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arXiv 2605.07148cs.CV

揭示和塑造视觉-语言模型中3D场景拓扑的潜在表示

Uncovering and Shaping the Latent Representation of 3D Scene Topology in Vision-Language Models

Department of Electrical and Computer Engineering(电气与计算机工程系)

Haoming Wang, Wei Gao

AI总结:

本文研究了视觉-语言模型是否能构建3D环境的拓扑表示,通过隔离空间子空间并数学塑造潜在表示,证明其与场景3D高斯核图的拉普拉斯特征映射一致,并在空间任务中提升性能。

摘要:

几十年的认知科学表明,人类通过形成认知图来导航环境,认知图被定义为3D空间的 allocentric 且拓扑保持的表示。尽管现代视觉-语言模型(VLMs)从2D egocentric输入中表现出涌现的空间推理能力,但尚不清楚它们是否构建了类似的3D内部表示。本文证明当前VLMs确实具有3D场景的潜在拓扑地图,但该地图被非几何视觉语义(如颜色和形状)严重掩盖。通过跨场景线性特征提取隔离空间子空间,我们提取出一个干净的空间子空间,该子空间因果控制模型的空间输出。我们数学上塑造了该潜在表示,并证明其与场景3D高斯核图的拉普拉斯特征映射一致,在连续极限下收敛到物理3D空间。受此几何识别的启发,我们进一步引入基于狄利克雷能量的数学原理性潜在正则化方法用于VLMs。将此单一项正则化器应用于最小的500步监督VLM微调(SFT)在简单合成数据上,显著提升了现实空间基准性能,在涉及场景拓扑理解的空间任务中,优于标准SFT和竞争基线,最高提升12.1%。源代码可在https://github.com/pittisl/vlm-latent-shaping获取。

英文摘要:

Decades of cognitive science establish that humans navigate environments by forming cognitive maps, defined as allocentric and topology-preserving representations of 3D space. While modern Vision-Language Models (VLMs) demonstrate emergent spatial reasoning from 2D egocentric inputs, it remains unclear whether they construct an analogous 3D internal representation. In this paper, we demonstrate that current VLMs do possess a latent topological map of 3D scenes, but it is heavily overshadowed by non-geometric visual semantics, such as color and shape. By isolating this spatial subspace through cross-scene linear feature extraction, we extract a clean spatial subspace that causally controls the model's spatial outputs. We mathematically shape this latent representation and prove its correspondence to the Laplacian eigenmaps of the scene's 3D Gaussian-kernel graph, converging to the physical 3D space in the continuous limit. Motivated by this geometric identification, we further introduce a mathematically principled latent regularization method for VLMs, based on Dirichlet energy. Applying this single-term regularizer to a minimal 500-step supervised VLM fine-tuning (SFT) on simple synthetic data yields significant improvements on real-world spatial benchmarks, outperforming standard SFT and competitive baselines by up to 12.1\% in spatial tasks involving scene topology understanding. Source code is available at https://github.com/pittisl/vlm-latent-shaping

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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