# When Does LeJEPA Learn a World Model?

arXiv: https://arxiv.org/abs/2605.26379 · HTML: https://mlsanity.com/paper/2605.26379/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Placed in Latent predictive world models, one of 11 directions in World models.
- Builds on 54 of its 95 references that are in the map.
- First posted on arXiv 25 May 2026.

## Placed in

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

## Builds on (most cited first, 30 of 54)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [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)
- [VICReg: Variance-Invariance-Covariance Regularization for Self-Supervised Learning](https://mlsanity.com/paper/2105.04906/) (2021)
- [Self-Supervised Learning from Images with a Joint-Embedding Predictive Architecture](https://mlsanity.com/paper/2301.08243/) (2023)
- [DeepMind Control Suite](https://mlsanity.com/paper/1801.00690/) (2018)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [WorldSimBench: Towards Video Generation Models as World Simulators](https://mlsanity.com/paper/2410.18072/) (2024)
- [V-JEPA 2: Self-Supervised Video Models Enable Understanding, Prediction and Planning](https://mlsanity.com/paper/2506.09985/) (2025)
- [Genie: Generative Interactive Environments](https://mlsanity.com/paper/2402.15391/) (2024)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [Revisiting Feature Prediction for Learning Visual Representations from Video](https://mlsanity.com/paper/2404.08471/) (2024)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [DINO-WM: World Models on Pre-trained Visual Features enable Zero-shot Planning](https://mlsanity.com/paper/2411.04983/) (2024)
- [Self-Supervised Learning with Data Augmentations Provably Isolates Content from Style](https://mlsanity.com/paper/2106.04619/) (2021)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Embed to Control: A Locally Linear Latent Dynamics Model for Control from Raw Images](https://mlsanity.com/paper/1506.07365/) (2015)
- [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)
- [Unsupervised Learning for Physical Interaction through Video Prediction](https://mlsanity.com/paper/1605.07157/) (2016)

## Built on by (most cited first, 30 of 30)

- [A Control Theory of Predictability in Latent World Models](https://mlsanity.com/paper/2607.10362/) (2026)
- [A Generalization Theory for JEPA-Based World Models](https://mlsanity.com/paper/2606.27014/) (2026)
- [What Can Latent World Models Know? Physical Parameter Identifiability in Multimodal Predictive Representations](https://mlsanity.com/paper/2607.27017/) (2026)
- [Diagnosing JEPA World Models with Action-Conditioned Predictive Consistency](https://mlsanity.com/paper/2608.12939/) (2026)
- [The SIGReg Objective as Variational Free Energy: A Theoretical Active-Inference Account of JEPA World Models](https://mlsanity.com/paper/2607.13612/) (2026)
- [Identifiability Without Gaussianity: Symbolic World Models and Near-Infinite Temporal Consistency](https://mlsanity.com/paper/2606.12471/) (2026)
- [Beyond Gaussian Worlds: Latent Geometry Matters for JEPAs](https://mlsanity.com/paper/2609.21656/) (2026)
- [MotionJEPA: Preventing Temporal Feature Collapse by Capturing Visual Changes in Latent Space](https://mlsanity.com/paper/2609.23881/) (2026)
- [World-as-Graph: Relational World Modeling Through Latent Space Graphs](https://mlsanity.com/paper/2609.38927/) (2026)
- [DALE-CT: Depth-Aware 2D Slice Encoders Learn an Anatomical World Model of Chest CT](https://mlsanity.com/paper/2606.07775/) (2026)
- [Information Lattice Learning as Probabilistic Graphical Model Structure Learning](https://mlsanity.com/paper/2606.19366/) (2026)
- [Reduced-Order Models: The Mother of World Models](https://mlsanity.com/paper/2607.03198/) (2026)
- [CellWorld: From Gene-Level Reconstruction to Latent Cell Prediction in Spatial Transcriptomics Foundation Models](https://mlsanity.com/paper/2608.06659/) (2026)
- [Finite-Sample Metric Non-Collapse for Geometrically Supervised Latent World Models in Control](https://mlsanity.com/paper/2608.07265/) (2026)
- [A Unifying Perspective on Causal World Models: From Observations to Representations to Structure](https://mlsanity.com/paper/2608.13456/) (2026)
- [Capturing Cardiac Cyclicity through Phase-Equivariant Self-Supervised Learning](https://mlsanity.com/paper/2608.21147/) (2026)
- [High-probability guarantees for linear accessibility in feature superposition](https://mlsanity.com/paper/2609.09556/) (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)
- [MA-JEPA: Joint-Embedding World Models for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2609.33563/) (2026)
- [LRC-JEPA: Disentangling Dynamics and Residual Context for Efficient World Models](https://mlsanity.com/paper/2609.34375/) (2026)
- [PDE-JEPA: Predictive Representation Learning of Latent Dynamics Modeling for Parametric PDEs](https://mlsanity.com/paper/2609.34715/) (2026)
- [λ-JEPA Spectral Anti-Collapse Regularization for Self-Supervised Learning](https://mlsanity.com/paper/2609.35288/) (2026)
- [Anisotropic Representations Improve Planning in JEPA World Models](https://mlsanity.com/paper/2609.37441/) (2026)
- [Beyond a single latent space: a dual-latent world model for long-horizon planning](https://mlsanity.com/paper/2609.37644/) (2026)
- [GLaS-JEPA: Gaussian-Regularized Speech SSL without Engineered Prediction Targets](https://mlsanity.com/paper/2609.37798/) (2026)
- [Frozen in a Frame: The Velocity Blind Spot in JEPA World Models](https://mlsanity.com/paper/2610.04585/) (2026)
- [DSReg: Provably Recovering Individual World Latents without Reconstruction](https://mlsanity.com/paper/2610.09457/) (2026)
- [Shared Gaussianization: What Gaussian Regularizers Certify About Contrastive Learning, and What They Miss](https://mlsanity.com/paper/2610.10299/) (2026)
- [SplitJEPA: Learning Invariant and Variant Latent Worlds without Reconstruction](https://mlsanity.com/paper/2610.12349/) (2026)

## Abstract (arXiv)

A representation that scrambles the true degrees of freedom of the world cannot support reliable planning or compositional generalization. We prove that LeJEPA (alignment plus Gaussian regularization) linearly recovers the world's latent variables from nonlinear observations, a property known as linear identifiability, in a broad class of worlds where latents evolve under stationary, additive-noise transitions. Our main result is that among all such worlds, the Gaussian is the unique latent distribution for which this guarantee holds. The forward direction rests on a spectral decomposition in which each degree of nonlinearity is strictly penalized by alignment, making the linear map the optimum; the converse rules out every non-Gaussian alternative. We further prove an approximate identifiability result where the guarantee degrades gracefully, and show that linear, orthogonal identifiability enables optimal latent-space planning. We validate the theory with experiments ranging from 2D examples to 1024-dimensional latents, including distributional ablations and pixel-based robotic control. Our theory turns an empirically successful recipe into a mathematical guarantee, providing the foundation for building World Models that provably recover the structure of the world.