Every Error has Its Magnitude: Asymmetric Mistake Severity Training for Multiclass Multiple Instance Learning

Sungrae Hong; Jiwon Jeong; Jisu Shin; Donghee Han; Sol Lee; Kyungeun Kim; Mun Yong Yi

cs.CVMar 14, 2026

Every Error has Its Magnitude: Asymmetric Mistake Severity Training for Multiclass Multiple Instance Learning

Authors: Sungrae Hong, Jiwon Jeong, Jisu Shin, Donghee Han, Sol Lee, Kyungeun Kim, Mun Yong Yi

Organizations: Korea Advanced Institute of Science and Technology, Daejeon, South Korea · Seegene Medical Foundation, Seoul, South Korea

Abstract

Multiple Instance Learning (MIL) has emerged as a promising paradigm for Whole Slide Image (WSI) diagnosis, offering effective learning with limited annotations. However, existing MIL frameworks overlook diagnostic priorities and fail to differentiate the severity of misclassifications in multiclass, leaving clinically critical errors unaddressed. We propose a mistake-severity-aware training strategy that organizes diagnostic classes into a hierarchical structure, with each level optimized using a severity-weighted cross-entropy loss that penalizes high-severity misclassifications more strongly. Additionally, hierarchical consistency is enforced through probabilistic alignment, a semantic feature remix applied to the instance bag to robustly train class priority and accommodate clinical cases involving multiple symptoms. An asymmetric Mikel's Wheel-based metric is also introduced to quantify the severity of errors specific to medical fields. Experiments on challenging public and real-world in-house datasets demonstrate that our approach significantly mitigates critical errors in MIL diagnosis compared to existing methods. We present additional experimental results on natural domain data to demonstrate the generalizability of our proposed method beyond medical contexts.

Figures & tables

Figure 1: The label characteristics that multiclass WSI have and the risks of applying MIL in the medical domain without accounting for mistake severity. (a) While every object in the natural domain is typically labeled, WSI only assigns the most urgent diagnosis among all observed complex findings. (b) Let $\prec$ denotes more urgent diagnosis. Despite the model MIL-A being considered a traditionally ”better” model than MIL-B because of high accuracy, it exhibits a higher number of severe misclassifications, which are shown in colored squares . This comparison highlights that conventional MIL approaches can lead to unreliable assessments for medical applications.

Figure 2: Structured class relationships from the finest hierarchy

\mathcal{H}

to the root

\mathcal{R}

Figure 3: Conceptual Descriptions of SFR. Dashed figures represent unique symptoms in $Y_{a}$ , where all figures are unlabeled and unknown. SFR extracts target cases and generates synthetic samples using only the available label $Y_{a}$ .

Figure 4: Two types of Mikel’s Wheel, where

\bullet

is the true class and

\blacktriangleright

is the predicted class. (a) In a symmetric wheel, the distance between two classes

i

and

j

is the absolute difference. (b) Proposed asymmetric wheel imposes a penalty

P

for misclassifying a high-priority true class.

	BRACS [ 5 ]								In-house
	TransMIL [ 35 ]				DTFD-MIL-AFS [ 42 ]				TransMIL [ 35 ]				DTFD-MIL-AFS [ 42 ]
	ACC	AUC	AsCC	AsMC	ACC	AUC	AsCC	AsMC	ACC	AUC	AsCC	AsMC	ACC	AUC	AsCC	AsMC
Cross Entropy (CE)	40.23 $\pm$ 5.54	74.90 $\pm$ 3.26	58.48 $\pm$ 4.12	50.18 $\pm$ 2.99	45.98 $\pm$ 0.94	82.03 $\pm$ 1.92	61.98 $\pm$ 1.43	48.07 $\pm$ 3.54	90.41 $\pm$ 0.81	99.16 $\pm$ 0.01	93.13 $\pm$ 0.79	44.16 $\pm$ 5.92	91.45 $\pm$ 0.49	99.33 $\pm$ 0.06	93.71 $\pm$ 0.30	39.10 $\pm$ 1.65
Weighted CE (2:3:5)	42.15 $\pm$ 4.82	78.15 $\pm$ 3.58	59.22 $\pm$ 3.68	47.90 $\pm$ 0.76	47.51 $\pm$ 1.95	81.57 $\pm$ 1.63	63.16 $\pm$ 2.50	47.91 $\pm$ 4.78	91.88 $\pm$ 0.41	99.41 $\pm$ 0.04	94.27 $\pm$ 0.41	46.32 $\pm$ 3.90	91.65 $\pm$ 1.23	99.33 $\pm$ 0.09	93.99 $\pm$ 0.91	43.55 $\pm$ 2.52
Weighted CE (1:2:7)	41.76 $\pm$ 1.43	76.37 $\pm$ 0.90	58.96 $\pm$ 1.96	46.92 $\pm$ 3.85	45.21 $\pm$ 1.08	80.23 $\pm$ 0.16	62.77 $\pm$ 1.08	52.69 $\pm$ 3.34	89.17 $\pm$ 0.85	99.14 $\pm$ 0.08	92.29 $\pm$ 0.61	44.60 $\pm$ 0.52	91.57 $\pm$ 0.45	99.34 $\pm$ 0.05	93.95 $\pm$ 0.24	42.99 $\pm$ 3.79
Chang et al. [ 6 ]	47.51 $\pm$ 2.17	79.48 $\pm$ 1.55	63.98 $\pm$ 1.81	51.02 $\pm$ 1.66	45.21 $\pm$ 4.82	81.80 $\pm$ 2.21	61.31 $\pm$ 4.14	47.77 $\pm$ 2.55	91.42 $\pm$ 0.41	99.27 $\pm$ 0.02	94.01 $\pm$ 0.06	49.07 $\pm$ 1.14	91.07 $\pm$ 0.98	99.29 $\pm$ 0.10	93.61 $\pm$ 0.83	44.67 $\pm$ 0.41

Table 1: Classification results on various mistake severity comparison methods and our proposed method. The best performance is denoted in bold, and the second best is underlined.

Figure 5: Data class hierarchy diagram of In-house and BRACS [ 5 ] dataset. The In-house is presented in an italic font, whereas BRACS is underlined. We denote the class priority in each hierarchy using

\prec

and

\equiv

Figure 6: Performance comparison on 182 mixed-symptom cases. Recall ‡ is measured by designating Adenoma (i.e., TA, TVA, TSA) as the positive class.

TransMIL [ 35 ]
Ablation	ACC	AUC	AsCC	AsMC
w.o. $\mathcal{L}_{MSCE}$	45.59 -2.46	78.79 -1.54	61.88 -2.52	47.10 -4.84
w.o. $\mathcal{L}_{HA}$	45.21 -2.84	79.61 -0.72	62.14 -2.26	51.41 -0.53
w.o. SFR	47.51 -0.54	76.88 -3.45	62.99 -1.41	47.92 -4.02
Ablated All	40.23 -7.82	74.90 -5.43	58.48 -5.92	50.18 -1.76
DTFD-MIL-AFS [ 42 ]

Table 2: Ablation results for both models on the BRACS dataset. The red values denote the difference in metrics between the fully-equipped model and the ablated results.

Figure 7: Visualization of various instance remix strategies. The green polygon indicates the most severe diagnosis labeled by the experts. Red boxes highlight the patches selected by the remix approach to synthesize a new sample without pixel-level annotation.

	BRACS [ 5 ]		In-house
	ACC	AsMC	ACC	AsMC
-	40.23 $\pm$ 5.54	50.18 $\pm$ 2.29	90.41 $\pm$ 0.81	44.16 $\pm$ 5.92
ReMix [ 41 ]	40.61 $\pm$ 4.63	52.37 $\pm$ 4.45	90.84 $\pm$ 0.62	51.64 $\pm$ 1.66
PseudoMix [ 26 ]	43.30 $\pm$ 1.43	51.07 $\pm$ 0.40	89.25 $\pm$ 0.45	51.64 $\pm$ 2.99
RandomMix [ 17 ]	44.06 $\pm$ 1.08	53.65 $\pm$ 4.45	89.25 $\pm$ 1.75	54.34 $\pm$ 2.22
SFR (Ours)	45.59 $\pm$ 3.55	53.18 $\pm$ 1.78	91.34 $\pm$ 0.09	55.86 $\pm$ 0.52

Table 3: Various instance remix strategies and their performance.

Figure 8: The confusion matrix simulates the predictions of the two models, with severe errors highlighted by color. The more in-depth analysis and computation of

\mathbb{E}(\textit{Risk})

are detailed in the supplementary material.

	ACC	AUC	AsCC	AsMC
Cross Entropy (CE)	83.24 $\pm$ 0.20	98.57 $\pm$ 0.04	87.23 $\pm$ 0.18	34.84 $\pm$ 0.77
Weighted CE (1:10)	73.69 $\pm$ 0.15	95.90 $\pm$ 0.16	79.79 $\pm$ 0.13	33.55 $\pm$ 0.21
CO2 [ 2 ]	83.97 $\pm$ 0.18	98.55 $\pm$ 0.03	87.77 $\pm$ 0.15	34.73 $\pm$ 0.29
CDW-CE [ 32 ]	84.11 $\pm$ 0.24	98.57 $\pm$ 0.01	87.87 $\pm$ 0.16	34.63 $\pm$ 0.40
MSCE (Ours)	85.64 $\pm$ 0.22	98.80 $\pm$ 0.02	89.12 $\pm$ 0.17	35.70 $\pm$ 0.61

Table 4: CIFAR-10 performance on varietal entropy terms.

Figure 9: Visualization of the expected class for various misclassified predictions. The values on the horizontal axis are the class index.

In-house
	TA	TVA	TSA	HP	SSL	IP	LP	$\sum$
Train	950	343	387	602	282	181	445	3,190
Validation	205	74	82	127	59	37	94	678
Test	300(95)	81(6)	102(18)	136(8)	114(55)	38	95	866(182)
BRACS [ 5 ]
	IC	DCIS	FEA	ADH	UDH	PB	N	$\sum$

Table 5: Data distribution over the classes. The values in parentheses represent 182 mixed cases, which were curated by the pathology experts.

Figure 10: Performance plot according to

\lambda_{1},\lambda_{2}

, and

\alpha

Figure 11: Performance plot according to

L

and

k

Figure 12: Performance according to the refinement iterations

T

Figure 13: Ablation results for both models on the In-house dataset. The red values denote the difference in metrics between the fully-equipped model and the ablated results.

Method	Time Complexity	Mean Implementation Time (s) / Sample
Method	Time Complexity	BRACS [ 5 ]	In-house
ReMix [ 41 ]	$\mathcal{O}(L{\cdot}k{\cdot}T{\cdot}D{\cdot}n(X_{i}))$	0.233	0.061
PseudoMix [ 26 ]	$\mathcal{O}(L{\cdot}{k}{\cdot}T{\cdot}{n(X_{i})})$	0.015	0.004
RandomMix [ 17 ]	$\mathcal{O}(1)$	0.005	0.003
SFR (Ours)	$\mathcal{O}(L{\cdot}{k}{\cdot}T{\cdot}{n(X_{i}})\log{n(X_{i}}))$	0.023	0.005

Table 6: Time complexity of various remix methods and their practical implementation time on the training set of the two datasets.

Figure 14: Additional visualization results on various remix strategies. The green polygon indicates the most severe diagnosis labeled by the experts. Red boxes highlight the patches selected by the remix methodology to synthesize the sample without pixel-level annotation.

Figure 15: Visualization of failure cases. The green polygon indicates the most severe diagnosis labeled by the experts. Red boxes highlight the patches selected by the remix methodology to synthesize the sample without pixel-level annotation.

Method	Equation	Distance Penalty	Asymmetric Penalty
Cross Entropy (CE)	$-\sum_{c}{\tilde{Y}[c]}\log{\hat{p}[c]}$	✗	✗
Weighted CE	$-\sum_{c}{\tilde{Y}[c]}{w_{c}}\log{\hat{p}[c]}$	✗	✗
HXE [ 4 ]	$-\sum_{h}\exp{(-\alpha{h}(N^{h}))}\log{p(N^{h}\|N^{h+1})}$ , where $h(N)\text{ is depth of node }N$ , $p(N^{h}\|N^{h+1})=\frac{\sum_{A\in\text{Leaves}(N^{h})}{p(A)}}{\sum_{B\in\text{Leaves}(N^{h+1})}{p(B)}}$ , and $p(N)=\prod_{h}p(N^{h}\|N^{h+1})$	$\bigtriangleup$	✗
CO2 [ 2 ]	$-\sum_{c}{\tilde{Y}[c]}\log{\hat{p}[c]}+$ $\lambda\sum_{c}\mathbb{1}(c\geq{c^{\prime}})\times\text{ReLU}(\delta+\hat{p}[c+1]-\hat{p}[c])+$ $\lambda\sum_{c}\mathbb{1}(c\leq{c^{\prime}})\times\text{ReLU}(\delta+\hat{p}[c]-\hat{p}[c+1])$ , where $c^{\prime}=\operatorname{argmax}_{c}\tilde{Y}$	✓	✗
CDW-CE [ 32 ]	$-\sum_{c}\left(\log(1-\hat{p}[c])\times\|c-c^{\prime}\|^{\alpha}\right)$ , , where $c^{\prime}=\operatorname{argmax}_{c}\tilde{Y}$	✓	✗
MSCE (Ours)	$-\hat{p}{W}Y^{\top}\sum_{c}{\tilde{Y}[c]}\log{\hat{p}[c]}$	✓	✓

Table 7: The Cross Entropy and its associated severity loss terms.

\tilde{Y}\in\mathbb{R}^{1\times{C}}

and

\hat{p}\in\mathbb{R}^{1{\times}C}

indicate one-hot vectorized true label and predicted probability, respectively.

Multiple Instance Learning

Multiple Instance Learning learns from labeled sets of instances when labels apply to bags, enabling prediction without dense annotations.

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May 17, 2026J/K move · Enter open · S save

GCE-MIL: Faithful and Recoverable Evidence for Multiple Instance Learning in Whole-Slide Imaging

Xiangyu Li, Ran Su

College of Intelligence and Computing Tianjin University

Explainable Medical Image Analysis Histopathology Image Classification Multiple Instance Learning Whole-Slide Image Analysis

Open paper AskPDF arXiv

Multiple instance learning (MIL) is the standard approach for whole-slide image (WSI) classification and survival prediction, where attention-based models ag gregate patch features into slide-level predictions. These models treat attention weights as evidence for their predictions, but attention is optimized for classi fication, not for identifying which patches actually support the diagnosis. This conflation leads to three failures: selected patches are insufficient (keeping them alone drops Macro-F1 by 0.078), unnecessary (removing them barely changes the prediction), and unrecoverable (continuous attention scores disagree with discrete patch subsets used at inference). The central premise is that evidence quality should be optimized directly through explicit criteria- Sufficiency, Necessity, and Recov erability (S/N/R)- rather than inherited as a byproduct of classification. GCE-MIL is a backbone-agnostic wrapper implemented through three injection modes and three evidence components: a grounding mechanism that aligns selection with domain-specific concepts, noisy-OR coverage that acts as a differentiable proxy for interventional evidence search, and threshold-plus-repair recovery that converts continuous selectors into discrete subsets through marginal-guided repair. Across 9 backbones and 9 datasets (81 configurations), GCE-MIL improves average Macro-F1 by 0.024 and C-index by 0.014, reduces the continuous-discrete gap by 4-7, and increases complement degradation by 2-4. With optional tile prefiltering after discrete recovery, inference runs up to 5 faster while retaining 0.989 full-bag utility.

Abstract

Multiple Instance Learning

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