DSReg: Provably Recovering Individual World Latents without Reconstruction

DSReg. Provably Recovering Individual World Latents without Reconstruction. By Yujia Zheng and three others, from the University of Illinois Urbana-Champaign, Cold Spring Harbor Laboratory, and three other institutions. Published on the seventh of October.

A whole family of methods sets out to recover the individual latent variables of the world: nonlinear ICA, dictionary learning, causal representation learning. Each of them ties the latents to the observations through some kind of anchor. That anchor might be reconstruction, auxiliary supervision, or a distributional asymmetry such as non-Gaussianity. Methods that go without those anchors pay for it. Joint-embedding predictive architectures, or JEPAs, identify the latent state only up to a linear transformation. The information is there, but the individual latents stay mixed together, and no single coordinate corresponds to a single factor of the world.

The authors claim to close that gap. Individual world latents, they argue, can be provably recovered with no reconstruction, no decoder, and no labels. The condition that makes it possible is called Structural Diversity. Different latents leave distinct dependency footprints on the observations, in the same way that no two snowflakes are alike. If each latent touches the observations in its own recognisable pattern, that pattern is enough to tell the latents apart.

The method starts from the linear identifiability that LeJEPA already provides, and takes the last step from there. DSReg, short for Dependency-Sparsity Regularization, is proved to recover individual world latents up to signed permutation under Structural Diversity, still without reconstruction or a decoder. Signed permutation means each recovered coordinate is one true latent, possibly reordered and possibly flipped in sign. DSReg applies post hoc to any representation that is already linearly identified. Trained checkpoints can be reused, at no loss compared with training jointly. Put together, the authors describe this as the first fully identifiable JEPA that recovers every world latent.

There is a theoretical comparison as well as an empirical one. As a condition on dependency footprints, Structural Diversity is strictly weaker than all the structural conditions of prior identifiable latent variable models, so it asks less of the world than those earlier guarantees did. The experiments cover synthetic regimes, world model probes, learned visual encoders, and external renderers. Across them, DSReg preserves dense prediction while improving the recovery of individual latents, and improves downstream use as scale grows.

The contribution lands between two traditions. One recovers individual factors but needs a decoder or labels to do it. The other drops the decoder and settles for a linear mixture. DSReg keeps the second tradition's freedom and asks only that the latents leave different footprints, which turns a mixed representation into one where each world latent can be read off on its own.