Attribute Scoring in MIL

• Attribute scoring in MIL is the quantification of each instance’s impact on bag-level predictions using attention-based mechanisms.
• Recent advances incorporate permutation-invariant, neighbor-aware, and multi-stream methods to yield calibrated and meaningful attributions.
• Empirical results in fields like computational pathology and biomedical imaging confirm enhanced interpretability and prediction accuracy.

Attribute scoring in Multiple Instance Learning (MIL) refers to the quantification of each instance’s contribution to the overall bag prediction. Within neural attention-based MIL frameworks, such scoring is central to both the interpretability and accuracy of weakly-supervised models, especially in complex domains like computational pathology and biomedical image analysis. Over the past decade, advances in MIL have focused on learning instance‐level attributions by leveraging permutation-invariant attention mechanisms, neighbor-aware representations, and explicit score regularization. This article surveys the mathematical formulations, methodological advances, interpretive frameworks, and empirical performance associated with attribute scoring in MIL, referencing both foundational contributions and recent state-of-the-art models.

1. Formal Foundations and Attribute Score Definitions

Multiple Instance Learning (MIL) considers a two-level structure: each sample (bag) $X = \{x_1, \ldots, x_n\}$ comprises $n$ instances; only the bag label $Y$ is observed during training. A key development in attention-based MIL is to learn, jointly with the bag classifier, a set of instance scores or attribute scores $\{a_i\}$ that reflect the contribution of each instance $x_i$ to the bag prediction (Ilse et al., 2018). The canonical plain attention pooling, as standardized by Ilse et al., is

$$a_i = \frac{\exp(w^{T}\,\tanh(V\,h_i))}{\sum_{j=1}^{n} \exp(w^{T}\,\tanh(V\,h_j))}$$

where $h_i$ is the instance embedding, $V$ and $w$ are learnable parameters.

The attention weights $\{a_i\}$ satisfy $a_i \geq 0$, $\sum_i a_i=1$, and the bag representation is the weighted sum

$z = \sum_{i=1}^{n} a_i h_i.$

In the binary setting, the bag label probability is $p(Y=1|X) = \sigma(u^\top z)$, where $u$ is learned.

Attribute scoring in this framework corresponds precisely to the per-instance values $\{a_i\}$: a higher $a_i$ denotes greater impact of instance $i$ in shaping the bag-level output (Ilse et al., 2018). These scores can be extracted, visualized, or subject to further regularization for downstream interpretability (Adelipour et al., 5 Sep 2025, Abdulsadig et al., 2024).

2. Advanced Attribute Scoring: Extensions and Generalizations

Beyond the vanilla attention weights, recent works argue that in standard attention-based MIL (ABMIL), $\{a_i\}$ reflect only the importance in the aggregation step, not the full contribution to the bag prediction (Cai et al., 2024). AttriMIL, for example, decomposes the prediction head as

$$\hat Y = b + \sum_{i=1}^N a_i (\mathbf{h}_i\,\mathbf{c}),$$

and defines the unnormalized attribute score as

$$s_i = u_i\,(\mathbf{h}_i\,\mathbf{c}), \qquad u_i = \exp\Bigl\{ w^{T} [\tanh(V\,h_i^T)\odot\sigma(U\,h_i^T)] \Bigr\}.$$

The sign of $s_i$ indicates whether instance $i$ is pushing the logit toward positive or negative, and $|s_i|$ measures the strength. The normalization across instances reconstructs the bag logit. This richer attribute score formulation yields more calibrated, semantically meaningful attributions and enables advanced constraints and out-of-distribution detection (Cai et al., 2024).

Multi-attention MIL (MAMIL) architectures generalize further by deploying multiple attention modules, neighbor-aware embedding fusion, and template-based attention to create diverse feature representations and derive instance scores through attention flow across modules. The ultimate per-instance score is then a sum over attention modules and local neighborhoods (Konstantinov et al., 2021).

3. Algorithms and Implementation Protocols

The following table summarizes the main architectural components and attribute scoring strategies in prominent attention-MIL models:

Model/Framework	Attribute Score Definition	Key Additional Mechanism
ABMIL (Ilse et al.) (Ilse et al., 2018)	$a_i$ via softmaxed $w^\top\,\tanh(V\,h_i)$	Optional gating, interpretable $\{a_i\}$
AttriMIL (Cai et al., 2024)	$s_i = u_i(\mathbf{h}_i\,\mathbf{c})$	Spatial/Ranking constraints, adaptive backbone
MAMIL (Konstantinov et al., 2021)	$w_i = \sum_k \gamma_k \beta_i^{(k)}$	Neighbor-aware, template/fusion attention
DSMIL (Li et al., 2020)	$\alpha_i$ softmax over self-attention to top instance	Max-pooling + attention dual stream

Each framework shares the bag-level aggregation by weighted sum but differs in (1) whether and how instance context is used, (2) explicit regularization strategies, and (3) the possibility of fusing multiple attention streams.

In practical implementations, instance features are typically extracted via a frozen CNN backbone (e.g., ResNet-50 (Adelipour et al., 5 Sep 2025), AlexNet (Abdulsadig et al., 2024)) and projected via learnable attention modules. Dropout and weight decay serve as explicit regularizers. Importantly, frameworks such as AttriMIL progressively train adapter modules at various depths to specialize backbone representations for the MIL regime (Cai et al., 2024).

4. Visualization and Interpretation

Attribute scores provide direct interpretability to MIL predictions by mapping the relevance of each instance (e.g., image patch) to the bag-level decision. At test time, the attention weights $a_i$ or richer scores $s_i$ can be visualized as spatial heatmaps, exposing model focus areas.

For example, in sebocyte droplet counting, heatmaps derived from $a_i$ identify image patches most influential for inferring droplet count distributions (Adelipour et al., 5 Sep 2025). In histopathology, attention score heatmaps highlight cancerous regions or localize HER2-positive tissue in breast cancer slides (Abdulsadig et al., 2024). MAMIL derives composite per-patch scores $v_i$ incorporating neighbor and template information, further aligning visual explanations with anatomical features (Konstantinov et al., 2021).

5. Regularization, Task Alignment, and Limitations

Unregularized attention in MIL can be unstable, often assigning high weights to very few instances—especially problematic when the signal is diffuse (e.g., distributed pathologies). Empirical evidence from sebocyte counting shows that simple bag-level aggregation outperforms unregularized attention pooling in regression settings (mean MAE $=5.65$ for pooled MLP vs. $10.68\pm3.46$ for attention-MIL) (Adelipour et al., 5 Sep 2025). Attention regularization, such as entropy maximization or top-$K$ masking, and distribution-aware pooling are suggested to mitigate attention collapse (Adelipour et al., 5 Sep 2025, Cai et al., 2024). AttriMIL introduces spatial smoothness and attribute ranking constraints, further stabilizing instance scores and enhancing model discriminability (Cai et al., 2024).

A plausible implication is that attribute scoring can only provide reliable instance-level explanations and localization if pooling and regularization are closely matched to the bag-labeling structure of the task.

6. Empirical Results and Comparative Analysis

Evidence across domains demonstrates the practical importance of attribute scoring for both performance and interpretability:

• In histological WSI classification, AttriMIL achieves AUC 93.90% on CAMELYON16, outperforming baseline ABMIL by over 5 percentage points (Cai et al., 2024).
• In HER2 breast cancer scoring, patch-level attention weights visualize HER2-positive regions and enable heatmap-based annotation, while transfer-learned embeddings significantly improve AUC-ROC (e.g., 0.622 for PCAM pretrain) (Abdulsadig et al., 2024).
• MAMIL’s refined instance scores yield higher F1 and accuracy on MNIST-Bags and classical tabular MIL datasets compared to standard attention MIL methods, with patch-level attributions aligning to expert annotations (Konstantinov et al., 2021).
• In sebocyte droplet counting, attention-based attribute scoring provides interpretable patch attributions but is less numerically stable than global aggregation unless further regularized (Adelipour et al., 5 Sep 2025).

7. Future Directions and Open Challenges

Current research identifies several limitations and opportunities in attribute-based MIL. Enhancements under study include entropy- and diversity-promoting attention constraints, hybrid pooling that fuses global statistics, explicit modeling of spatial and semantic instance dependencies, and progressive adaptation of backbone features (Cai et al., 2024, Adelipour et al., 5 Sep 2025, Konstantinov et al., 2021). Another open frontier is calibrating attribute scores for out-of-distribution detection and enhancing reliability in rare or fine-grained classes. Ongoing work emphasizes more faithful attributions for regulatory and clinical acceptance in biomedical contexts.

Attention-based attribute scoring provides a mathematically principled, empirically validated, and practically useful mechanism to decompose bag predictions into meaningful instance-level contributions across a range of MIL applications (Ilse et al., 2018, Cai et al., 2024, Adelipour et al., 5 Sep 2025, Abdulsadig et al., 2024, Konstantinov et al., 2021, Li et al., 2020).