DSReg: Provably Recovering Individual World Latents without Reconstruction

Methods that recover individual latent variables of the world, from nonlinear ICA to dictionary learning and causal representation learning, anchor the latents to observations through reconstruction, auxiliary supervision, or distributional asymmetries such as non-Gaussianity. Methods without these anchors, including joint-embedding predictive architectures (JEPAs), identify the latent state only up to a linear transformation, so individual latents remain mixed. We close this gap: individual world latents can be provably recovered with no reconstruction, no decoder, and no labels. The key condition is Structural Diversity: different latents leave distinct dependency footprints on observations, just as no two snowflakes are alike. Building on the linear identifiability that LeJEPA provides, we prove that under Structural Diversity and a standard faithfulness condition, DSReg (Dependency-Sparsity Regularization) recovers individual world latents up to signed permutation. It applies post hoc to any linearly identified representation, reusing trained checkpoints at no loss over joint training, and establishes the first fully identifiable JEPA that recovers every world latent. Moreover, as a condition on dependency footprints, Structural Diversity is strictly weaker than all structural conditions of prior identifiable latent variable models. Across synthetic regimes, world model probes, learned visual encoders, and external renderers, DSReg preserves dense prediction while improving individual-latent recovery and downstream use with scales.