David Klindt

David Klindt, Yann LeCun, Randall Balestriero

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.

Christian Internò, Alexander Pondaven, Habon Issa et al.

While humans can identify physically implausible events within milliseconds, machine learning approaches addressing the same problem are extremely slow and expensive. They either rely on external multimodal-LLM judges or require ad-hoc modifications to the training procedure. In this work, we argue that indicators of physical plausibility are implicitly captured by five geometric properties of the per-frame embeddings produced by frozen image encoders. In aggregate, we call them GEOPHYS. First, we show that these signals correlate with human EEG responses to two forms of object-permanence violations. Second, GEOPHYS robustly discriminates physically implausible videos from realistic ones, achieving state-of-the-art physics-violation detection: 98.3% on LikePhys and 93.3% on IntPhys2, whereas V-JEPA 2, GPT-4o, Gemini, and twelve modern video diffusion models perform near chance. Third, used as a best-of-N verifier for physical alignment during video generation, GEOPHYS lifts MAGI-1 24B from 50.01% to 64.50% on PhysicsIQ at 1.5x lower wall-clock and 4.65x lower memory than the V-JEPA 2 world-model verifier. Ultimately, GEOPHYS demonstrates that physical plausibility in videos can be assessed by leveraging the emergent geometric properties of temporal features extracted from image encoders.