# Where Does Randomness Matter in Neural Cellular Automata?

arXiv: https://arxiv.org/abs/2609.36797 · HTML: https://mlsanity.com/paper/2609.36797/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 44 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 24 of 24)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Deep Networks with Stochastic Depth](https://mlsanity.com/paper/1603.09382/) (2016)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Stable Architectures for Deep Neural Networks](https://mlsanity.com/paper/1705.03341/) (2017)
- [Exponential expressivity in deep neural networks through transient chaos](https://mlsanity.com/paper/1606.05340/) (2016)
- [Deep Information Propagation](https://mlsanity.com/paper/1611.01232/) (2016)
- [Cellular automata as convolutional neural networks](https://mlsanity.com/paper/1809.02942/) (2018)
- [Noisy Recurrent Neural Networks](https://mlsanity.com/paper/2102.04877/) (2021)
- [Lenia - Biology of Artificial Life](https://mlsanity.com/paper/1812.05433/) (2018)
- [Growing 3D Artefacts and Functional Machines with Neural Cellular Automata](https://mlsanity.com/paper/2103.08737/) (2021)
- [Learning Graph Cellular Automata](https://mlsanity.com/paper/2110.14237/) (2021)
- [Variational Neural Cellular Automata](https://mlsanity.com/paper/2201.12360/) (2022)
- [Attention-based Neural Cellular Automata](https://mlsanity.com/paper/2211.01233/) (2022)
- [Growing Isotropic Neural Cellular Automata](https://mlsanity.com/paper/2205.01681/) (2022)
- [HyperNCA: Growing Developmental Networks with Neural Cellular Automata](https://mlsanity.com/paper/2204.11674/) (2022)
- [DyNCA: Real-time Dynamic Texture Synthesis Using Neural Cellular Automata](https://mlsanity.com/paper/2211.11417/) (2022)
- [It's Hard for Neural Networks To Learn the Game of Life](https://mlsanity.com/paper/2009.01398/) (2020)
- [Self-Replication, Spontaneous Mutations, and Exponential Genetic Drift in Neural Cellular Automata](https://mlsanity.com/paper/2305.13043/) (2023)
- [A New Kind of Network? Review and Reference Implementation of Neural Cellular Automata](https://mlsanity.com/paper/2604.24990/) (2026)
- [Reservoir Computing with Evolved Critical Neural Cellular Automata](https://mlsanity.com/paper/2508.02218/) (2025)
- [Identity Increases Stability in Neural Cellular Automata](https://mlsanity.com/paper/2508.06389/) (2025)
- [Stability and Geometry of Attractors in Neural Cellular Automata](https://mlsanity.com/paper/2604.12720/) (2026)
- [Structured Fluctuations and the Information Dynamics of Self-Maintenance in Growing Neural Cellular Automata](https://mlsanity.com/paper/2607.12403/) (2026)
- [Transient State Reorganization and Cell Differentiation in the Developmental Dynamics of Growing Neural Cellular Automata](https://mlsanity.com/paper/2607.15726/) (2026)

## Abstract (arXiv)

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.