Symbolic World Model Breaks the Gaussian Barrier for Temporal Consistency シンボリック・ワールド・モデル

Klindt, LeCun, and Balestriero (arXiv:2605.26379) proved Joint-Embedding Predictive Architectures (JEPAs) hit a hard limit: linear identifiability — the ability to recover the world's true latent variables up to a linear transformation — requires Gaussian, stationary latent dynamics. Take any non-Gaussian physical system and representation error grows monotonically with time, no matter how much data or capacity you throw at it.

A new preprint from a team of researchers shows that limit isn't fundamental to world models. It's an artifact of the statistical alignment mechanism. They introduce the Physics-Grounded Symbolic Architecture (PGSA) and prove three claims that would have sounded like magic before this paper: (1) PGSA achieves exact linear identifiability for all physical regimes, Gaussian or not; (2) per-step error is bounded by floating-point precision alone; (3) temporal consistency holds for an unbounded number of transitions — they call it near-infinite temporal consistency.

Why Gaussian Was a Prison

Prior work cast the identifiability problem in statistical terms: JEPAs learn representations by aligning embeddings across time, and that alignment only works when the underlying dynamics are Gaussian. The authors show this is a weakness of the architecture, not the objective. Statistical world models, including JEPAs, cannot maintain temporal coherence for non-Gaussian systems. The proof is general — no escape via bigger models or more data.

PGSA takes a different route. Instead of statistical alignment, it grounds representations in the causal generator of the world's dynamics using symbolic primitives. The algebraic cores of four theorems are formalized in Lean 4 with Mathlib4 v4.31.0, with zero sorry placeholders. That means the proof is machine-checked for those components.

Numerical Precision as the Only Error Source

For PGSA, error doesn't accumulate with time. It's bounded by the precision of the numerical representation — float32 or float64 — and that's it. For any transition count $N$, the error remains $\mathcal{O}(\epsilon_{\text{machine}})$. Contrast that with a JEPA on a non-Gaussian system, where even $N=10$ steps can corrupt the latent estimate beyond recognition.

The paper further proves that statistical world models cannot achieve near-infinite temporal consistency for any non-Gaussian system, regardless of model capacity or training data volume. That's a no-go theorem for a whole class of architectures.

What This Unlocks

Symbolic grounding in the causal generator of dynamics is the sufficient condition — and in non-Gaussian regimes, the only condition — for temporal consistency without drift. The immediate consequence: any robotics or simulation task with non-Gaussian physics (collisions, discrete modes, hybrid dynamics) can now in principle maintain exact latent representations forever, as long as you build the world model symbolically. The formal verification in Lean 4 means this isn't just a plausible claim; it's a theorem with machine-checked confidence. Expect a wave of symbolic-physics world models aimed at exactly those regimes where statistical methods currently fail around step 20.

Source: Identifiability Without Gaussianity: Symbolic World Models and Near-Infinite Temporal Consistency
Domain: arxiv.org