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

Abstract

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).

Authors 2

Hao Shi, Xi Li

Specification

Official page: arxiv.org/abs/2609.11014
Source:arXiv (Atom API + RSS)T1observed 43 min agohigh
Arxiv announce type: new
Source:arXiv (Atom API + RSS)T1observed 43 min agohigh
arXiv id: 2609.11014
Source:arXiv (Atom API + RSS)T1observed 43 min agohigh
Categories: cs.LG, cs.AI, cs.RO
Source:arXiv (Atom API + RSS)T1observed 43 min agohigh
PDF: arxiv.org/pdf/2609.11014
Source:arXiv (Atom API + RSS)T1observed 43 min agohigh
Primary category: cs.LG
Source:arXiv (Atom API + RSS)T1observed 43 min agohigh
Published: 11 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 43 min agohigh

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9

Source tiers

T19

Freshest observation

43 min ago

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None

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Authors: Hao Shi, Xi Li

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Claim history for arXiv id
Value	Valid from → to	Status	Source	Confidence	Extractor
2609.11014	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Claims are temporal and append-only: a new observation closes the previous claim (valid_to) instead of overwriting it. Conflicting claims from different sources are kept side by side and flagged — never averaged. Methodology →

11 Sept 2026
New paperPaperTopological Necessities: Mechanism-Invariant Strategic Subgoals for Cross-Embodiment Goal-Conditioned Control
New paper: Topological Necessities: Mechanism-Invariant Strategic Subgoals for Cross-Embodiment Goal-Conditioned Control
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Source documents
Source	Document	Type	Tier	Last observed	Snapshots
arXiv (Atom API + RSS)	rss.arxiv.org/rss/cs.LG	feed	T1· Official	43 min ago	1

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