发表机构
National Engineering Research Center of Robot Visual Perception and Control Technology（机器人视觉感知与控制技术国家工程研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出了由单个因果对比损失训练的连续度量场框架，可跨维度发现几何结构，在机器人导航和黑洞场景中均表现出良好性能，具备零样本泛化能力。
AI 中文摘要
我们提出了一种由单个因果对比损失训练的连续度量场框架。该框架将场景编码为固定对称矩阵基的系数，组装成李代数元素，并将结果指数化为黎曼或洛伦兹度量。在跨维度场景中，该场发现了完整的几何结构谱：从机器人导航中平面和机械臂配置空间里避障测地线，到洛伦兹时空中黑洞的事件视界。大量零样本泛化研究表明，该场捕获的是可迁移的几何结构，而非对特定配置的记忆。在黑洞场景中，因果损失自发演化出具有正确洛伦兹符号的类黑洞真实结构。相同的损失、相同的架构和相同的训练协议，可在跨维度场景中产生全范围的几何现象。该场知晓几何，而几何知晓物理。
英文摘要
We introduce a continuous metric field framework trained by a single causal contrastive loss. The framework encodes a scene into coefficients of a fixed symmetric matrix basis, assembles them into a Lie algebra element, and exponentiates the result to a Riemannian or Lorentzian metric. Across dimensions, this field discovers the full spectrum of geometric structures: from obstacle-avoiding geodesics in robot navigation across planar and manipulator configuration spaces, to event horizons of black holes in Lorentzian spacetime. Extensive zero-shot generalization studies demonstrate that the field captures transferable geometric structure rather than memorizing specific configurations. In the black hole setting, the causal loss spontaneously evolves genuine black-hole-like structures with the correct Lorentzian signature. The same loss, the same architecture, and the same training protocol produce the full range of geometric phenomena across dimensions. The field knows geometry, and geometry knows physics.
