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

arXiv: https://arxiv.org/abs/2606.12471 · HTML: https://mlsanity.com/paper/2606.12471/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Latent predictive world models, one of 11 directions in World models.
- Builds on 12 of its 27 references that are in the map.
- First posted on arXiv 9 Jun 2026.

## Placed in

- World models / [Latent predictive world models](https://mlsanity.com/wm/latent-predictive-world-models/)

## Builds on (most cited first, 12 of 12)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Self-Supervised Learning from Images with a Joint-Embedding Predictive Architecture](https://mlsanity.com/paper/2301.08243/) (2023)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Recurrent World Models Facilitate Policy Evolution](https://mlsanity.com/paper/1809.01999/) (2018)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Revisiting Feature Prediction for Learning Visual Representations from Video](https://mlsanity.com/paper/2404.08471/) (2024)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [LeJEPA: Provable and Scalable Self-Supervised Learning Without the Heuristics](https://mlsanity.com/paper/2511.08544/) (2025)
- [When Does LeJEPA Learn a World Model?](https://mlsanity.com/paper/2605.26379/) (2026)

## Built on by (most cited first, 1 of 1)

- [I Act Therefore I Am: When Is JEPA's Action-Conditioning Enough to Learn Causal Mechanisms?](https://mlsanity.com/paper/2609.31161/) (2026)

## Abstract (arXiv)

Klindt, LeCun, and Balestriero (arXiv:2605.26379) proved that Joint-Embedding Predictive Architectures (JEPAs) achieve linear identifiability, the linear recovery of the world's true latent variables, if and only if the world's latent dynamics follow a Gaussian, stationary process. This Gaussian boundary implies a fundamental limit on temporal consistency: for any non-Gaussian physical system, the representation error of a statistical World Model grows monotonically with time. We prove that this limit is an artifact of the statistical alignment mechanism, not a property of World Models in general. We introduce the Physics-Grounded Symbolic Architecture (PGSA) and prove three results: (1) a PGSA achieves exact linear identifiability for all physical regimes, regardless of the latent distribution; (2) the per-step error of a PGSA is bounded by numerical precision alone; and (3) as a direct consequence, a PGSA maintains temporal consistency for an unbounded number of transitions, a property we term near-infinite temporal consistency. We further prove that statistical World Models cannot achieve this property for any non-Gaussian system, regardless of model capacity or the volume of training data. The algebraic cores of four of the theorems are formalized in Lean 4 with Mathlib4 v4.31.0 (zero sorry placeholders); the Klindt et al. converse is taken as an external premise. The contrast establishes that symbolic grounding in the causal generator of the world's dynamics is the sufficient condition and, in non-Gaussian regimes, the only condition for near-infinite temporal consistency.