Identifiability Without Gaussianity: Symbolic World Models and Near-Infinite Temporal Consistency

2026-06-09 · Source: Computation and Language · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Robotics & Autonomous Systems · Depth: Expert, quick

Summary

A new paper introduces the Physics-Grounded Symbolic Architecture (PGSA), which addresses a fundamental limitation in Joint-Embedding Predictive Architectures (JEPAs). Previous work by Klindt, LeCun, and Balestriero (arXiv:2605.26379) established that JEPAs achieve linear identifiability only if the world's latent dynamics are Gaussian and stationary, leading to monotonically growing representation error for non-Gaussian physical systems. The PGSA overcomes this "Gaussian boundary" by achieving exact linear identifiability across all physical regimes, irrespective of the latent distribution. Its per-step error is bounded solely by numerical precision, enabling near-infinite temporal consistency—maintaining accuracy for an unbounded number of transitions. This contrasts sharply with statistical World Models, which cannot achieve this property for non-Gaussian systems, regardless of their capacity or training data volume. The authors formalize four key theorems in Lean 4 with Mathlib4 v4.31.0, highlighting symbolic grounding in causal dynamics as the critical condition for this advanced temporal consistency.

Key takeaway

For AI Scientists developing world models for complex, non-Gaussian physical systems, recognize that purely statistical approaches like JEPAs face fundamental limits in achieving long-term temporal consistency and exact identifiability. You should investigate architectures that incorporate symbolic grounding in the world's causal dynamics, such as the Physics-Grounded Symbolic Architecture (PGSA). This approach offers near-infinite temporal consistency and identifiability, overcoming the Gaussianity constraint and ensuring model accuracy over extended prediction horizons.

Key insights

Symbolic grounding in causal dynamics enables near-infinite temporal consistency and exact identifiability in world models, overcoming Gaussianity limits.

Principles

• Statistical World Models require Gaussian latent dynamics for identifiability.
• Symbolic grounding ensures exact identifiability across all regimes.
• Temporal consistency limits are an artifact of statistical alignment.

Method

Physics-Grounded Symbolic Architecture (PGSA) achieves identifiability by symbolically grounding in the causal generator of the world's dynamics, bounding per-step error by numerical precision.

Topics

• World Models
• Identifiability
• Temporal Consistency
• Symbolic AI
• Joint-Embedding Predictive Architectures
• Lean 4

Best for: Research Scientist, AI Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Computation and Language.