Beyond Gaussian Worlds: Latent Geometry Matters for JEPAs

The paper extends the analysis of Joint-Embedding Predictive Architectures (JEPAs) beyond Euclidean latent spaces to Riemannian manifolds. It shows that when latent variables lie on a sphere and the target distribution matches this spherical geometry, every optimal representation recovers the latent state up to an orthogonal transformation, demonstrating that Gaussian uniqueness is not universal. Experiments confirm that geometrically compatible targets improve linear recovery, especially in high-dimensional toroidal settings.

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