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arXiv Machine Learning By Hao Shi, Xi Li

Topological Necessities: Mechanism-Invariant Strategic Subgoals for Cross-Embodiment Goal-Conditioned Control

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The paper introduces topological necessities—mechanism‑invariant subgoals derived from the topology of successful trajectories—used to guide long‑horizon goal‑conditioned reinforcement learning. By computing homology in dimensions 0 and 1 over a transport‑weighted carrier, the authors obtain an enumerable gate set that forms a recursive topological gate hierarchy. These certified gates transfer across different embodiments (e.g., from PointMaze to Ant and Humanoid) without retraining, achieving state‑of‑the‑art performance on several benchmark tasks.

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