One-Step Next-Latent Prediction Is Not a World Model

Abstract:Next-latent prediction fits a map from the current embedding to the next one. LeNEPA carries this objective to time series, replacing the stop-gradient of next-embedding prediction with the isotropy penalty of LeJEPA. A world model is a transition kernel that can be rolled out. The one-step regression identifies a conditional mean, and a mean is a kernel only in special cases. For a linear-Gaussian Markov latent, the mean transition and the innovation covariance are fixed by the one-step problem, and the open-loop squared error at horizon $K$ equals the trace of the sum of the pushed-forward innovation covariances. That error grows with $K$ after the one-step fit is exact. If the conditional mean is nonlinear, composing it is not the multi-step conditional mean. If the observation is a non-injective function of a Markov state, a memoryless one-step map does not determine future observations, while a short window can. An isotropy penalty is a function of the embedding marginal, so its partial derivative in the transition weights is zero. On a scalar autoregression with coefficient $0.9$, the one-step mean squared error is $0.998$ and the $16$-step open-loop error is $5.10$. On a hidden rotation, an eight-step window reaches $16$-step error $0.056$, while the current scalar alone reaches $0.778$. Raising the isotropy weight from $0.1$ to $10$ leaves eight-step latent error inside $[0.78,0.85]$ on three seeds.

Machine Learning (stat.ML); Computer Vision and Pattern Recognition (cs.CV); Machine Learning (cs.LG)

I.2.6; G.3; I.5.1

arXiv:2609.36227 [stat.ML]

(or arXiv:2609.36227v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2609.36227 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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