Symbolic world models break Gaussian limit with near-infinite temporal consistency
New architecture achieves exact identifiability for any physical system, even non-Gaussian...
A new paper by Seth Dobrin and Łukasz Chmiel tackles a fundamental limitation of statistical world models. Previous work by Klindt, LeCun, and Balestriero proved that Joint-Embedding Predictive Architectures (JEPAs) can only recover the true latent variables of a system (linear identifiability) if the underlying dynamics follow a Gaussian, stationary process. This imposes a hard ceiling: for any non-Gaussian physical system, the representation error grows monotonically over time, making long-horizon predictions unreliable. The new work shows this limit is not fundamental to world models, but an artifact of statistical alignment.
Enter the Physics-Grounded Symbolic Architecture (PGSA). Dobrin and Chmiel prove three key results: PGSA achieves exact linear identifiability for any latent distribution, its per-step error is bounded only by numerical precision (not model capacity or data volume), and consequently it maintains temporal consistency for an unbounded number of transitions—a property they call near-infinite temporal consistency. They further prove that no statistical world model can achieve this for non-Gaussian systems. The algebraic cores of four theorems are formalized in Lean 4 with Mathlib4, containing zero sorry placeholders. This work positions symbolic grounding as the sufficient (and for non-Gaussian regimes, the only) condition for stable, long-horizon world modeling.
- PGSA achieves exact linear identifiability for all physical systems, regardless of whether the latent dynamics are Gaussian or non-Gaussian.
- Per-step error is bounded solely by numerical precision, not by model capacity or training data volume.
- Near-infinite temporal consistency is proven for symbolic models, while statistical models provably fail for non-Gaussian systems.
Why It Matters
Symbolic grounding could unlock AI systems that maintain accurate world models indefinitely, crucial for long-horizon reasoning and physical simulation.