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

2026-06-12 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences, Robotics & Autonomous Systems · Depth: Expert, long

Summary

The Physics-Grounded Symbolic Architecture (PGSA) is introduced as a novel approach to World Models, directly challenging prior findings that statistical models like Joint-Embedding Predictive Architectures (JEPAs) achieve linear identifiability only under Gaussian, stationary latent dynamics. Research by Klindt, LeCun, and Balestriero (June 2026) established this Gaussian boundary, implying that for non-Gaussian physical systems, statistical World Models' representation error grows monotonically, limiting temporal consistency. This paper proves this limit is an artifact of statistical alignment, not a general property of World Models. The PGSA achieves exact linear identifiability across all physical regimes, irrespective of latent distribution, with per-step error bounded solely by numerical precision. This enables "near-infinite temporal consistency" for an unbounded number of transitions, a capability statistical World Models cannot match for non-Gaussian systems, even with increased capacity or training data. Key theorems are formalized in Lean 4 with Mathlib4 v4.31.0, highlighting symbolic grounding as the sufficient and, for non-Gaussian regimes, necessary condition for near-infinite temporal consistency.

Key takeaway

For AI Architects designing long-horizon World Models, recognize that statistical approaches like JEPAs inherently fail for non-Gaussian physical systems due to compounding representation bias. You should consider physics-grounded symbolic architectures (PGSAs) to achieve near-infinite temporal consistency. This paradigm shift separates perceptual error from simulation, ensuring your models maintain accuracy over unbounded transitions, a critical factor for real-world reliability.

Key insights

Symbolic grounding in causal dynamics enables near-infinite temporal consistency in World Models, surpassing statistical models' Gaussian limitations.

Principles

• Statistical models incur compounding representation bias.
• Identifiability is crucial for long-term consistency.
• Physics-grounded architectures separate perception and simulation.

Method

The Physics-Grounded Symbolic Architecture (PGSA) defines an Atom Registry of executable physical laws, a State Graph of typed variables, and a Causal Basis for the world generator.

In practice

• Formalize physical laws using Lean 4.
• Separate perceptual encoding from simulation.
• Evaluate models on non-Gaussian physical systems.

Topics

• World Models
• Identifiability
• Temporal Consistency
• Physics-Grounded AI
• Symbolic AI
• JEPA Architectures

Code references

• ARYA-Labs-PBC/pgsa-world-model-proofs
• leanprover-community/mathlib4

Best for: Research Scientist, AI Scientist, Machine Learning Engineer, AI Architect

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.