BPPL: Bag Prototypes-based Pseudo-Labeling

• Bag Prototypes-based Pseudo-Labeling (BPPL) is a method that aggregates positive and negative prototypes from bag-level data to generate reliable pseudo-labels for individual instances.
• It employs attention-based instance aggregation, cosine similarity separation, and adaptive filtering to ensure discriminative feature learning under weak supervision.
• Experimental results show BPPL significantly enhances localization and classification accuracy in applications such as histopathological image analysis and continual learning.

Bag Prototypes-based Pseudo-Labeling (BPPL) is a methodological family designed to generate reliable pseudo-labels for instances within groups of data (bags) when only coarse or weak supervision is available at the bag level. BPPL is particularly impactful in Multiple Instance Learning (MIL), Learning from Label Proportions (LLP), and continual learning settings where fine-grained labels are absent but bag-level signals and feature aggregation can guide instance-level discovery and localization.

1. Methodological Principles

At the core of BPPL methods is the construction and utilization of “bag prototypes”—feature aggregates that represent the positive and negative class signatures within each bag. In settings such as MIL for histopathology, a bag may correspond to a whole slide image with hundreds of thousands of patches (instances). The BPPL framework seeks to:

• Encode each bag's content through attention-based or similarity-based instance aggregation.
• Derive prototypes for both positive and negative regions using weighted summation of instance features, where the weights reflect either learned attention (e.g., via the MIL model) or reversed attention for negatives.
• Calculate the similarity of each instance to these prototypes, thus yielding a pseudo-probability or hard label for the instance, which serves as a surrogate signal for supervised learning.

BPPL further improves reliability by filtering pseudo-labels, typically requiring both high classifier confidence and correct bag-level prediction before pseudo-supervised losses are employed for instance optimization (2507.02395).

2. Technical Implementation and Mathematical Formulation

The BPPL process is implemented as follows (2507.02395):

1. Prototype Computation Given attention weights $\alpha_m$ and instance features $x_m$ for $m=1,...,M$ instances in a bag:
   • Positive prototype:

   $$x_\text{bag} = \sum_{m=1}^M a_m x_m, \quad \text{where} \ a_m = \frac{\alpha_m}{\sum_j \alpha_j}$$

• Negative prototype:

  $$\tilde{x}_\text{bag} = \sum_{m=1}^M \tilde{a}_m x_m, \quad \tilde{a}_m = \frac{1 - \alpha_m}{\sum_j (1 - \alpha_j)}$$

1. Prototype Separation Loss To guarantee that prototypes are discriminative, a separation loss based on cosine similarity is applied:

$$L_{\text{sep}} = \text{sim}(x_\text{bag}, \tilde{x}_\text{bag})$$

1. Instance-wise Residual Analysis and Pseudo-labeling For each instance $x_m$:
   • Compute the mean prototype $$\,\bar{x} = (x_\text{bag} + \tilde{x}_\text{bag})/2$$
   • Compute directional vectors: $r = x_\text{bag} - \bar{x}$ and $\tilde{r} = \tilde{x}_\text{bag} - \bar{x}$
   • Define class probabilites via temperature-scaled softmax:

   $$p_m = \operatorname{Softmax} \left( \left[ \frac{\text{sim}(x_m - \bar{x}, r)}{T},\ \frac{\text{sim}(x_m - \bar{x}, \tilde{r})}{T} \right] \right )$$

• The instance pseudo-label is $\, \hat{y}_m = \arg\max(p_m)$

1. Filtering and Loss Accumulation Only if (a) the bag-level prediction is correct and (b) $\max(p_m)$ exceeds an adaptive threshold $\tau_1$, is the loss for that instance

$$L_m = \mathbb{1}(\hat{Y} = Y) \cdot \mathbb{1}(\max(p_m) > \tau_1) \cdot H(\hat{y}_m, \alpha_m)$$

included in the total pseudo-labeling loss.

1. Overall Instance Loss For a positive bag, the total loss combines instance-wise pseudo-labeling and separation loss:

$$L_\text{inst} = \mathbb{1}(Y \in Y_\text{pos}) \left( \frac{\lambda_1}{M} \sum_{m=1}^M L_m + \lambda_2 L_\text{sep} \right)$$

3. Advantages and Innovations

BPPL provides several critical benefits in weakly supervised and continual learning contexts:

• Instance-level Supervision without Annotations: By leveraging bag-level supervision and prototype aggregation, BPPL enables fine-grained instance labeling in domains such as histopathological image analysis, where explicit annotation is infeasible (2507.02395).
• Discriminative Representation through Separation Loss: The explicit minimization of positive and negative prototype similarity encourages the learning of features that are more class-separable at the instance level.
• Adaptive and Reliable Filtering: By requiring high confidence and bag-level accuracy before utilizing pseudo-labels, BPPL reduces the risk of noisy supervision and error propagation through continual learning sequences.
• Integrability with Continual Learning and Domain Adaptation: BPPL operates in concert with modules handling catastrophic forgetting (e.g., Orthogonal Weighted Low-Rank Adaptation in the CoMEL framework) and attention-based instance encoding (e.g., GDAT), supporting robust learning across task sequences (2507.02395).

4. Experimental Validation and Performance Metrics

In extensive experimentation across three publicly available whole slide image datasets (2507.02395):

• BPPL integrated into the CoMEL framework yielded up to 23.4% improvement in localization (instance-level) accuracy and up to 11% gain in bag-level classification accuracy compared to prior methods under continual MIL settings.
• Qualitative visualizations substantiated BPPL’s capacity to maintain localization consistency on held-out regions as new tasks are introduced.
• Ablation studies demonstrated that both the separation loss and confidence filtering are vital—removing either reduced localization performance significantly.

Performance metrics included instance-level accuracy (ACC_inst), intersection over union (IoU), and Dice score for localization, with BPPL-enabled models maintaining superior scores across all.

5. Comparative Perspective

BPPL is distinguished from classical pseudo-label selection and MIL approaches by:

• Exploiting both positive and negative prototypes derived from adaptive attention, whereas traditional approaches often rely solely on attention maxima or bag-level statistical summaries.
• Employing residual feature projections against the mean prototype, a refinement over direct attention weighting or simple threshold-based scoring.
• Incorporating an adaptive, confidence-driven sampling mechanism to mitigate noisy supervision—a critical necessity in continual and weakly supervised learning scenarios.

Related methods, such as “prototype pseudo-labeling” for clustering in SPICE and similarity-based pseudo-labeling in SPLAL, employ prototype-centric strategies, but may not employ dual prototypes, explicit separation loss, or filtering conditioned on bag-level prediction as realized in BPPL (2103.09382, 2307.04610).

6. Applications and Broader Context

BPPL has demonstrated utility in histopathological whole slide image analysis, where precise cell- or region-level localization is required, but annotation is costly (2507.02395). Its architecture—emphasizing prototype generation, similarity-based instance analysis, and adaptive reliability checks—aligns closely with the needs of continual MIL. More broadly, prototype-based pseudo-labeling mechanisms inspired by BPPL offer a promising path for robust learning in domains where weak supervision, continual updates, and fine-grained decisions intersect, including medical imaging, remote sensing, and multi-instance target detection.

7. Limitations and Future Directions

The filtration criterion for pseudo-labels in BPPL, while effective for error minimization, may limit the volume of usable training supervision if model calibration is poor or if the bag-level classifier lags in accuracy. Additionally, the dual-prototype mechanism presumes adequate separation between classes within a bag; highly ambiguous or low-signal bags could weaken prototype fidelity. Future research may investigate dynamic prototype refinement, integration with more expressive attention backbones, principled threshold calibration, or the extension of BPPL concepts to multiclass and multitask MIL environments.