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CurveBench: A Benchmark for Exact Topological Reasoning over Nested Jordan Curves

NeurIPS 2026 · Vision-language and multimodal › Multimodal LLMs · approach: Chain-of-thought multimodal reasoning · 0 citations (OpenAlex)

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Introduces CurveBench, a 756-image benchmark requiring VLMs to recover exact rooted containment trees from nested disjoint Jordan curves, and shows RLVR (Dr.GRPO + LoRA) fine-tuning of Qwen3-VL-8B improves exact tree accuracy on the Easy split.

Problem

Vision-language models struggle to recover exact hierarchical containment (rooted region trees) from images of pairwise non-intersecting Jordan curves, a topological reasoning capability not measured by existing diagram or VQA benchmarks.

Approach

A deterministic structured-prediction benchmark where the target is the exact rooted containment tree of planar regions, scored by exact tree isomorphism, paired with verifiable-reward RL fine-tuning of open VLMs using a combined node-count and tree reward.

Key results

• Gemini 3.1 Pro achieves 71.1% tree accuracy on CurveBench-Easy and 19.1% on CurveBench-Hard.
• RLVR-tuned Qwen3-VL-8B raises Easy tree accuracy from 2.8% (base Thinking) to 33.3%, exceeding GPT-5.4 (30.6%) and Claude Opus 4.5 (32.2%).
• On CurveBench-Hard, the tree-only Qwen3-VL-8B variant reaches 7.0% tree accuracy versus 4.2% for its base model.

Surprising findings

• Qwen3-VL-8B-Instruct outperforms the Thinking variant on CurveBench-Easy average reward (0.108 vs 0.038), partly due to the 8192-token limit truncating thinking outputs.
• Fine-tuned model regressed on the Maze subset relative to the Thinking base model.

Limitations

• Benchmark is small (756 images) and synthetic/hand-drawn, limiting ecological validity.
• RL training uses only the Easy split; transfer to Hard is limited.
• Exact tree match is coarse and does not grade near-correct predictions.

Experimental setup

Datasets: CurveBench-Easy CurveBench-Hard

Benchmarks: CurveBench-Easy CurveBench-Hard

Metrics: tree generation accuracy node count accuracy average reward

Baselines: Gemini 3.1 Pro Gemini 3 Pro GPT-5.4 Claude Opus 4.5 GPT-5.2 Qwen3-VL-8B-Thinking Qwen3-VL-8B-Instruct Gemma-3-12B-it

Builds on: GRPO Dr.GRPO LoRA RLVR VLM-R1

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