Where Does Randomness Matter in Neural Cellular Automata?

2026-09-29

AI Summary

This study addresses the frequent conflation of stochastic update mechanisms during the training and execution phases of Neural Cellular Automata (NCA), which complicates the attribution of system stability. To resolve this, we propose a framework that decouples execution modes from task behaviors by separating the training and evaluation stages. Through controlled experiments, we analyze the impact of asynchronous updates on rule learning and long-term stability, and derive an exact mean-variance criterion to rectify misclassification issues. Experimental results demonstrate that asynchronously trained models achieve a 100% pass rate on short-term tests, while full-scale models attain deterministic stability over 4,096 steps. This performance significantly surpasses synchronous and partial growth strategies, providing both theoretical and empirical foundations for optimizing NCA reliability.

Abstract

Stochastic cell updates are often used throughout the life of a neural cellular automaton (NCA), from backpropagation through time to final rollout. This leaves two questions entangled: does update randomness help learn a useful rule, and must that randomness remain at execution? We separate training and evaluation update modes in controlled Growing NCA experiments, then vary the states shown during training. Under the standard constant-rate persist recipe, asynchronous training passes the short-horizon quality test in 10/10 runs, compared with 3/10 synchronous runs. All ten asynchronous models also retain the target for 4,096 steps under deterministic evaluation. For a scalar translation-invariant lattice, we derive an exact mean-square criterion: random masking can damp mean modes, but it also injects variance, and a mean-only test misclassifies four non-marginal settings. Finally, among 30 models that all pass the same reconstruction test, eight of ten grow-trained models become off-target at 4,096 steps, while all persist and regenerate models retain the target; damage recovery separates persist from regenerate. The results distinguish optimization reliability, execution mode, and task-specific behavior instead of treating them as one stability property.

Problem

• Neural Cellular Automata
• Stochastic Updates
• Randomness
• Asynchronous Training
• Stability

Innovation

• Neural Cellular Automata
• Stochastic Updates
• Asynchronous Training
• Mean-Square Criterion
• Update Mode Decoupling