Topo-R1: Detecting Topological Anomalies via Vision-Language Models

Meilong Xu; Qingqiao Hu; Xiaoling Hu; Shahira Abousamra; Xin Yu; Weimin Lyu; Kehan Qi; Dimitris Samaras

cs.CVMar 13, 2026

Topo-R1: Detecting Topological Anomalies via Vision-Language Models

Authors: Meilong Xu, Qingqiao Hu, Xiaoling Hu, Shahira Abousamra, Xin Yu, Weimin Lyu, Kehan Qi, Dimitris Samaras,

Organizations: Stony Brook University · Massachusetts General Hospital and Harvard Medical School · Stanford University · Penn State University

Abstract

Topology is critical in tubular structures such as blood vessels, nerve fibers, and road networks, where connectivity and loop structure govern downstream functional analysis. Vision-Language Models (VLMs) are promising candidates for understanding such structures, given their reasoning and grounding capabilities. To probe their topological perception, we systematically evaluate leading closed- and open-source VLMs on localizing and classifying four canonical topological anomalies (broken/spurious connections, missing/extra branches) in tubular-network segmentation masks. They perform nearly at random, indicating that topology-aware perception is largely absent from current general-purpose VLMs. As no existing resource pairs segmentation masks with localized anomaly annotations, we build an automated, multi-domain data-curation pipeline that synthesizes diverse topological perturbations with verifiable Betti-number annotations across graduated difficulty levels, yielding the first systematic benchmark with a large-scale training set and held-out in-distribution (ID) and out-of-distribution (OOD) test suites. Building on this benchmark, we introduce Topo-R1, centered on a topology-aware composite reward that jointly scores localization, classification, and skeleton-level structural fidelity. Supervised fine-tuning cold-starts schema-compliant outputs, and Group Relative Policy Optimization (GRPO) then optimizes the policy against this reward, steering predictions toward topologically meaningful structure rather than superficial pixel overlap. Extensive experiments show that Topo-R1 substantially outperforms general-purpose VLMs and matches or exceeds supervised baselines across ID, OOD, and real-segmentation-output protocols, establishing a strong foundation for VLM-based topological understanding of structured visual data.

Figures & tables

Figure 1: Intuition of the framework. (a) A segmentation mask can achieve a high Dice score (0.91) yet contain critical topological anomalies, such as broken or spurious connections, that are visible only upon close structural inspection. (b) State-of-the-art VLMs, including GPT-5.2 and Gemini-2.5-Flash, fail to detect these topological anomalies (near-zero Detection F1@0.5). (c) Topo-R1 successfully detects and classifies the topological anomaly with structured, typed bounding-box outputs. — Figure 1: Intuition of the framework. (a) A segmentation mask can achieve a high Dice score (0.91) yet contain critical topological anomalies, such as broken or spurious connections, that are visible only upon close structural inspection. (b) State-of-the-art VLMs, including GPT-5.2 and Gemini-2.5-Flash, fail to detect these topological anomalies (near-zero Detection [email protected]). (c) Topo-R1 successfully detects and classifies the topological anomaly with structured, typed bounding-box outputs.

Figure 2: The performance of state-of-the-art VLMs and our Topo-R1 on the topological anomaly detection task.

Figure 3: Overview of the automatic data curation pipeline.

Figure 4: Qualitative results of topological anomaly detection on samples containing 0-dim ( $\beta_{0}$ ) and 1-dim ( $\beta_{1}$ ) topological anomalies. Topo-R1 demonstrates superior capability in the localization and classification of diverse topological anomalies.

			@IoU=0.3			@IoU=0.5			@IoU=0.75
Category	Model	Method	P $\uparrow$	R $\uparrow$	F1 $\uparrow$	P $\uparrow$	R $\uparrow$	F1 $\uparrow$	P $\uparrow$	R $\uparrow$	F1 $\uparrow$	aF1 $\uparrow$
Closed- Source	GPT-4o	ZS	0.6	0.3	0.4	0.3	0.1	0.1	0.0	0.0	0.0	0.0
	GPT-5.2	ZS	2.4	1.7	2.0	1.0	0.7	0.8	0.2	0.1	0.1	0.3
	Gemini-2.5-Flash	ZS	3.0	2.4	2.7	1.0	0.9	0.9	0.1	0.1	0.1	0.3
	Qwen3.5-Plus	ZS	3.1	3.2	3.2	1.4	1.5	1.5	0.2	0.2	0.2	0.5
Detection / VLM	YOLOv8 [ 86 ] (img $\oplus$ mask)	Sup.	46.5	37.5	41.5	34.5	27.6	30.7	16.5	13.1	14.6	16.4

Table 1: Main results on topological anomaly detection on the in-distribution test set. We report detection precision (P), recall (R), and F1 at IoU thresholds 0.3, 0.5, and 0.75, along with the COCO-style average F1 (aF1, IoU 0.5:0.95). Closed-source models are evaluated in a zero-shot setting. “ZS” denotes zero-shot inference, “Sup.” denotes supervised training of a dataset-specific detector on our anomaly bounding-box labels, “SFT” denotes supervised fine-tuning, and “Topo-R1” denotes our topology-aware reinforcement fine-tuning. Bold indicates the best result in each block.

Category	Model	Method	BC	SC	MB	EB	Macro $\uparrow$
Closed- Source	GPT-4o	ZS	0.0	0.6	0.0	0.1	0.2
	GPT-5.2	ZS	0.0	3.5	0.0	0.1	0.9
	Gemini-2.5-Flash	ZS	0.1	4.2	0.1	0.0	1.1
	Qwen3.5-Plus	ZS	0.1	7.2	0.0	0.0	1.8
Open- Source	InternVL-2.5-2B	ZS	0.0	0.0	0.0	0.0	0.0
		SFT	1.6	24.5	4.2	1.9	8.1

Table 2: Detection F1 (%) by anomaly type at IoU=0.5. Higher is better. BC = Broken Connection, SC = Spurious Connection, MB = Missing Branch, EB = Extra Branch. Macro is the unweighted average across the four types.

Setting	Method	[email protected] $\uparrow$	[email protected] $\uparrow$	[email protected] $\uparrow$	aF1 $\uparrow$	Macro [email protected] $\uparrow$
OOD	Zero-shot (Qwen3-VL-4B)	0.1	0.0	0.0	0.0	0.0
	SFT only	33.9	24.4	14.8	14.9	21.8
	Topo-R1	58.4	45.5	23.2	25.5	43.2
Real- world	GPT-5.2 (zero-shot)	1.8	0.6	0.0	0.2	0.4
	Gemini-2.5-Flash (zero-shot)	2.1	0.8	0.0	0.3	0.5
	SFT only	26.4	18.1	7.8	9.3	15.6

Table 3: Out-of-distribution generalization and evaluation on real segmentation-model outputs. All methods receive identical

(I,M)

inputs at test time and have no access to ground-truth masks. OOD : held-out HALVS leaf-vein and DRIVE retinal-fundus imagery; Real-world : nnU-Net predictions on Roads and Crack. Topo-R1 is instantiated on Qwen3-VL-4B. Numbers in %; bold: best per block.

Table 8

Parameter	Symbol	Value
Top-level weights
Format weight	$w_{\mathrm{fmt}}$	0.10
Accuracy weight	$w_{\mathrm{acc}}$	0.85
Topological weight	$w_{\mathrm{topo}}$	0.05
Hungarian matching
Matching IoU threshold	$\tau_{m}$	0.10

Table 6: Reward function hyperparameters.

Model	Setting	P	R	F1	P	R	F1	P	R	F1	aF1
		@IoU=0.3			@IoU=0.5			@IoU=0.75
Qwen2.5-VL-3B	ZS	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
	1-shot	0.7	0.1	0.1	0.3	0.0	0.0	0.0	0.0	0.0	0.0
	3-shot	0.5	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
	5-shot	2.3	0.2	0.3	0.4	0.0	0.1	0.0	0.0	0.0	0.0
Qwen3-VL-4B	ZS	0.1	0.1	0.1	0.0	0.0	0.0	0.0	0.0	0.0	0.0

Table 7: Few-shot evaluation (1, 3, and 5 in-context examples). We report detection precision (P), recall (R), and F1 at IoU thresholds 0.3, 0.5, and 0.75, along with the COCO-style average F1 (aF1, IoU 0.5:0.95). “ZS” denotes zero-shot inference. Both zero-shot and few-shot results are almost random, confirming that in-context learning alone cannot elicit topology-aware perception.

Category	Model	Method	Count Acc $\uparrow$	Count MAE $\downarrow$	[email protected] $\uparrow$
Closed- Source	GPT-4o	ZS	26.3	2.28	10.3
	GPT-5.2	ZS	20.3	2.24	8.6
	Gemini-2.5-Flash	ZS	22.0	2.35	10.5
	Qwen3.5-Plus	ZS	15.5	2.27	5.2
Open- Source	InternVL-2.5-2B	ZS	21.0	3.10	20.4
		SFT	42.8	1.65	21.9

Table 8: Sample-level metrics on the in-distribution test set. Count Acc/MAE measures error counting ability (% and mean absolute error). [email protected]: mean per-sample F1 at IoU

\geq

0.5 (%), capturing partial credit.

Category	Model	Method	Roads $\uparrow$	OCTA-3M $\uparrow$	OCTA-6M $\uparrow$	Crack $\uparrow$
Closed- Source	GPT-4o	ZS	0.1	0.1	0.3	0.1
	GPT-5.2	ZS	0.5	1.3	1.4	0.3
	Gemini-2.5-Flash	ZS	0.5	2.3	1.2	0.5
	Qwen3.5-Plus	ZS	0.7	3.4	2.0	0.8
Open- Source	InternVL-2.5-2B	ZS	0.0	0.0	0.0	0.0
		SFT	11.9	12.2	10.1	7.3

Table 9: Detection F1 (%) by dataset at IoU=0.5. The benchmark spans four imaging domains: road networks (Roads), retinal vasculature at two scales (OCTA-3M, OCTA-6M), and crack patterns (Crack).

	Overall [email protected]		Macro [email protected]		aF1 (COCO)
Model	SFT	$\Delta$	SFT	$\Delta$	SFT	$\Delta$
InternVL-2.5-2B	9.0	+23.0	8.1	+17.2	4.0	+13.1
Qwen2.5-VL-3B	11.9	+31.1	9.8	+29.3	5.3	+16.1
Qwen3-VL-4B	23.0	+22.2	19.7	+21.7	12.8	+11.9
Qwen3-VL-8B	20.2	+23.7	16.2	+24.3	11.8	+12.5

Table 10: Absolute improvement (

\Delta

) from SFT to Topo-R1. F1 (%) at IoU=0.5 for overall, macro (unweighted per-type average), and COCO aF1.

Model	Method	Single	2–5	6–10
InternVL-2.5-2B	SFT	18.8	9.7	7.8
InternVL-2.5-2B	Topo-R1	35.8	32.4	25.3
Qwen2.5-VL-3B	SFT	13.8	12.8	11.1
Qwen2.5-VL-3B	Topo-R1	47.6	47.1	38.2
Qwen3-VL-4B	SFT	33.2	25.5	19.4
Qwen3-VL-4B	Topo-R1	53.7	49.0	40.1

Table 11: Detection F1 (%) by anomaly complexity at IoU=0.5. Samples grouped by ground-truth anomaly count: single (n=833), 2–5 (n=1712), 6–10 (n=835). Topo-R1 maintains strong performance on complex multi-anomaly samples.

Figure 5: IoU-to-score mapping

\phi

for different reward designs. Our piecewise non-linear curve (Topo-R1) provides sharp reward shaping near the tier boundaries, while the raw-IoU baseline produces a flat, unshaped slope.

Backbone	Reward	[email protected]	[email protected]	[email protected]	aF1	[email protected]	Cnt.Acc
Qwen2.5-VL-3B	Raw IoU	22.4	14.9	5.6	6.9	29.9	50.1
Qwen2.5-VL-3B	Topo-R1	57.8	43.0	18.4	21.4	56.2	51.5
Qwen3-VL-8B	Raw IoU	29.7	22.3	12.3	12.6	37.5	43.5
Qwen3-VL-8B	Topo-R1	57.0	43.9	22.4	24.3	57.5	54.9

Table 12: Ablation on raw IoU vs. non-linear tiered reward. All metrics in %; bold : best per backbone.

Method	[email protected]	[email protected]	[email protected]	aF1	[email protected]	Cnt.Acc
SFT	31.9	23.0	12.1	12.8	37.7	42.0
Linear	56.8	43.0	20.7	23.2	57.1	54.9
COCO	57.2	43.5	21.7	23.9	57.5	54.1
Topo-R1	58.3	45.2	22.5	24.7	58.5	54.2

Table 13: Ablation on IoU threshold set (Qwen3-VL-4B). Linear : piecewise linear interpolation between tier boundaries; COCO : thresholds

\{0.5,0.75,0.9\}

. All metrics in %; bold : best per column.

$\rho$	[email protected]	[email protected]	[email protected]	aF1
25%	53.8	41.2	19.4	21.6
50%	56.7	43.6	21.0	23.3
100%	58.3	45.2	22.5	24.7

Table 14: SFT data-fraction ablation (Qwen3-VL-4B).

\rho

: fraction of SFT samples used; GRPO data fixed.

Subset	FP-rate on GT loops $\downarrow$	Injected-only [email protected] $\uparrow$
(i) Clean GT (no injection)	4.7%	—
(ii) Injected near GT loop	7.3%	41.5

Table 15: Robustness to ground-truth loops on Roads (Qwen3-VL-4B). FP-rate on GT loops: fraction of GT loops that Topo-R1 incorrectly flags as spurious; Injected-only [email protected]: F1 measured only against the injected error (lower is better for false alarms on the GT loop, higher is better for detection of the injected error).

Method	Roads (held-out)	Crack (held-out)	Retina (held-out)
SFT only	21.6	11.4	16.8
Topo-R1	43.7	30.2	34.6

Table 16: Leave-one-domain-out generalization ([email protected], %). The held-out domain is excluded from training; the other two domains are used to train under the standard SFT

+

GRPO pipeline. Backbone: Qwen3-VL-4B.

Stratum	#Samples	HALVS	DRIVE	#Anomalies / sample
no_anomaly	314	274	40	0
single_anomaly	312	272	40	1
multi_anomaly_2_5	626	546	80	2–5
multi_anomaly_6_10	312	272	40	6–10
Total	1564	1364	200	—

Table 17: Composition of the OOD test set :

1{,}564

samples drawn from HALVS leaf-vein and DRIVE retinal-fundus images, stratified by ground-truth anomaly count per sample.

Method	[email protected]	[email protected]	[email protected]	aF1	Macro [email protected]	[email protected]
GPT-5.2 (zero-shot)	2.7	1.0	0.1	0.3	0.8	6.4
Gemini-2.5-Flash (zero-shot)	2.9	1.2	0.1	0.4	0.9	7.1
SFT only	33.9	24.4	14.8	14.9	21.8	36.6
Topo-R1	58.4	45.5	23.2	25.5	43.2	42.4

Table 18: OOD evaluation on HALVS leaf-vein and DRIVE retinal-fundus imagery (Qwen3-VL-4B).

Figure 6: Out-of-distribution qualitative results on leaf venation networks. Topo-R1 generalizes to an unseen domain (HALVS leaf veins) and correctly detects topological anomalies, such as broken and spurious connections, in the corrupted masks. From left to right: original image, ground-truth mask, corrupted mask with injected anomalies, and Topo-R1’s prediction. Red boxes denote predicted error regions.

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