Close Read: When Does LeJEPA Learn a World Model?
The claim: train a representation to pull positive pairs together while forcing its embeddings to be an isotropic Gaussian, and (in a Gaussian world with Ornstein-Uhlenbeck transitions) the only way to win is to recover the true latent variables up to a rotation. The paper proves this is an if and only if: the Gaussian latent distribution is the unique choice for which LeJEPA is linearly identifiable. My verdict: the forward theorem is clean, correct, and genuinely illuminating; the converse and the "Lean-verified" framing are weaker than they sound, because the load-bearing analysis facts are assumed rather than proven, and the central Gaussian-world assumption is exactly the one their own robotics experiment violates.