New Architecture Achieves Temporal Consistency in World Models Without Gaussian Assumption
Researchers introduced the Physics-Grounded Symbolic Architecture (PGSA), which achieves exact linear identifiability and near-infinite temporal consistency in world models regardless of whether latent dynamics follow a Gaussian distribution. Previous work by Klindt, LeCun, and Balestriero showed that Joint-Embedding Predictive Architectures (JEPAs) could only maintain temporal consistency under Gaussian assumptions, implying fundamental limits for non-Gaussian physical systems. This finding challenges a previously established theoretical boundary and suggests that symbolic grounding in causal dynamics, rather than statistical alignment, is the key to maintaining consistency across extended time horizons.
Researchers have proven that a new symbolic architecture can overcome a fundamental limitation in world models identified in recent work. The prior result showed that statistical world models like JEPAs can achieve linear identifiability—the ability to recover true latent variables—only when latent dynamics follow a Gaussian, stationary process, and that representation error grows monotonically over time for non-Gaussian systems. The new Physics-Grounded Symbolic Architecture (PGSA) proves that this limitation is not inherent to world models themselves but rather an artifact of statistical alignment mechanisms. The authors demonstrate three key results: PGSA achieves exact linear identifiability across all physical regimes regardless of latent distribution, per-step error is bounded only by numerical precision, and PGSA maintains temporal consistency across an unbounded number of transitions. Notably, the researchers formalized four theorem proofs in Lean 4, establishing that symbolic grounding in the causal generator of world dynamics is both necessary and sufficient for near-infinite temporal consistency in non-Gaussian regimes.
What's missing
The paper does not discuss computational complexity or practical scalability of PGSA compared to statistical approaches, nor does it provide empirical validation on real-world datasets or benchmarks. The study's own limitations regarding the assumption that the causal generator can be perfectly identified or accessed are not explicitly addressed in the abstract.
What different sources said
- arXiv stat.MLCenter
Identifiability Without Gaussianity: Symbolic World Models and Near-Infinite Temporal Consistency
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