让空间本身具备智能，用几何路径代替传统规划。
Space Is Intelligence: Neural Semigroup Superposition for Riemannian Metric Generation
- 将智能融入场景空间，通过黎曼度量生成最优路径。
- 单场景训练后零样本泛化，障碍物穿透路径代价高出数个数量级。
- 适合研究具身智能、机器人路径规划的读者。
传统方法将智能赋予智能体自身，如学习策略或搜索过程。本文则将智能置于空间本身：场景在配置流形上诱导出黎曼度量，行动转化为遵循该度量的测地线，无需独立规划器或碰撞检测。一个编码器-路由网络通过三组互补参数实现此思想——帧参数用于定向生成器，调制参数控制其空间传播，基础系数决定其强度。这些参数通过共享的半群叠加机制结合，生成单一黎曼度量场，形成紧凑架构，其几何复杂度可自然随场景变化。模型在单一双障碍物场景上训练，即展现出对未见障碍配置的稳健零样本泛化，碰撞规避路径与障碍穿透路径的成本之间存在数量级差异。
原文摘要 · Abstract (English)
Traditional approaches place intelligence in the agent, whether as a learned policy or a search procedure. We instead place intelligence in the space itself: a scene induces a Riemannian metric on the configuration manifold, and action reduces to following the geodesics of that metric rather than invoking a separate planner or collision checker. A single Encoder-Router network realizes this idea through three complementary parameter groups -- frame parameters that orient the generators, modulation parameters that govern their spatial propagation, and basic coefficients that determine their strength. These groups combine through a shared semigroup-superposition mechanism to produce a single Riemannian metric field, yielding a compact architecture whose geometry scales naturally with scene complexity. Trained on a single two-obstacle scene, the model demonstrates robust zero-shot generalization across unseen obstacle configurations, with orders-of-magnitude separation between collision-free and obstacle-penetrating path costs.
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