Cellular automata expose the gap between accurate pixels and correct world-model rollouts

A world model can predict almost every cell correctly and still produce the wrong future. Why Do Conventional World Models Fail to Learn Cellular Automata? investigates that difference using systems with explicit local update rules. The authors report a CNN with 96.3% cell accuracy but only 18.9% fully correct rollouts.

Testing complete continuations

The main testbed uses binary cellular automata on an 8-by-8 torus. A model observes eight frames and predicts the next eight. Strict sequence accuracy requires all 512 predicted cells to be correct.
The evaluation separates executing a known rule, continuing previously seen rule families, inferring held-out rules from context, and handling deliberately withheld evidence with a supplied family-level prior. Outside the final setting, the researchers filter examples so the observed transitions contain the information required for the queried situations.
That construction prevents missing evidence from being confused with failure to use available evidence. It also makes the problem narrower than unrestricted video prediction, where the governing rule may be unknown or unidentifiable from the observation.

Locality includes where and when

Spatial structure matters when a transformer reads a grid as a flat token sequence. In the Game of Life experiment, switching from one-dimensional rotary positions to two-dimensional positions raises exact-rollout performance from 39.1% to 100%, with the same parameters.
The authors do not conclude that attention cannot represent neighborhood structure. Learned positions can solve the known-rule setting; the concern is whether training learns a reliable representation across the tested cases.
Temporal locality concerns binding an observed situation to what followed it. Giving a raster token its cell's previous-frame neighborhood raises one tested transformer from 25.8% to 99.9% on unseen rules. Other experiments build situation–outcome pairs with short convolutions or shifted keys and values.
Those interventions provide structured information flow, not a universal replacement for scale. Some configurations still fail on rare situations or on the withheld-evidence setting, where matching an observed case is insufficient.

Settling a frame before predicting from it

A separate experiment keeps diffusion-model weights fixed and changes generation order. Under causal freezing, a generated frame becomes clean context before the next frame is completed.
For a plain depth-eight denoiser trained on the Game of Life, this raises exact continuation from 42.2% to 99.9%. The same sampling comparison changes billiards performance only slightly, from 99.2% to 100%. Generation order therefore has different consequences for the two tested dynamics.
The paper also reports materially different improvement sizes under alternative training recipes. Its evidence supports diagnosing the missing information-flow property, not promising the largest reported gain for every diffusion model.
For world-model evaluation, the distinction between a plausible frame and a correct continuation is consequential. These experiments show how small local errors can spoil an exact rollout and how controlled rules make their causes testable. They do not establish that the same modifications solve complex physical scenes or make learned simulators generally reliable.