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Life sciences · Preprint
arXiv · September 10, 2026
Early or partial results. Treat as a signal, not a conclusion.
This is an unreviewed preprint introducing a topological method for extracting reusable subgoals from reinforcement learning trajectories, tested on three simulated robotic control environments. The method shows transfer across different robot morphologies (PointMaze to Ant to Humanoid) without retraining, but has not undergone peer review and is restricted to simulation with no clinical or real-world validation.
Simulation-based algorithm development study with transfer learning experiment. Simulated robotic agents in three environments; no human, animal, or clinical population. Intervention: Topological necessities: mechanism-invariant strategic subgoals extracted as certified gates from offline trajectories and applied via recursive topological gate hierarchy. Compared with: Map-privileged reference and baseline methods on AntMaze and Kitchen tasks.
Humanoid aggregate performance on unified interface: 96.1, with +36.0 improvement over map-privileged reference on multi-route task (p=1.4e-5) PointMaze planner saturates performance at 100+/-0 AntMaze: +22.9 over strongest baselines
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An unreviewed machine learning methods paper presenting a novel algorithm on simulated robotic control tasks with no clinical or direct human outcomes, and no comparison to human performance or real-world deployment.
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Long-horizon goal-conditioned reinforcement learning delegates control to a high-level module that proposes subgoals, but existing subgoals are implicit byproducts of value functions or latent actions, tied to the executor that produced them. We study a different object: a route-conditioned order of unavoidable stages that every successful executor must traverse, recoverable from offline trajectories and belonging to none of them. Its defining properties are topological: an unskippable stage is a separating set that every admissible path must cross, and a loop in free space forces a route choice. We read the two by homology in dimensions 0 and 1 over a transport-weighted carrier built from successful trajectories, yielding an enumerable gate set with shell-level certificates; the certified gates are what we call topological necessities. Certified gates enter the decision loop as a recursive topological gate hierarchy. Under a fixed, isomorphic free space, the object survives executor replacement: gates frozen on PointMaze data transfer without retraining to Ant and Humanoid, attaining the highest Humanoid aggregate under a unified interface (96.1), with +36.0 over a map-privileged reference on the multi-route task (p=1.4e-5); the planner saturates PointMaze (100+/-0) and matches or exceeds the strongest baselines on AntMaze (giant +22.9) and Kitchen (+15.8/+12.6).
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