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<!DOCTYPE html>
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<div id="root">
<div class="min-h-screen bg-white">
<!-- Header Section -->
<div class="container mx-auto px-6 pt-12 pb-4">
<!-- Publication Venue -->
<div class="text-center mb-2">
<span class="text-sm text-gray-500 uppercase tracking-wider"></span>
<!-- Venue to be added -->
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<!-- Title -->
<h1 class="text-3xl md:text-4xl font-bold text-center mb-4">
Transductive Visual Programming:<br>
Evolving Tool Libraries from Experience for Spatial Reasoning
</h1>
<!-- Authors -->
<p class="text-center text-gray-600 mb-4">
<a href="https://danielwusg.github.io/" target="_blank" class="hover:text-blue-600">Shengguang Wu</a><sup>1</sup>,
<a href="https://ai.stanford.edu/~xhanwang/" target="_blank" class="hover:text-blue-600">Xiaohan Wang</a><sup>1</sup>,
<a href="https://cs.stanford.edu/~yuhuiz/" target="_blank" class="hover:text-blue-600">Yuhui Zhang</a><sup>1</sup>,
<a href="https://hao.computer/" target="_blank" class="hover:text-blue-600">Hao Zhu</a><sup>1</sup>,
<a href="https://ai.stanford.edu/~syyeung/" target="_blank" class="hover:text-blue-600">Serena Yeung-Levy</a><sup>1</sup>
</p>
<p class="text-center text-gray-600 text-base mb-6">
<sup>1</sup>Stanford University
</p>
<!-- Links -->
<div class="flex justify-center gap-4 mb-2">
<a href="https://arxiv.org/abs/2512.20934" class="icon-link">
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Read Paper
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<a href="https://github.com/transductive-visualprogram/tvp" class="icon-link">
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GitHub
</a>
<a href="https://x.com/ShengguangWu/status/2008713289568596267" class="icon-link">
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<h2 class="section-title">Abstract</h2>
<p class="text-gray-700 leading-relaxed">
Spatial reasoning in 3D scenes requires precise geometric calculations that challenge vision-language models.
Visual programming addresses this by decomposing problems into steps calling specialized tools,
yet existing methods rely on either fixed toolsets or speculative tool induction before solving problems, resulting in suboptimal programs and poor utilization of induced tools.
We present <strong>Transductive Visual Programming (TVP)</strong>, a novel framework that builds new tools from its own experience rather than speculation.
TVP first solves problems using basic tools while accumulating experiential solutions into an Example Library, then abstracts recurring patterns from these programs into reusable higher-level tools for an evolving Tool Library. This allows TVP to tackle new problems with increasingly powerful tools learned from experience.
On Omni3D-Bench, TVP achieves state-of-the-art performance, outperforming GPT-4o by <strong>22%</strong> and the previous best visual programming system by <strong>11%</strong>.
Our transductively learned tools are used <strong>5×</strong> more frequently as core program dependency than inductively created ones, demonstrating more effective tool discovery and reuse.
The evolved tools also show strong generalization to unseen spatial tasks, achieving superior performance on benchmarks from SpatialScore-Hard collection without any testset-specific modification.
Our work establishes experience-driven transductive tool creation as a powerful paradigm for building self-evolving visual programming agents that effectively tackle challenging spatial reasoning tasks.
</p>
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</div>
<!-- Method Section -->
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<h2 class="section-title">Method: TVP's Dual-Library Architecture</h2>
<p class="text-gray-700 mb-4">
TVP implements a closed-loop paradigm via two interconnected libraries: an <strong>Example Library</strong> that accumulates program solutions as experience, and a <strong>Tool Library</strong> that maintains functions abstracted from these programs. The dual-libraries enable the circular <strong>program-tool-program</strong> cycle: solving problems generates experience, experience guides tool creation, and newly created tools improve future problem-solving.
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<p class="figure-caption">
<strong>Figure:</strong> TVP's dual-library architecture. <strong>(Phase I)</strong> Problem-solving and experience accumulation: For each query, TVP retrieves similar examples from the Example Library and generates programs using the current Tool Library; high-quality solutions join the Example Library. <strong>(Phase II)</strong> Tool abstraction: Accumulated examples are clustered, and common patterns are abstracted into new tools, which, if passed validation, are added to the Tool Library for future use. <strong style="color: #3b82f6; cursor: pointer;" onclick="playVideo()">Click to play the animation.</strong>
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<h2 class="section-title">Results on Omni3D-Bench</h2>
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<button class="tab-btn active" onclick="switchTab('tab1')">Main Results</button>
<button class="tab-btn" onclick="switchTab('tab2')">Program Analysis</button>
<button class="tab-btn" onclick="switchTab('tab3')">Complexity Effects</button>
<button class="tab-btn" onclick="switchTab('tab4')">Model Scaling</button>
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<!-- Tab 1: Main Results Table -->
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<div class="finding-box">
<strong>TVP achieves state-of-the-art through experience-grounded tool creation.</strong>
On the challenging <a href="https://huggingface.co/datasets/dmarsili/Omni3D-Bench" target="_blank" class="text-blue-600 hover:underline">Omni3D-Bench</a>, TVP outperforms the previous best visual programming system <a href="https://glab-caltech.github.io/vadar" target="_blank" class="text-blue-600 hover:underline">VADAR</a> by +11% and GPT-4o by +22%.
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<table>
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<tr>
<th>Method</th>
<th>Yes/No</th>
<th>Multiple Choice</th>
<th>Counting</th>
<th>Float MRA</th>
<th>Float (±10%)</th>
<th>Overall (%)</th>
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</thead>
<tbody>
<tr><td colspan="7" class="font-semibold bg-gray-50">Generic VLMs</td></tr>
<tr>
<td>GPT-4o</td>
<td class="best-value">65.3</td>
<td class="second-best">60.5</td>
<td>18.6</td>
<td>26.7</td>
<td>8.2</td>
<td>27.2</td>
</tr>
<tr>
<td>Qwen2-VL-7B-Inst</td>
<td>58.7</td>
<td>33.7</td>
<td>12.9</td>
<td>21.5</td>
<td>10.0</td>
<td>21.8</td>
</tr>
<tr>
<td>LLaVA-OV-7B-Chat</td>
<td class="second-best">60.0</td>
<td>27.9</td>
<td class="second-best">22.9</td>
<td>26.8</td>
<td>11.1</td>
<td>23.0</td>
</tr>
<tr>
<td>Molmo-7B-D</td>
<td>46.7</td>
<td>41.9</td>
<td>18.6</td>
<td>28.4</td>
<td>8.9</td>
<td>21.6</td>
</tr>
<tr><td colspan="7" class="font-semibold bg-gray-50">Spatial-Finetuned VLMs</td></tr>
<tr>
<td>SpaceMantis</td>
<td>53.3</td>
<td>30.2</td>
<td>4.3</td>
<td>21.4</td>
<td>8.2</td>
<td>18.2</td>
</tr>
<tr>
<td>SpatialBot-3B</td>
<td class="second-best">60.0</td>
<td>30.2</td>
<td>0.0</td>
<td>17.7</td>
<td>8.5</td>
<td>18.8</td>
</tr>
<tr><td colspan="7" class="font-semibold bg-gray-50">Visual Programming</td></tr>
<tr>
<td>VisProg</td>
<td>54.7</td>
<td>25.9</td>
<td>2.9</td>
<td>0.9</td>
<td>-</td>
<td>-</td>
</tr>
<tr>
<td>ViperGPT</td>
<td>56.0</td>
<td>42.4</td>
<td>20.0</td>
<td>15.4</td>
<td>-</td>
<td>-</td>
</tr>
<tr>
<td>VADAR</td>
<td>56.0</td>
<td>57.6</td>
<td>21.7</td>
<td class="second-best">35.5</td>
<td>15.9</td>
<td>29.9</td>
</tr>
<tr class="highlight-row">
<td><strong>TVP (Full System)</strong></td>
<td class="second-best">60.0</td>
<td class="best-value">61.6</td>
<td class="best-value">24.3</td>
<td class="best-value">36.5</td>
<td class="best-value">19.3</td>
<td class="best-value">33.3</td>
</tr>
<tr>
<td>TVP (Example-Lib-Only, w/o Tool Lib)</td>
<td class="second-best">60.0</td>
<td class="best-value">61.6</td>
<td>21.4</td>
<td>35.5</td>
<td>17.0</td>
<td>31.7</td>
</tr>
</tbody>
</table>
</div>
<p class="text-sm text-gray-500 mt-3">
<strong>Best</strong> in bold, <span class="second-best">second best</span> underlined. Performance on Omni3D-Bench across different question types.
</p>
</div>
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<div class="finding-box">
<strong>TVP enables simpler, more accurate, and continuously improving programs.</strong>
(a) Program complexity steadily decreases; (b) programs gain +3.4% accuracy when switching to abstracted tools; (c) programs utilizing abstracted tools improve +38% across iterations.
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<img src="imgs/complexity_evol_acc_evol_with_newAPI_panela.png" alt="Complexity Reduction" class="w-full rounded-lg" />
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<strong>(a) CNN reduction</strong> as abstracted tools replace multi-step patterns.
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<img src="imgs/complexity_evol_acc_evol_with_newAPI_panelb.png" alt="Accuracy Gain" class="w-full rounded-lg" />
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<strong>(b) Accuracy gains</strong> +3.4% when switching from basic tools to abstracted tools.
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<strong>(c) Iterative improvement</strong> (+38%) with abstracted tools (22.4% → 31.0%).
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<p class="figure-caption mt-4">
<strong>Figure:</strong> TVP's closed-loop learning produces three measurable benefits. These improvements stem from experience-grounded tool creation: each abstracted function encapsulates recurring high-quality program solutions and passes rigorous validation.
</p>
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<div class="finding-box">
<strong>Tool abstraction facilitates progressive self-improvement, especially on hard problems.</strong>
On the hardest batch, TVP-Full (= with active tool creation) shows the most significant improvement trajectory, starting at -4.5% relative to Example-Lib-Only (=no tool creation) variant in iteration 1, but ultimately surpassing it by +6.7% in iteration 3.
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<img src="imgs/complexity_buckets_overall_performance.png" alt="Complexity Comparison" class="w-full rounded-lg" />
<p class="figure-caption">
<strong>Figure:</strong> Performance comparison across question complexity levels (Easy, Medium, Hard). TVP-full-system delivers the best performance on both Easy and Hard batches.
</p>
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<img src="imgs/complexity_buckets_delta_examplelibonly.png" alt="Performance Delta" class="w-full rounded-lg" />
<p class="figure-caption">
<strong>Figure:</strong> Performance delta between TVP (Full) and TVP (Example-Lib-Only) across iterations for each complexity level. The hardest questions show the largest improvement (+6.7% by iteration 3) enabled by active tool creation.
</p>
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<strong>Key Insight:</strong> For easy questions, thoroughly validated created tools avoid potential reimplementation errors, leading to more stable performance. For harder questions, created tools provide simpler solution steps that eliminate complicated logic, thus easing the program reasoning.
</p>
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<!-- Tab 4: Model Scaling -->
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<div class="finding-box">
<strong>TVP shows a clear scaling trend with backbone model sizes.</strong>
Using an open-source 32B model, TVP achieves competitive performance close to the GPT-4o-backed variant (30.7% vs. 31.3%).
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<img src="imgs/scaling_trend.png" alt="Model Scaling Trend" class="w-full rounded-lg" />
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<strong>Figure:</strong> TVP performance scales consistently with backbone model capacity.
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<h4 class="font-semibold text-blue-800 mb-2">Scaling Behavior</h4>
<p class="text-gray-700">Using the Qwen2.5-Coder-Instruct family (7B → 14B → 32B), TVP exhibits clear performance improvement with increasing model capacity. TVP's architecture is model-agnostic and holds future potential as foundation models improve.
</p>
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<h4 class="font-semibold text-green-800 mb-2">Practical Implication</h4>
<p class="text-gray-700">TVP does not rely on proprietary-specific optimal LLMs but can achieve strong performance with more accessible open-source alternatives, making this transductive tool creation paradigm highly accessible for research and deployment.
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<!-- Tab 5: Library Evolution -->
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<div class="finding-box">
<strong>TVP's dual libraries evolve steadily through closed-loop dual-library interaction.</strong>The Example Library grows to 304 high-quality solutions while the Tool Library expands strategically—creating 61 tools total but maintaining 11 active abstractions through periodic merging.
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<strong>Figure:</strong> Evolution trajectory of TVP's dual libraries. The Example Library grows steadily to 304 solutions while the Tool Library expands with controlled maintenance.
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<!-- Text Explanation (Right) -->
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<h4 class="font-semibold text-purple-800 mb-2">Example Library</h4>
<p class="text-gray-700 text-sm">
Grows from 0 to <strong>304</strong> high-quality solutions, accumulating concrete problem-solving experience that grounds tool abstraction.
</p>
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<h4 class="font-semibold text-orange-800 mb-2">Tool Library</h4>
<p class="text-gray-700 text-sm">
<strong>61</strong> tools created total, <strong>11</strong> remain active after periodic merging to reduce redundancy and improve tool selection.
</p>
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<h4 class="font-semibold text-blue-800 mb-2">Key Insight</h4>
<p class="text-gray-700 text-sm">
Selective retention ensures a manageable Tool Library capturing genuinely reusable abstractions with minimal redundancy.
</p>
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</div>
<!-- Generalization Section -->
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<div class="card">
<h2 class="section-title">Generalizing To Unseen Spatial Reasoning Queries</h2>
<p class="text-gray-700 mb-4">
Through TVP's transductive paradigm, tools abstracted from experience on one benchmark should capture fundamental reasoning patterns that generalize to new questions. As shown below, TVP's dual libraries, built only on Omni3D-Bench, transfer to unseen spatial reasoning queries from <a href="https://haoningwu3639.github.io/SpatialScore" target="_blank" class="text-blue-600 hover:underline">SpatialScore-Hard collection</a> without any modification.
</p>
<div class="finding-box">
<strong>Transductively created tools generalize with strong zero-shot performance.</strong>
TVP's experience-grounded tools and libraries still lead to superior solutions even in zero-shot transfer.
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<h3 class="font-semibold mb-3">Results on Sampled SpatialScore-Hard Collection</h3>
<div class="overflow-x-auto flex-1">
<table>
<thead>
<tr>
<th>Method</th>
<th>3DSR-Bench</th>
<th>SpatialSense</th>
<th>VG-Bench</th>
<th>Overall</th>
</tr>
</thead>
<tbody>
<tr><td colspan="5" class="font-semibold bg-gray-50">Generic VLMs</td></tr>
<tr>
<td>GPT-4o</td>
<td class="second-best">52.1</td>
<td>46.5</td>
<td>20.3</td>
<td class="second-best">42.6</td>
</tr>
<tr>
<td>LLaVA-OV-7B-Chat</td>
<td>12.4</td>
<td>9.9</td>
<td>9.4</td>
<td>10.9</td>
</tr>
<tr>
<td>Qwen2-VL-Inst</td>
<td>49.6</td>
<td>32.4</td>
<td>7.8</td>