Skip to content
AI Atlas
PaperActive

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

arxiv.org/abs/2609.11014

Updated 15 min ago · first seen 11 Sept 2026

paper_01M294FNYAF3FJCMH6BPTT0BMD

Published
11 Sept 2026
T1 · 15 min ago
arXiv
2609.11014
T1 · 15 min ago
Category
cs.LG
T1 · 15 min ago

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

Source:arXiv (Atom API + RSS)T1observed 15 min agohigh

Arxiv announce type
new

Source:arXiv (Atom API + RSS)T1observed 15 min agohigh

arXiv id
2609.11014

Source:arXiv (Atom API + RSS)T1observed 15 min agohigh

Categories
cs.LG, cs.AI, cs.RO

Source:arXiv (Atom API + RSS)T1observed 15 min agohigh

PDF

Source:arXiv (Atom API + RSS)T1observed 15 min agohigh

Primary category
cs.LG

Source:arXiv (Atom API + RSS)T1observed 15 min agohigh

Published
11 Sept 2026

Source:arXiv (Atom API + RSS)T1observed 15 min agohigh

Each value shows its source, tier and observation time. Conflicting claims are kept side by side and flagged — never averaged. How AI Atlas records facts →

Provenance

Attributed facts

9

Source tiers

T19

Freshest observation

15 min ago

Conflicts

None