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

arXiv:2609.36227v1 Announce Type: cross 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.

Source: arXiv cs.CV | 2026-09-30