# On the Identifiability of Controlled World Models

arXiv: https://arxiv.org/abs/2607.22430 · HTML: https://mlsanity.com/paper/2607.22430/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in Latent predictive world models, one of 11 directions in World models.
- Builds on 14 of its 23 references that are in the map.
- First posted on arXiv 24 Jul 2026.

## Placed in

- World models / [Latent predictive world models](https://mlsanity.com/wm/latent-predictive-world-models/)

## Builds on (most cited first, 14 of 14)

- [Dream to Control: Learning Behaviors by Latent Imagination](https://mlsanity.com/paper/1912.01603/) (2019)
- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [TD-MPC2: Scalable, Robust World Models for Continuous Control](https://mlsanity.com/paper/2310.16828/) (2023)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [LeWorldModel: Stable End-to-End Joint-Embedding Predictive Architecture from Pixels](https://mlsanity.com/paper/2603.19312/) (2026)
- [LeJEPA: Provable and Scalable Self-Supervised Learning Without the Heuristics](https://mlsanity.com/paper/2511.08544/) (2025)
- [Nonparametric Identifiability of Causal Representations from Unknown Interventions](https://mlsanity.com/paper/2306.00542/) (2023)
- [Identifiability of latent-variable and structural-equation models: from linear to nonlinear](https://mlsanity.com/paper/2302.02672/) (2023)
- [General Identifiability and Achievability for Causal Representation Learning](https://mlsanity.com/paper/2310.15450/) (2023)
- [On the Stability of Datatic Control Systems](https://mlsanity.com/paper/2401.16793/) (2024)

## Built on by (most cited first, 9 of 9)

- [What Can Latent World Models Know? Physical Parameter Identifiability in Multimodal Predictive Representations](https://mlsanity.com/paper/2607.27017/) (2026)
- [Finite-Sample Metric Non-Collapse for Geometrically Supervised Latent World Models in Control](https://mlsanity.com/paper/2608.07265/) (2026)
- [FIRM-WM: State-factorized factual-interventional recurrent modeling for reward-free visual planning](https://mlsanity.com/paper/2609.22816/) (2026)
- [I Act Therefore I Am: When Is JEPA's Action-Conditioning Enough to Learn Causal Mechanisms?](https://mlsanity.com/paper/2609.31161/) (2026)
- [Adaptive Latent Capacity for World Models](https://mlsanity.com/paper/2609.32921/) (2026)
- [LRC-JEPA: Disentangling Dynamics and Residual Context for Efficient World Models](https://mlsanity.com/paper/2609.34375/) (2026)
- [Control-Geometry Straightening for Sampling-Based Latent Planning](https://mlsanity.com/paper/2609.35603/) (2026)
- [Action-Consequence Alignment for Reliable Planning and Self-Improving in Latent World Models](https://mlsanity.com/paper/2610.04539/) (2026)
- [When Low Prediction Error Misleads Planning: Diagnosing Representation, Dynamics, and Decision Failures in Latent World Models](https://mlsanity.com/paper/2610.05550/) (2026)

## Abstract (arXiv)

World model serves as a promising tool to infer environment dynamics under high-dimensional observations and candidate actions. Recently, LeCun's JEPA provides a compelling framework for learning such models in representation space. Its action-conditioned extension plays a central role in visual control and latent-space planning, but leaves a fundamental question: can it recover the controlled dynamics from nonlinear observations? This paper presents a joint identifiability condition for controlled world models with Gaussian latent states, which consists of two coupled components: (1) representation identifiability and (2) transition identifiability. The former depends on the spectral separation property while the latter is related to non-degenerate variation of conditional action. We prove that when this condition holds, minimizing the LeJEPA-style predictive objective can recover both latent states and controlled dynamics in the sense of orthogonal transformation. We further prove that the upper bound of transition prediction error is inversely proportional to the spectral separation margin. We also characterize an attainable amplification of counterfactual prediction error that scales inversely with the weakest conditional action-excitation margin. The theoretical predictions are empirically supported across four nonlinear observation settings.