LeCun's LeJEPA Proves Linear Identifiability for World Models

Yann LeCun and colleagues have published a theoretical breakthrough for self-supervised learning: a proof that LeJEPA (Joint Embedding Predictive Architecture) can guarantee learning a world model—a representation that captures the true degrees of freedom of the environment. The paper, authored by David Klindt, Yann LeCun, and Randall Balestriero, addresses a fundamental question: when does an SSL method actually recover the latent variables that drive observed data? Their answer: when the latent distribution is Gaussian and the transition dynamics are stationary with additive noise, LeJEPA’s combination of alignment and Gaussian regularization ensures that the learned representation is a linear map to the true latents—a property known as linear identifiability.

The proof relies on a spectral decomposition where nonlinearities are strictly penalized by alignment, making the linear map optimal. The converse is equally important: no other latent distribution satisfies this guarantee, establishing Gaussian as the unique case. The authors also prove an approximate identifiability result where the guarantee degrades gracefully under non-ideal conditions. Experimentally, they validate across 2D toy examples, 1024-dimensional latent spaces, and pixel-based robotic control tasks, demonstrating that the theory translates to real-world planning. This work provides the mathematical underpinning for building world models that enable reliable planning and compositional generalization—a critical step toward more capable AI systems.