Identity Increases Stability in Neural Cellular Automata

TL;DR

The paper addresses stability challenges in Neural Cellular Automata (NCAs) when multiple artificial organisms grow in proximity. It introduces an identity layer as a simple training constraint and compares three variants to show that identity promotes stability without needing multiple identities. The results demonstrate that models with identity constraints maintain macroscopic shapes better and exhibit emergent movement to avoid overlap, with movement more pronounced when multiple identities are used. This work advances the study of social interaction and individuality in artificial cellular systems and suggests future work on adaptive identities and information-theoretic analyses.

Abstract

Neural Cellular Automata (NCAs) offer a way to study the growth of two-dimensional artificial organisms from a single seed cell. From the outset, NCA-grown organisms have had issues with stability, their natural boundary often breaking down and exhibiting tumour-like growth or failing to maintain the expected shape. In this paper, we present a method for improving the stability of NCA-grown organisms by introducing an 'identity' layer with simple constraints during training. Results show that NCAs grown in close proximity are more stable compared with the original NCA model. Moreover, only a single identity value is required to achieve this increase in stability. We observe emergent movement from the stable organisms, with increasing prevalence for models with multiple identity values. This work lays the foundation for further study of the interaction between NCA-grown organisms, paving the way for studying social interaction at a cellular level in artificial organisms. Code/Videos available at: https://github.com/jstovold/ALIFE2025

Figures (11)

• Figure 1: Breakdown of NCA-grown organism's natural boundary, with tumour-like growths sprouting from the original organism.
• Figure 2: Diagram depicting one pass of our extended NCA update step (with 17 channels instead of 16). The diagram also shows the structure of the neural network. Image adapted from mordvintsev_growingneuralcellular, licenced under CC BY 4.0.
• Figure 3: Example idealised comparison images. Left image has distance of $6$ and relative offset $-15$, right image has distance $12$ and relative offset $5$. Note the saturation occurring when the two images intersect, which is a consequence of the production process, so unlikely to occur in the grown organisms.
• Figure 4: Graph showing the change in error range as a function of lateral distance between seeds. The error range is the difference between maximum and minimum errors in the distribution. The graph shows much larger ranges for model A compared with models B/C.
• Figure 5: Boxplots showing the distribution of error for each lateral distance, organised by model. Model A clearly demonstrates larger variance and less consistent behaviour compared with models B/C.