement Module refine bag composition to boost instance-level accuracy, proving effective in applications such as medical imaging.

Searching arXiv for the primary LML paper and direct follow-up to ensure current coverage. Learning from Majority Label (LML) is a multi-class Multiple-Instance Learning (MIL) setting in which each bag contains multiple instances from possibly different classes, the bag label is the majority class among its instances, and the learning objective is to recover an instance-level classifier using only bag-level majority labels. In this formulation, supervision is weaker than learning from label proportions and different from both classical binary MIL and multi-label MIL, because only a single majority class is observed while the identities and counts of non-majority classes remain latent. The problem was formalized as a distinct MIL regime together with a counting-based solution in 2024, and subsequently extended with a majority-proportion-oriented training module in 2025 (Shiku et al., 2024, Kaito et al., 4 Sep 2025).

1. Formal definition and supervision structure

In LML, the training data are bags with one observed label per bag: $$\mathcal{B} = \{(\mathbf{B}^i, \mathbf{Y}^i)\}_{i=1}^n,$$ where bag $i$ is

$$\mathbf{B}^i = \{\mathbf{x}_j^i\}_{j=1}^{|\mathbf{B}^i|},$$

and the unknown instance labels are one-hot vectors

$\mathbf{y}_j^i \in \{0,1\}^C.$

The observed bag label $\mathbf{Y}^i \in \{0,1\}^C$ is the one-hot encoding of the majority class in the bag (Shiku et al., 2024).

For bag $i$, the class count is defined as

$$N_k^i = \sum_{\mathbf{y}_j^i \in \mathbf{B}^i} y_{j,k}^i,$$

with counting vector

$\mathbf{N}^i = (N_1^i,\dots,N_C^i)^\top.$

The bag-level majority label is then

$$Y_c^i = \begin{cases} 1, & \text{if } c = \arg\max_k N_k^i,\ 0, & \text{otherwise}. \end{cases}$$

The target is not merely bag classification; it is to learn an instance-level classifier that predicts the latent $\mathbf{y}_j^i$ from only these majority labels (Shiku et al., 2024).

This makes LML an inverse problem of the map

$i$0

Because many different instance-label assignments can induce the same majority class, the problem is ill-posed. This suggests that architectural bias, rather than bag-level loss alone, is central to identifiability.

LML differs sharply from adjacent weak-supervision regimes. Standard binary MIL assumes a presence rule, not a majority rule. Standard multi-class mono-label MIL often leaves the bag–instance relation unspecified and delegates it to an aggregator. Multi-label MIL reveals which classes are present, whereas LML reveals only which class dominates. Learning from label proportions supplies approximate proportions; LML supplies only the argmax of the count vector, which is strictly weaker supervision (Shiku et al., 2024).

2. Motivation, applications, and data regimes

The majority-label assumption is motivated by settings in which a region, image, or video contains multiple latent classes but annotation protocols report only the dominant or diagnostically leading class. The motivating examples include pathological image diagnosis, other medical imaging tasks such as OCT and histopathology, and later work additionally lists pathology image segmentation, political voting prediction, customer sentiment analysis, and environmental monitoring (Shiku et al., 2024, Kaito et al., 4 Sep 2025).

In the pathology example, a whole-slide image or region is partitioned into patches, different patches may contain different tissue types or cancer subtypes, and clinical reporting may record only the majority cancer subtype. In that setting, the bag is a set of patches, the bag label is the dominant subtype, and the unobserved patch labels remain clinically important (Shiku et al., 2024).

The initial empirical study used synthetic bag construction on four benchmarks: CIFAR-10, SVHN, PATHMNIST, and OCTMNIST. Bags were formed as random subsets of instances, and bag labels were defined by the majority class of their constituent instances. Three majority-proportion scenarios were considered:

• Large: majority proportion in $i$1
• Small: majority proportion in $i$2
• Various: majority proportion in $i$3

These regimes operationalize the extent to which a bag is dominated by one class. The “Small” regime is the hardest because the majority class can be only slightly above uniform, leaving substantial ambiguity in the latent count vector (Shiku et al., 2024).

A later study retained the same four datasets and emphasized that bags with a high proportion of the majority class facilitate learning. This directly linked the geometry of bag composition to instance-level recoverability and motivated an explicit majority-proportion enhancement strategy (Kaito et al., 4 Sep 2025).

3. Why conventional MIL aggregation is misaligned with LML

Most standard MIL pipelines encode each instance, then aggregate instance features or class confidences with mean pooling, max pooling, $i$4-norm, log-sum-exp, or attention-weighted summation, and finally optimize bag-level cross-entropy. In output aggregation, if $i$5 is the instance confidence vector, the bag score may be

$i$6

The critical issue is that these methods aggregate confidences rather than counts of discrete instance labels (Shiku et al., 2024).

For LML, however, the semantic rule that defines the bag label is not “largest summed confidence” but “largest instance count.” The paper exhibits toy examples in which confidence summation predicts the correct bag label, yet hardening the instance predictions with $i$7 and counting them yields a different majority or a tie. Thus, bag-level correctness under conventional MIL does not imply that instance-level predictions are consistent with the majority-count semantics (Shiku et al., 2024).

This mismatch has several consequences. First, there is solution ambiguity: many incorrect instance configurations can satisfy the bag objective through soft aggregation. Second, optimization may favor bad local minima in which most or all instances are pushed toward the bag majority class. Third, bag accuracy can remain acceptable while instance-level accuracy is poor. The reported experiments show that standard MIL baselines such as mean, max, $i$8-norm, LSE, attention, AdditiveMIL, and TransMIL often overfit to the majority class and achieve low instance-level accuracy under LML (Shiku et al., 2024).

A related empirical diagnostic is the consistency rate: among bags whose bag-level prediction is correct, it measures the fraction for which the majority class induced by the model’s aggregation agrees with the majority class obtained by counting hard instance predictions. Feature-aggregation methods often have low consistency because bag decisions are taken in an aggregated feature space rather than derived directly from instance-wise counts (Shiku et al., 2024).

4. Counting networks and count-consistent optimization

The counting network was introduced to make the bag prediction structurally identical to the LML rule. It has two stages: instance-level classification with nearly discrete outputs, followed by bag-level classification by counting those outputs (Shiku et al., 2024).

Given an instance $i$9, the instance classifier is

$$\mathbf{B}^i = \{\mathbf{x}_j^i\}_{j=1}^{|\mathbf{B}^i|},$$0

where $$\mathbf{B}^i = \{\mathbf{x}_j^i\}_{j=1}^{|\mathbf{B}^i|},$$1 is a neural network and $$\mathbf{B}^i = \{\mathbf{x}_j^i\}_{j=1}^{|\mathbf{B}^i|},$$2 is a softmax with temperature: $$\mathbf{B}^i = \{\mathbf{x}_j^i\}_{j=1}^{|\mathbf{B}^i|},$$3 For small $$\mathbf{B}^i = \{\mathbf{x}_j^i\}_{j=1}^{|\mathbf{B}^i|},$$4, such as $$\mathbf{B}^i = \{\mathbf{x}_j^i\}_{j=1}^{|\mathbf{B}^i|},$$5, the output approaches a one-hot vector. In the experiments, $$\mathbf{B}^i = \{\mathbf{x}_j^i\}_{j=1}^{|\mathbf{B}^i|},$$6 is ResNet-18, randomly initialized (Shiku et al., 2024).

Bag-level soft counts are then formed by summation: $$\mathbf{B}^i = \{\mathbf{x}_j^i\}_{j=1}^{|\mathbf{B}^i|},$$7 Thus $$\mathbf{B}^i = \{\mathbf{x}_j^i\}_{j=1}^{|\mathbf{B}^i|},$$8 approximates the true count vector when per-instance outputs are pseudo-one-hot. Because $$\mathbf{B}^i = \{\mathbf{x}_j^i\}_{j=1}^{|\mathbf{B}^i|},$$9 on $\mathbf{y}_j^i \in \{0,1\}^C.$0 is non-differentiable, the model applies a second temperature-softmax: $\mathbf{y}_j^i \in \{0,1\}^C.$1 which approximates a one-hot majority prediction at bag level (Shiku et al., 2024).

Training uses only bag-level cross-entropy: $\mathbf{y}_j^i \in \{0,1\}^C.$2 There are no explicit instance-level labels, no instance-level losses, and no extra regularizers beyond low-temperature softmax and counting. The design intention is that, to minimize bag loss, the model must allocate pseudo-one-hot instance outputs so that the counted majority matches the observed bag label (Shiku et al., 2024).

This induces count consistency by construction. If the network predicts bag majority class $\mathbf{y}_j^i \in \{0,1\}^C.$3, then $\mathbf{y}_j^i \in \{0,1\}^C.$4 must be largest; if $\mathbf{y}_j^i \in \{0,1\}^C.$5 is largest, many instances must satisfy $\mathbf{y}_j^i \in \{0,1\}^C.$6. In contrast to standard MIL, the bag prediction is directly tethered to the majority of instance-level predictions.

Empirically, the counting network achieved the best average instance-level accuracy across all methods in all three majority-proportion scenarios. In the hardest “Small” scenario, reported averages over datasets were 0.228 for Output+Mean, 0.355 for Feature+Mean, 0.221 for Feature+Attention, 0.192 for AdditiveMIL, 0.305 for AdditiveTransMIL, and 0.446 for the counting network. In “Various,” the counting network reached 0.628 average instance accuracy, and in “Large,” 0.741 (Shiku et al., 2024).

Ablation studies separated two components: the count mechanism and an argmax-like bag decision on the count vector. Relative to Output+Mean, the version without counting but with argmax-like bag enforcement already improved performance, and the full counting version improved further, especially in the “Small” scenario. This suggests that both majority enforcement and pseudo-one-hot instance counting are important, with counting particularly valuable when class proportions are close (Shiku et al., 2024).

5. Majority proportion, MPEM, and the 2025 extension

Subsequent work analyzed a structural property of LML: bags with a high proportion of the majority class facilitate learning (Kaito et al., 4 Sep 2025). This observation was consistent with the 2024 experiments, where the “Large” regime was easier than “Various,” which in turn was easier than “Small.” A plausible implication is that the informativeness of a majority label depends not only on which class dominates but also on the dominance margin.

To exploit this, the 2025 paper introduced the Majority Proportion Enhancement Module (MPEM), a training-time procedure that increases the proportion of the majority class by removing minority-class instances within bags. The method is two-stage. First, a counting network is pre-trained on original bags. Second, that model is used to estimate instance classes and class prototypes, identify instances predicted as minority, rank them by distance from the majority prototype, remove a fraction $\mathbf{y}_j^i \in \{0,1\}^C.$7 of the most distant minority-predicted instances, and retrain the counting network from scratch on the modified bags (Kaito et al., 4 Sep 2025).

The prototype for class $\mathbf{y}_j^i \in \{0,1\}^C.$8 is computed from the feature extractor output over instances predicted as class $\mathbf{y}_j^i \in \{0,1\}^C.$9 in bags whose ground-truth majority label is $\mathbf{Y}^i \in \{0,1\}^C$0. For a bag with majority class $\mathbf{Y}^i \in \{0,1\}^C$1, the distance of a minority-predicted instance to the majority prototype is

$\mathbf{Y}^i \in \{0,1\}^C$2

Removing the most distant minority-predicted instances is intended to increase majority proportion while preserving the bag label (Kaito et al., 4 Sep 2025).

This procedure is not a differentiable module in the forward graph; it is a data modification strategy guided by a pre-trained model. The removal ratio $\mathbf{Y}^i \in \{0,1\}^C$3 is selected by validation loss. The paper reports that MPEM increases majority proportion, preserves the original bag majority label with agreement almost 1.0 in practice, and improves instance-level accuracy. In the “Various” scenario, average instance accuracy rose from about 0.628 without MPEM to about 0.642 with MPEM; in the harder “Small” scenario, it rose from 0.446 to 0.501 (Kaito et al., 4 Sep 2025).

This extension sharpens the interpretation of LML as a supervision regime whose difficulty is controlled by bag composition. Counting alone enforces semantic consistency, while MPEM alters the effective training distribution so that the majority-label signal becomes less ambiguous.

6. Empirical behavior, interpretability, limitations, and neighboring fields

Beyond accuracy, the LML literature emphasizes two empirical pathologies of non-counting methods: majority overestimation and bag–instance inconsistency. For the majority class in each bag, the subtraction

$\mathbf{Y}^i \in \{0,1\}^C$4

was used to quantify overestimation. Output+Mean tended to overestimate majority counts, especially in the “Small” scenario, while the counting network reduced this effect (Shiku et al., 2024). In a related 2025 analysis, the same logic was linked to the tendency of diffuse confidence aggregation to keep pushing mass toward the majority class even after bag-level correctness is attained (Kaito et al., 4 Sep 2025).

Interpretability in LML arises from the count vector itself. The estimated $\mathbf{Y}^i \in \{0,1\}^C$5 directly represents the approximate number of instances predicted for class $\mathbf{Y}^i \in \{0,1\}^C$6, so the bag prediction is transparently derived from “how many instances of each class” rather than from opaque feature aggregation. The papers do not present attention heatmaps or comparable visual explanations, but the counting mechanism is itself an interpretable operationalization of the majority rule (Shiku et al., 2024).

Several limitations are explicit. LML assumes a well-defined majority class. Ties or near-ties are more ambiguous, especially in the “Small” regime. The 2024 experiments are based on synthetically constructed bags from CIFAR-10, SVHN, PATHMNIST, and OCTMNIST, so real-world deployments may involve additional complications such as annotation noise and spatial correlation. The counting network relies on a low softmax temperature $\mathbf{Y}^i \in \{0,1\}^C$7; too low a value can cause gradient issues, while too high a value weakens the pseudo-one-hot effect. The method also uses only a single majority label and does not model label noise, soft majorities, or explicit class proportions (Shiku et al., 2024).

LML sits near several neighboring fields. The closest is learning from label proportions, where bag-level class proportions are known; LML can be viewed as the extreme case in which only the argmax of the proportion vector is observed (Shiku et al., 2024). A later semi-supervised study imported Proportion Loss from learning from label proportions into class-imbalanced SSL, using a global label proportion prior to regularize unlabeled predictions and counter majority-label dominance. That work does not formulate LML as majority-labeled MIL, but it reinforces the broader methodological theme that count- or proportion-aware constraints can correct majority bias that arises under weaker supervision (Akiba et al., 3 Mar 2026).

The principal contribution of LML research is therefore twofold. At the problem level, it isolates a weak-supervision setting in which the bag label is explicitly the majority class of latent instances. At the method level, it shows that respecting this semantics requires count-based architectures rather than generic MIL pooling. The counting network and its MPEM extension provide the first specialized solutions for this regime, and they position LML as a bridge between MIL, weak supervision, and label-proportion learning (Shiku et al., 2024, Kaito et al., 4 Sep 2025).