Topological Necessities: Mechanism-Invariant Strategic Subgoals for Cross-Embodiment Goal-Conditioned Control
Updated 1 h ago · first seen 11 Sept 2026
paper_01M294FNYAF3FJCMH6BPTT0BMD
- Published
- 11 Sept 2026
- T1 · 1 h ago
- arXiv
- 2609.11014
- T1 · 1 h ago
- Category
- cs.LG
- T1 · 1 h 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 1 h agohigh
- Arxiv announce type
- new
Source:arXiv (Atom API + RSS)T1observed 1 h agohigh
- arXiv id
- 2609.11014
Source:arXiv (Atom API + RSS)T1observed 1 h agohigh
- Categories
- cs.LG, cs.AI, cs.RO
Source:arXiv (Atom API + RSS)T1observed 1 h agohigh
Source:arXiv (Atom API + RSS)T1observed 1 h agohigh
- Primary category
- cs.LG
Source:arXiv (Atom API + RSS)T1observed 1 h agohigh
- Published
- 11 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 1 h 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
1 h ago
Conflicts
None
No models linked to this paper yet.
As of
Rewind the record: see this entity's attributes exactly as AI Atlas knew them on a given day.
Claim history
Official pageofficial_url1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| https://arxiv.org/abs/2609.11014 | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Abstractabstract1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| 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). | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Arxiv announce typearxiv_announce_type1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| new | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
arXiv idarxiv_id1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| 2609.11014 | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Categoriescategories1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| cs.LG, cs.AI, cs.RO | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
PDFpdf_url1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| https://arxiv.org/pdf/2609.11014 | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Primary categoryprimary_category1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| cs.LG | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Publishedpublished_at1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| 11 Sept 2026 | → 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 →
- 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
arxiv
| Source | Document | Type | Tier | Last observed | Snapshots |
|---|---|---|---|---|---|
| arXiv (Atom API + RSS) | rss.arxiv.org/rss/cs.LG | feed | T1· Official | 1 h ago | 1 |
Tier 1 = official/primary, 2 = quality secondary, 3 = community, 4 = unverified. Every snapshot is archived; see all sources and the methodology.