JEPA (Joint-Embedding Predictive Architectures) models are a popular type of world model. They learn to create predictions in a representation space, instead of pixel space. Because of this, they are very compute-efficient. They are also very capable in planning, image recognition, and other tasks [2, 3, 4].
A key question is: How do we know if a JEPA model has learned the world? A recent paper, When Does LeJEPA Learn a World Model? [1] seeks to answer part of this question. I will explain the concepts and basic arguments of this paper. I will also give recommendations for further reading.
LeJEPA is a JEPA model designed by Balestriero and LeCun. They created a regularization, SIGReg, which pushes the embeddings of a JEPA model to follow a Gaussian distribution [7]. Klindt, LeCun, and Balestriero, in When Does LeJEPA Learn a World Model?, proved that in LeJEPA with a Gaussian behavior policy, the embedding space identifies the original latent world space up to a rotation.
This paper deal with the question of identifiability.
What is identifiability?
JEPA models have an encoder network and a predictor network. The encoder network is tasked with learning a function which maps to a representation space. The encoder function takes real world latent variables to embeddings in this representation space. Meanwhile, the predictor network learns to predict a future representation given a previous one. It learns a predictor function that outputs a prediction, which is then compared with a target representation given by the encoder function. Loss is a combination of this loss between the prediction and the target, plus regularization loss.
The real world has "latent variables" – temperature, sound, physics, traffic, etc. Our observations of the world, though, are a function of these individual variables. For example, in a simple case, a model may view an object when it is at different distances d from the object. But to the model's viewing, the object's size changes as a function 1/d, depending on its distance from the object. We call this observation function . In other worlds, the function g may be a polynomial, sinusoidal, or another nonlinear function.
Identifiability of a JEPA model concerns its learned encoder. If a model is identifiable, its embedding space is a faithful representation of the original world. In math terms, if we denotethe encoder function h, and the map of observations g, then needs to be as close to the identity map as possible. Basically, h needs to recreate the original world from what it's learned from its observations. Typically, we consider the model to be identifiable if h is a rotation or some other simple map.
Why is identifiability helpful?
Identifiability helps with planning, training, and other applications. Since JEPA models use a predictor to make predictions in a representation space, planning (making sequences of predictions to achieve a goal) also occurs in this representation space. We want a model's plans to be applicable to the real world, where they may control a robot, drive a car, etc. If the model is identifiable, planning in the representation space is equivalent to planning in the real world; a model can plan in the representation space and its plans will succeed in the real world as well.
A Sketch of the Results
The paper makes a few assumptions about the world – additive noise, Gaussian latent variables – and about the model – observation pairs are generated by the Ornstein-Uhlenbeck process, the encoder maps to a space with equal dimension to the real world, the encoder minimizes loss. These assumptions may not hold in all systems, but they allow for a very elegant result.
Under these assumptions, the paper proves that , where is a rotation. The proof involves Hermite polynomials and other mathematical machinery [1].
The paper also includes other results, involving planning and approximate identifiability. We are focused on the first result; we have identifiability up to a rotation!
Further Reading
Identifiability up to a rotation is a powerful result. Intuitively, the representation space that the encoder learns has the same "shape" as the real world, meaning the model has learned something meaningful about the world. However, a rotation may still mix latent variables as linear combinations. DSREG, a tool created by Zheng, Klindt, Balestriero, and Schölkopf, learns a rotation which "unmixes" the world variables. It makes assumptions about the relationships between world variables [5].
Another natural question is: How do we know which latent variables a JEPA model will learn? Levy, Lidayan, and Goldberg made progress in answering this question, by hypothesizing that a model chooses from "feasible sets" of variables [6].
References
[1] Klindt, David, Yann LeCun, and Randall Balestriero. "When Does LeJEPA Learn a World Model?." arXiv preprint arXiv:2605.26379 (2026).
[2] S. S. A. Ghassemlou and S. Joseph. V-JEPA 2 Video Transcoders Find Motion-Based Features.Proceedings of the 1st IJCAI Workshop on Safe Physical AI, 2026.
[3] M. Assran, A. Bardes, D. Fan, Q. Garrido, R. Howes, M. Komeili, M. Muckley, A. Rizvi, C. Roberts, K. Sinha, A. Zholus, S. Arnaud, A. Gejji, A. Martin, F. R. Hogan, D. Dugas, P. Bojanowski, V. Khalidov, P. Labatut, F. Massa, M. Szafraniec, K. Krishnakumar, Y. Li, X. Ma, S. Chandar, F. Meier, Y. LeCun, M. Rabbat, N. Ballas. V-JEPA 2: Self-Supervised Video Models Enable Understanding, Prediction and Planning. arXiv:2506.09985, 2025.
[4] H. Ghaemi, E. B. Muller, S. Bakhtiari. seq-JEPA: Autoregressive Predictive Learning of Invariant-Equivariant World Models. arXiv:2505.03176, 2025.
[5] Zheng, Yujia, et al. "DSReg: Provably Recovering Individual World Latents without Reconstruction." arXiv preprint arXiv:2610.09457 (2026).
[6] Levy, Mosh, Aly Lidayan, and Yoav Goldberg. "Predictive Closure: A Set-Level Characterization of JEPA's Feature Selection." arXiv preprint arXiv:2610.27364 (2026).
[7] Balestriero, Randall, and Yann LeCun. "Lejepa: Provable and scalable self-supervised learning without the heuristics." arXiv preprint arXiv:2511.08544 (2025).
JEPA (Joint-Embedding Predictive Architectures) models are a popular type of world model. They learn to create predictions in a representation space, instead of pixel space. Because of this, they are very compute-efficient. They are also very capable in planning, image recognition, and other tasks [2, 3, 4].
A key question is: How do we know if a JEPA model has learned the world? A recent paper, When Does LeJEPA Learn a World Model? [1] seeks to answer part of this question. I will explain the concepts and basic arguments of this paper. I will also give recommendations for further reading.
LeJEPA is a JEPA model designed by Balestriero and LeCun. They created a regularization, SIGReg, which pushes the embeddings of a JEPA model to follow a Gaussian distribution [7]. Klindt, LeCun, and Balestriero, in When Does LeJEPA Learn a World Model?, proved that in LeJEPA with a Gaussian behavior policy, the embedding space identifies the original latent world space up to a rotation.
This paper deal with the question of identifiability.
What is identifiability?
JEPA models have an encoder network and a predictor network. The encoder network is tasked with learning a function which maps to a representation space. The encoder function takes real world latent variables to embeddings in this representation space. Meanwhile, the predictor network learns to predict a future representation given a previous one. It learns a predictor function that outputs a prediction, which is then compared with a target representation given by the encoder function. Loss is a combination of this loss between the prediction and the target, plus regularization loss.
The real world has "latent variables" – temperature, sound, physics, traffic, etc. Our observations of the world, though, are a function of these individual variables. For example, in a simple case, a model may view an object when it is at different distances d from the object. But to the model's viewing, the object's size changes as a function 1/d, depending on its distance from the object. We call this observation function
Identifiability of a JEPA model concerns its learned encoder. If a model is identifiable, its embedding space is a faithful representation of the original world. In math terms, if we denote the encoder function h, and the map of observations g, then
Why is identifiability helpful?
Identifiability helps with planning, training, and other applications. Since JEPA models use a predictor to make predictions in a representation space, planning (making sequences of predictions to achieve a goal) also occurs in this representation space. We want a model's plans to be applicable to the real world, where they may control a robot, drive a car, etc. If the model is identifiable, planning in the representation space is equivalent to planning in the real world; a model can plan in the representation space and its plans will succeed in the real world as well.
A Sketch of the Results
The paper makes a few assumptions about the world – additive noise, Gaussian latent variables – and about the model – observation pairs are generated by the Ornstein-Uhlenbeck process, the encoder maps to a space with equal dimension to the real world, the encoder minimizes loss. These assumptions may not hold in all systems, but they allow for a very elegant result.
Under these assumptions, the paper proves that
The paper also includes other results, involving planning and approximate identifiability. We are focused on the first result; we have identifiability up to a rotation!
Further Reading
Identifiability up to a rotation is a powerful result. Intuitively, the representation space that the encoder learns has the same "shape" as the real world, meaning the model has learned something meaningful about the world. However, a rotation may still mix latent variables as linear combinations. DSREG, a tool created by Zheng, Klindt, Balestriero, and Schölkopf, learns a rotation which "unmixes" the world variables. It makes assumptions about the relationships between world variables [5].
Another natural question is: How do we know which latent variables a JEPA model will learn? Levy, Lidayan, and Goldberg made progress in answering this question, by hypothesizing that a model chooses from "feasible sets" of variables [6].
References
[1] Klindt, David, Yann LeCun, and Randall Balestriero. "When Does LeJEPA Learn a World Model?." arXiv preprint arXiv:2605.26379 (2026).
[2] S. S. A. Ghassemlou and S. Joseph. V-JEPA 2 Video Transcoders Find Motion-Based Features. Proceedings of the 1st IJCAI Workshop on Safe Physical AI, 2026.
[3] M. Assran, A. Bardes, D. Fan, Q. Garrido, R. Howes, M. Komeili, M. Muckley, A. Rizvi, C. Roberts, K. Sinha, A. Zholus, S. Arnaud, A. Gejji, A. Martin, F. R. Hogan, D. Dugas, P. Bojanowski, V. Khalidov, P. Labatut, F. Massa, M. Szafraniec, K. Krishnakumar, Y. Li, X. Ma, S. Chandar, F. Meier, Y. LeCun, M. Rabbat, N. Ballas. V-JEPA 2: Self-Supervised Video Models Enable Understanding, Prediction and Planning. arXiv:2506.09985, 2025.
[4] H. Ghaemi, E. B. Muller, S. Bakhtiari. seq-JEPA: Autoregressive Predictive Learning of Invariant-Equivariant World Models. arXiv:2505.03176, 2025.
[5] Zheng, Yujia, et al. "DSReg: Provably Recovering Individual World Latents without Reconstruction." arXiv preprint arXiv:2610.09457 (2026).
[6] Levy, Mosh, Aly Lidayan, and Yoav Goldberg. "Predictive Closure: A Set-Level Characterization of JEPA's Feature Selection." arXiv preprint arXiv:2610.27364 (2026).
[7] Balestriero, Randall, and Yann LeCun. "Lejepa: Provable and scalable self-supervised learning without the heuristics." arXiv preprint arXiv:2511.08544 (2025).