On the Identifiability of Controlled World Models
Mirrored from arXiv — Machine Learning for archival readability. Support the source by reading on the original site.
Computer Science > Machine Learning
Title:On the Identifiability of Controlled World Models
Abstract:Learning world models that infer environment dynamics from high-dimensional observations and predict outcomes under candidate actions is central to planning and control. Joint-Embedding Predictive Architectures (JEPAs) provide a compelling framework for learning such models in representation space. Recent action-conditioned extensions perform promisingly in visual control and latent-space planning, but leave a fundamental question unresolved: when does controlled latent prediction identify both the underlying state and the controlled dynamics? This is challenging under nonlinear observations and behavior policies with limited conditional action variation, where state-dependent evolution and action effects can be statistically confounded. We establish a joint identifiability theory for controlled world models with Gaussian latent states under state-dependent Gaussian behavior policies. We identify two policy-dependent conditions: spectral separation of the predictable signal governs representation identifiability, while non-degenerate conditional action variation governs transition identifiability. We prove that when both conditions hold, every global minimizer of the JEPA objective identifies the latent state and controlled transition up to an orthogonal transformation. We further derive quantitative bounds on representation and transition identifiability under approximate optimization. Finally, we construct predictor perturbations along weakly excited action directions whose counterfactual-to-on-policy error ratio is the inverse transition-identifiability margin, revealing the cost of limited action coverage. Experiments across nonlinear observation maps and behavior policies corroborate the theory and demonstrate implications for transition identifiability, counterfactual prediction, and goal-conditioned latent planning.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2607.22430 [cs.LG] |
| (or arXiv:2607.22430v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2607.22430
arXiv-issued DOI via DataCite (pending registration)
|
Access Paper:
- View PDF
- HTML (experimental)
- TeX Source
References & Citations
Bookmark
Bibliographic and Citation Tools
Code, Data and Media Associated with this Article
Demos
Recommenders and Search Tools
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
More from arXiv — Machine Learning
-
LoKiFormer: Locality-aware Attention with Decoupled Knowledge Memory for Efficient Large Language Model Pretraining
Aug 14
-
Which Site, and When: A Free-Satellite-Data Test of Himalayan Glacial Lake Bursts, Landslides, and Ice Floods
Aug 14
-
MARCH: Scaling Recurrent Memory with Content-Routed State Anchors
Aug 14
-
Multi-AUV Ad-hoc network-based Target Tracking: A Value Gradient Guidance Multi-Agent Diffusion Reinforcement Learning Approach
Aug 14
Discussion (0)
Sign in to join the discussion. Free account, 30 seconds — email code or GitHub.
Sign in →No comments yet. Sign in and be the first to say something.