Space Is Intelligence: Neural Semigroup Superposition for Riemannian Metric Generation

Published June 18, 2026 · Category: Robotics

Overview

arXiv:2606.18828v1 Announce Type: new Abstract: 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.

Source

Originally published at arxiv.org.

Related Articles

• Self-Supervised Mask-Aware Transformers for Fault-Tolerant FBG Force Sensing in Minimally Invasive Surgical Robotics
• EffiNav: Fusing Depth and Vision-Language for Efficient Object Goal Navigation
• A Scalable Embodied Intelligence Platform for Seamless Real-to-Sim-to-Real Transfer of Household Mobile Manipulation Tasks