Space Is Intelligence: Neural Semigroup Superposition for Riemannian Metric Generation

• URL: http://arxiv.org/abs/2606.18828v1
• Date: Wed, 17 Jun 2026 09:03:18 GMT
• Title: Space Is Intelligence: Neural Semigroup Superposition for Riemannian Metric Generation
• Abstract summary: A single-magnitude network realizes this idea through three complementary parameter groups.<n>Trained on a single two-obstacle scene, the model demonstrates robust zero-shot generalization across unseen obstacle configurations.
• Score: 10.790210744021069
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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