TopoCL: Topological Contrastive Learning for Medical Imaging

Guangyu Meng; Pengfei Gu; Peixian Liang; John P. Lalor; Erin Wolf Chambers; Danny Z. Chen

cs.CVMar 15, 2026

TopoCL: Topological Contrastive Learning for Medical Imaging

Authors: Guangyu Meng, Pengfei Gu, Peixian Liang, John P. Lalor, Erin Wolf Chambers, Danny Z. Chen

Organizations: Dept. of Computer Science and Engineering, University of Notre Dame · The University of Texas Rio Grande Valley · Dept. of IT, Analytics, and Operations, University of Notre Dame

Abstract

Contrastive learning (CL) has become a powerful approach for learning representations from unlabeled images. However, existing CL methods focus predominantly on visual appearance features while neglecting topological characteristics (e.g., connectivity patterns, boundary configurations, cavity formations) that provide valuable cues for medical image analysis. To address this limitation, we propose a new topological CL framework (TopoCL) that explicitly exploits topological structures during contrastive learning for medical imaging. Specifically, we first introduce topology-aware augmentations that control topological perturbations using a relative bottleneck distance between persistence diagrams, preserving medically relevant topological properties while enabling controlled structural variations. We then design a Hierarchical Topology Encoder that captures topological features through self-attention and cross-attention mechanisms. Finally, we develop an adaptive mixture-of-experts (MoE) module to dynamically integrate visual and topological representations. TopoCL can be seamlessly integrated with existing CL methods. We evaluate TopoCL on five representative CL methods (SimCLR, MoCo-v3, BYOL, DINO, and Barlow Twins) and five diverse medical image classification datasets. The experimental results show that TopoCL achieves consistent improvements: an average gain of +3.26% in linear probe classification accuracy with strong statistical significance, verifying its effectiveness.

Figures & tables

Figure 1: Visualization of failure cases corrected by TopoCL on ISIC2019 [ 39 ] . Two dermatofibroma (DF) cases are misclassified by the baseline MoCo-v3 [ 9 ] as actinic keratosis (AK, top) and melanocytic nevi (NV, bottom). MoCo-v3+TopoCL correctly classifies both as DF by capturing characteristic topological features: circular-to-oval boundary patterns with uniform internal connectivity (top) and radial pigmentation structures with a consistent boundary configuration despite hair overlay (bottom). Grad-CAM [ 35 ] heatmaps show that TopoCL focuses on lesion boundaries and internal structural patterns, while the baseline exhibits scattered attention on peripheral or irrelevant regions.

Figure 2: An overview of our TopoCL framework. (a) Topological Contrastive Learning : Given an input image $x$ , we generate two views with topology-weak ( $x_{\text{topo}}^{w}$ ) and topology-strong ( $x_{\text{topo}}^{s}$ ) augmentations, and compute their persistence diagrams $\text{topo}^{w}$ and $\text{topo}^{s}$ . The visual encoder processes $x_{\text{topo}}^{w}$ , $x_{\text{topo}}^{s}$ while the topology encoder processes $\text{topo}^{w}$ , $\text{topo}^{s}$ , with projection heads producing visual features $\mathbf{f}^{w}$ , $\mathbf{f}^{s}$ and topological features $\mathbf{t}^{w}$ , $\mathbf{t}^{s}$ . The TopoCL MoE module fuses these features through five experts (the colors distinguish the fusion strategies: Vis-Only, Topo-Only, Concat, Gated, and Cross-Attn) with learned gating weights, producing fused representations $\mathbf{h}^{w}$ , $\mathbf{h}^{s}$ . A projection head maps these to the final representations $\mathbf{z}^{w}$ , $\mathbf{z}^{s}$ , optimized via contrastive loss. (b) The structure of H-Topo. Encoder : It uses hierarchical self- and cross-attention to capture topological features from PDs with both $H_{0}$ and $H_{1}$ homology dimensions.

Category	Operations	Topological Effect
Homeomorphism	Flips, rotations	Topology-preserving ( $d_{B}^{\text{rel}}\!\approx\!0$ )
Boundary perturb.	Gaussian noise	Perturb boundary structures
Smoothing	Gaussian blur	Merge/separate features
Intensity	Contrast, brightness	Shift feature prominence
Morphological	Dilation, erosion	Modify connectivity and holes

Table 1: Topology-aware augmentation categories. All topological effects (except homeomorphism) are parameter-dependent.

Dataset	Modality	Classes	Train / Test
PathMNIST	Colon Pathology	9	89,996 / 7,180
OCTMNIST	Retinal OCT	4	97,477 / 1,000
OrganSMNIST	Abdominal CT (Sagittal)	11	13,940 / 8,829
ISIC2019	Skin Lesion Dermoscopy	8	25,331 / 8,238
Kvasir	GI Endoscopy	8	3,200 / 800

Table 2: Dataset statistics for the five medical image datasets.

	Path		OrganS		OCT		ISIC		Kvasir		Avg.
Method	ACC	AUC	ACC	AUC	ACC	AUC	ACC	AUC	ACC	AUC	ACC	AUC
SimCLR [ 8 ]	$92.57_{\pm 0.31}$	$99.12_{\pm 0.11}$	$77.12_{\pm 0.26}$	$96.41_{\pm 0.26}$	$69.41_{\pm 0.56}$	$91.83_{\pm 0.43}$	$66.04_{\pm 2.29}$	$88.01_{\pm 1.11}$	$74.33_{\pm 1.28}$	$95.89_{\pm 0.76}$	$75.89_{\pm 0.51}$	$94.25_{\pm 0.11}$
+TopoCL	$93.21_{\pm 0.14}^{*}$	$99.28_{\pm 0.05}$	$78.62_{\pm 0.06}^{***}$	$96.75_{\pm 0.33}^{*}$	$73.10_{\pm 0.21}^{***}$	$93.41_{\pm 0.26}^{**}$	$71.62_{\pm 0.21}^{**}$	$89.82_{\pm 0.77}^{**}$	$78.61_{\pm 0.41}^{**}$	$97.11_{\pm 0.32}^{*}$	$79.03_{\pm 0.10}^{***}$	$95.27_{\pm 0.15}^{***}$
MoCo-v3 [ 9 ]	$93.13_{\pm 0.42}$	$99.07_{\pm 0.09}$	$78.02_{\pm 0.34}$	$99.57_{\pm 0.31}$	$80.02_{\pm 0.34}$	$96.01_{\pm 0.04}$	$74.98_{\pm 2.01}$	$92.86_{\pm 1.12}$	$88.42_{\pm 2.01}$	$97.37_{\pm 2.01}$	$82.91_{\pm 0.66}$	$96.98_{\pm 0.60}$
+TopoCL	$94.55_{\pm 0.20}^{**}$	$99.24_{\pm 0.09}^{**}$	$80.58_{\pm 0.09}^{***}$	$98.75_{\pm 0.21}^{\dagger}$	$82.09_{\pm 0.26}^{***}$	$97.09_{\pm 0.13}^{***}$	$78.44_{\pm 0.83}^{*}$	$93.26_{\pm 0.97}$	$91.17_{\pm 0.83}^{*}$	$98.81_{\pm 0.46}$	$85.37_{\pm 0.11}^{***}$	$97.43_{\pm 0.27}$
BYOL [ 17 ]	$93.42_{\pm 0.09}$	$99.31_{\pm 0.14}$	$76.41_{\pm 0.19}$	$97.33_{\pm 0.08}$	$76.02_{\pm 0.26}$	$95.89_{\pm 0.25}$	$73.82_{\pm 3.19}$	$90.75_{\pm 0.79}$	$85.67_{\pm 0.98}$	$96.91_{\pm 0.13}$	$81.07_{\pm 0.49}$	$96.04_{\pm 0.20}$

Table 3: Performance comparison across five medical image datasets. The results show mean

\pm

standard deviation over five independent runs. Statistical significance is assessed via paired t-tests: ∗∗∗ :

p<0.001

, ∗∗ :

p<0.01

, ∗ :

p<0.05

. † indicates performance decrease. The Avg. columns report dataset-averaged metric values.

Configuration	OrganS	ISIC	Kvasir
TopoCL (weak+strong)	75.51 ±1.56	72.92 ±2.32	84.63 ±1.85
TopoCL (full image)	76.34 ±1.46	74.35 ±1.58	87.41 ±1.88
TopoCL (topo-weak+topo-weak)	78.98 ±0.37	76.39 ±0.55	90.01 ±0.28
TopoCL (topo-strong+topo-strong)	78.02 ±0.68	75.99 ±1.02	89.64 ±0.91
TopoCL (topo-weak+topo-strong)	80.58 ±0.99	78.44 ±0.83	91.17 ±0.43

Table 4: Ablation of topology-aware augmentation configurations using MoCo-v3+TopoCL. ACC results (%) are reported.

Configuration	Path	OrganS	OCT
w/o pretraining	$68.98_{\pm 1.43}$	$50.61_{\pm 0.87}$	$48.72_{\pm 1.77}$
w/o vis. pretrain	$81.53_{\pm 0.98}$	$64.72_{\pm 1.21}$	$66.98_{\pm 0.83}$
w/o topo. pretrain	$87.64_{\pm 0.92}$	$72.56_{\pm 1.11}$	$69.37_{\pm 0.89}$
w/o hier. attn	$86.51_{\pm 0.93}$	$72.85_{\pm 0.76}$	$67.62_{\pm 1.03}$
w/o self-attn	$91.24_{\pm 0.85}$	$76.03_{\pm 0.56}$	$70.28_{\pm 0.66}$
w/o cross-attn	$87.59_{\pm 0.85}$	$74.66_{\pm 0.71}$	$69.38_{\pm 0.57}$

Table 5: Ablation with SimCLR+TopoCL on three datasets. We evaluate: (1) pretraining strategies (rows 1-3); (2) hierarchical topology encoder components (rows 4-6); (3) MoE expert choices (rows 7-11). ACCs (%) averaged over five runs are reported.

Figure 3: Expert gating analysis for TopoCL integrated with BYOL on five datasets. Error bars show standard deviation across test samples. Five experts: visual-only (Vis), topology-only (Topo), concatenation (Conc), gated blending (Gate), and cross-attention (Attn).

Method	Train (h)	Params (M)	FLOPs (G)	Tput.	Overhead
SimCLR	1.58	24.89	4.11	668	-
+TopoCL	1.84	31.08	6.11	574	+16%
BYOL	1.72	53.28	2.88	614	-
+TopoCL	1.96	60.48	4.58	539	+14%
DINO	1.79	45.16	5.23	590	-
+TopoCL	1.99	51.00	7.03	531	+11%

Table 6: Computational cost comparison on ISIC2019.

Component	Training		Inference
Component	Time (h)	%	Params (M)	FLOPs (G)
Visual Encoder	1.06	57.61	24.03	4.11
Topo Encoder	0.35	19.02	3.83	1.99
MoE+Proj	0.43	23.37	3.23	0.01
Total	1.84	100.0	31.08	6.11

Table 7: Training and inference cost breakdown for SimCLR+TopoCL on ISIC2019.

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Topological data analysis (TDA), particularly persistent homology (PH), captures geometric structural properties in medical images (e.g., connected components, loops, shape characteristics), which conventional pixel-level deep learning approaches often neglect. While many topological descriptors are known for converting persistence diagrams (PDs) or raw images into topological feature vectors, existing methods mostly default to a single fixed descriptor (e.g., persistence images), leaving the diversity of topological representations largely unexplored. To the best of our knowledge, there is no known large language model (LLM)-based agentic framework that can automatically determine the most suitable topological descriptors for a given image dataset and produce the corresponding topological feature vectors for downstream tasks. To fill this gap, we propose TopoAgent, an LLM-based agentic framework that automates topology learning for medical image analysis.TopoAgent operates through a Perception--Reasoning--Action--Reflection loop supported by 21 domain-specific tools and dual memory that accumulates experience across runs. Its skill set is distilled from systematic evaluation of 15 topological descriptors across 26 datasets with six classifiers. TopoAgent analyzes input images and their topological characteristics, reasons about which topological descriptors best suit the input, and determines the optimal descriptor and its configuration, all without task-specific training.

Abstract

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