Nonparametric Distribution Matching for Self-Supervised Whole-Slide Image Condensation

Duong M. Nguyen; Trong Nghia Hoang; Hang Thi Nguyen; Thanh Trung Huynh; Phi Le Nguyen; Minh N. Do

eess.IVSep 30, 2026

Nonparametric Distribution Matching for Self-Supervised Whole-Slide Image Condensation

Authors: Duong M. Nguyen, Trong Nghia Hoang, Hang Thi Nguyen, Thanh Trung Huynh, Phi Le Nguyen, Minh N. Do

Organizations: University of Illinois Urbana-Champaign · Washington State University · Hanoi Medical University · VinUniversity · Hanoi University of Science and Technology

Abstract

Histological whole-slide images (WSIs) are central to computational pathology but pose severe computational challenges due to their extremely high resolution, often spanning several gigabytes per slide. To enable scalable learning, existing methods apply self-supervised data condensation to reduce computational cost, but typically rely on heuristic prototype learning and do not explicitly preserve learning-relevant feature distributions for downstream tasks. In response, we introduce a principled reformulation of WSI condensation as a distribution-matching problem under a fixed representational lens, and develop NICER, a tractable approximation framework based on a nonparametric prior with slide-adaptive capacity. Experiments on five histopathology datasets, together with clinical evaluation from a board-certified pathologist, show that NICER consistently outperforms prior methods, achieving an average accuracy improvement of 7.44% while offering improved efficiency-accuracy trade-offs, highlighting the benefits of principled, distribution-aware condensation for scalable histological representation learning. Source codes are available in https://github.com/nmduonggg/NICER.

Figures & tables

Figure 3 : Overview of NICER. NICER provides a learning-based approximation by decoupling patterns $\mathcal{Z}$ and concepts $\Phi$ , learned via two stages: pattern exploration to capture diverse information, and condensation to merge redundancies into compact concepts driven by a nonparametric prior.

Method	Decoder	Cancer Subtyping						Survival Prediction
		PANDA			NSCLC			LUAD	BRCA	CPTAC
		Kappa	Accuracy	F1	Kappa	Bal. Acc.	F1	C-Index	C-Index	C-Index
Whole Bag	ABMIL	91.93 ± 0.48	76.21 ± 1.53	76.37 ± 1.38	90.31 ± 1.65	94.52 ± 1.19	95.19 ± 0.78	62.12 ± 1.27	78.52 ± 3.82	48.26 ± 4.87
DeepSets		57.26 ± 38.13	51.60 ± 17.98	46.42 ± 23.91	79.51 ± 1.80	89.82 ± 0.88	89.73 ± 0.91	59.89 ± 5.34	49.23 ± 3.59	49.80 ± 7.96
ProtoCount		0.83 ± 9.55	24.24 ± 1.21	11.77 ± 1.28	10.69 ± 3.54	55.34 ± 1.78	53.86 ± 3.15	51.91 ± 5.75	56.47 ± 12.03	51.72 ± 8.97
H2T		75.03 ± 1.08	53.91 ± 1.10	50.66 ± 1.01	79.45 ± 1.80	89.67 ± 0.88	89.72 ± 0.90	51.83 ± 2.59	45.86 ± 4.29	45.34 ± 0.67

Table 1 : Performance of baselines on Condensation tasks. The best and second-best results are highlighted in bold red , and blue . Here, Whole Bag serves as a full-feature reference, not a baseline.

Metric	Whole Bag	PANTHER	NICER
Storage (GB)	194	3.2	5.7
Condense GPU (MB)	-	5.30	9.17
Condense Time (s)	-	0.05	1.51
Mean F1	93.58	90.69	94.23

Table 4 : Computation cost comparison of NICER and baselines on NSCLC subtyping with ILRA

Figure 6 : Morphological annotations of prototypes learned from NICER’s learned global concepts by a board-certified pathologist on a WSI in the TCGA cohort (BRCA). Further details are in App. L

Appendix figures & tables14 assets

Supplementary material from the paper’s appendix.

Appendix

Theoretical object	Role	NICER approximation
$\mu_{w}$	Empirical slide distribution	Reduced support $\mathcal{Z}_{w}$
$OT(\mu_{w},\nu_{\Phi_{w}})$	Distribution matching	Gaussian pattern-concept likelihood
$\lambda\|\Phi_{w}\|$	Cardinality penalty	Active concept set $\|\Phi_{w}^{+}\|$
PPP prior $\Pi_{\rho}(\Phi_{w})$	Variable-capacity prior	Pruning unassigned concepts
MAP inference	Prototype selection	Alternating updates over $(\Phi,\gamma,\zeta)$ and $b$

Appendix

Table 5 : Connection between the theoretical objective and NICER.

Method	Predictor	Kappa	Bal. Acc.	F1
OT	ABMIL	$-0.0045\pm 0.0417$	$0.5000\pm 0.0208$	$0.3193\pm 0.0915$
H2T		$-0.0303\pm 0.0379$	$0.4837\pm 0.0204$	$0.4397\pm 0.0122$
PANTHER		$0.1206\pm 0.1917$	$0.5357\pm 0.1359$	$0.4759\pm 0.2117$
NICER (Ours)		$0.8471\pm 0.0512$	$0.9175\pm 0.0253$	$0.9262\pm 0.0247$
OT	DSMIL	$0.1307\pm 0.1693$	$0.5735\pm 0.0936$	$0.4006\pm 0.1937$
H2T		$0.0495\pm 0.0533$	$0.5575\pm 0.0308$	$0.4047\pm 0.0243$

Appendix

Table 6 : Performance of baselines on Condensation tasks on Camelyon 16. The best and second-best results are highlighted in bold red , and blue .

Method	Predictor	Kappa	Accuracy	F1
OT	ABMIL	0.0264 ± 0.0849	0.2036 ± 0.0158	0.1213 ± 0.0318
H2T		0.5318 ± 0.1789	0.4034 ± 0.0736	0.3439 ± 0.1228
PANTHER		0.0467 ± 0.1002	0.2373 ± 0.0807	0.1341 ± 0.0659
NICER (Ours)		0.8392 ± 0.0514	0.6398 ± 0.0365	0.6332 ± 0.0327
OT	DSMIL	0.6253 ± 0.0944	0.4430 ± 0.0636	0.4436 ± 0.0843
H2T		0.6548 ± 0.0411	0.4183 ± 0.0083	0.3494 ± 0.0205

Appendix

Table 7 : Performance of baselines on Condensation tasks on PANDA dataset using CONCH as a pretrained encoder. The best and second-best results are highlighted in bold red , and blue .

Figure 7 : 2D t-SNE visualizations of NICER’s concept prototypes learned over five iterations using three representative TCGA slides. These plots highlight that NICER can capture different diverse information across different WSIs.

Figure 8 : 2D t-SNE visualization of original WSI feature bags and learned concept prototypes, comparing our method (NICER) with a representative prior approach (PANTHER).

PANDA	NSCLC	LUAD (Survival)	BRCA (Survival)
62.80	154.67	157.40	158.60

Appendix

Table 8 : Average number of final concept prototypes across different datasets

Figure 10 : Number of prototypes tracked over the first 8 iterations on PANDA and NSCLC dataset. The values are reported at log10 scale

Method	Config	% Input	F1
Whole Bag (Upperbound)	-	100%	74.42
PANTHER	K=16	2.58%	41.11
	K=64	10.39%	55.93
	K=128	20.78%	69.45
NICER (Ours)	M=50	5.79%	67.64
	M=200	11.32%	73.04

Appendix

Table 10 : Performance-Efficiency trade-offs comparison of NICER and the SOTA method, on PANDA using ABMIL under the same seed.

Predictor	ABMIL			DSMIL			ILRA
Top- $\kappa$	Kappa	Acc.	F1	Kappa	Acc.	F1	Kappa	Acc.	F1
1	90.18	70.02	69.87	85.42	64.65	65.95	89.17	64.88	64.24
3	91.48	74.94	75.00	88.73	68.46	67.52	92.25	73.83	74.55
5	90.47	72.93	72.72	88.80	68.46	66.66	88.66	71.36	71.47
10	89.52	70.47	70.49	85.42	66.89	66.94	88.88	68.90	68.92

Appendix

Table 11 : Ablation study of top-

\kappa

on downstream tasks performance across different predictor architectures. The experiments are conducted on PANDA dataset.

Method	Head	NSCLC - Match			LUAD-Match
Method	Head	Kappa	Bal. Acc.	F1	C-Index
PANTHER	ABMIL	9.67 ± 3.23	54.84 ± 1.59	52.51 ± 4.27	52.79 ± 10.26
OT		82.04 ± 2.96	91.03 ± 1.54	91.02 ± 1.47	62.60 ± 2.22
NICER		89.73 ± 1.81	94.84 ± 0.92	94.87 ± 0.91	64.67 ± 2.11
PANTHER	DSMIL	1.21 ± 2.01	48.70 ± 2.66	42.41 ± 8.36	40.03 ± 3.11
OT		78.74 ± 12.13	89.24 ± 6.15	89.20 ± 6.33	56.54 ± 1.61

Appendix

Table 12 : Performance comparison of NICER and selected baselines in Mean-Prototype settings

Method	Head	NSCLC - Max
Method	Head	Kappa	Bal. Acc.	F1
PANTHER	ABMIL	2.35 ± 5.56	51.19 ± 2.80	41.52 ± 7.33
OT		73.84 ± 15.46	87.01 ± 7.60	86.51 ± 8.41
NICER		89.73 ± 1.81	94.84 ± 0.92	94.87 ± 0.91
PANTHER	DSMIL	6.97 ± 0.96	53.46 ± 0.47	44.10 ± 3.38
OT		82.06 ± 5.54	91.06 ± 2.75	91.02 ± 2.78

Appendix

Table 13 : Performance comparison of NICER and selected baselines in Max-Prototype settings

Figure 11 : Visualization of prototype assignments on whole-slide images (WSIs) produced by PANTHER and NICER (ours). From left to right, the WSIs correspond to TCGA-E2-A570-01Z-00-DX1.64E5F2CA-9396-40DC-A300-04A54657BDE6 and TCGA-LL-A8F5-01Z-00-DX1.7579425E-1425-4160-A9DD-3D50F4C5428D from the TCGA-BRCA cohort. NICER yields more coherent prototype assignments and more accurately delineates tumor regions in both cases, highlighting its strong unsupervised learning capability. Best to view in color

Figure 12 : Different 2D projections of original WSI feature bags and learned concept prototypes, showing that our observation on diversity preservation is consistent across multiple projection space. The experiment is conducted on a WSI in TCGA-BRCA with the slide id TCGA-49-4514-01Z-00-DX2.f1565a36-257d-432e-a84d-47c1d7a0185f

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Histopathological whole slide images (WSIs) are central to cancer diagnosis, but their gigapixel scale, tissue heterogeneity, weak slide-level supervision, sparse diagnostic regions, and multi-scale evidence make robust automated analysis challenging. Multiple instance learning (MIL) is widely used to aggregate tile-level features into slide-level predictions, yet existing augmentation strategies often perturb tissue regions without preserving diagnostic relevance, slide context, or cross-scale structure. We propose SlideMix, a model-agnostic multimodal augmentation framework for MIL-based WSI analysis. SlideMix uses a retrieval-augmented vision-language model (VLM)-based Visual-Language Adaptive Region selector to identify diagnostically relevant regions and reduce weak-label noise. It then performs In-place Tile Shuffling within meaningful tissue regions to mix feature embeddings while preserving slide-level context. A VLM-based soft-labeling module supervises mixed samples, while a multi-factor, loss-driven online Curriculum-Learning Feedback scheme adaptively controls shuffle granularity, feature similarity, and shuffle ratio to promote cross-scale representation learning. Across 11 WSI datasets comprising 20,523 slides, 8 diagnostic tasks, and 10 WSI backbones, SlideMix improves accuracy and generalization in most settings and compares favorably with established augmentation baselines, providing a simple plug-and-play approach for more robust and scalable digital pathology models. Source code: https://github.com/Xia-Research-Lab/SlideMix

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