Neural Cellular Automata Can Respond to Signals

TL;DR

This work extends Neural Cellular Automata by enabling responses to signals, introducing two modalities: internal signals encoded in the seed-cell genome and external signals delivered through a read-only environment channel. By expanding the NCA input to $17$ channels and using a single network per experiment with training regimes that emphasize memory and regeneration, the authors demonstrate that NCAs can grow into morphologies determined by seed-genome and can repeatedly change color in response to environmental signals. Key findings include: (i) internal genome-encoded signals driving distinct shapes and colors (e.g., hearts and geckos), (ii) external signals enabling stable, repeatable color changes in fully grown organisms, and (iii) memory mechanisms rooted in morphology rather than fixed cell identities. These results advance artificial morphogenesis, enabling dynamic, signal-driven behavior and suggesting future avenues for embedding more complex biological processes such as innervation and mitosis, albeit with challenges in interpretability of neural-network-based rules.

Abstract

Neural Cellular Automata (NCAs) are a model of morphogenesis, capable of growing two-dimensional artificial organisms from a single seed cell. In this paper, we show that NCAs can be trained to respond to signals. Two types of signal are used: internal (genomically-coded) signals, and external (environmental) signals. Signals are presented to a single pixel for a single timestep. Results show NCAs are able to grow into multiple distinct forms based on internal signals, and are able to change colour based on external signals. Overall these contribute to the development of NCAs as a model of artificial morphogenesis, and pave the way for future developments embedding dynamic behaviour into the NCA model. Code and target images are available through GitHub: https://github.com/jstovold/ALIFE2023

Figures (13)

• Figure 1: Diagram depicting one pass of the NCA update step. The diagram also shows the structure of the neural network. Image adapted from mordvintsev_growingneuralcellular, licenced under CC BY 4.0.
• Figure 2: Diagram depicting the role of the alpha channel in the NCA for indicating which cells are alive and which are eligible to come to life in the next step. Image from mordvintsev_growingneuralcellular, licenced under CC BY 4.0.
• Figure 3: Example batches from the 'growing' (top), and 'regenerating' (bottom) training regimes. Each example comprises two rows, the upper row shows the initial state of the CA, the lower row shows the state of the CA after it has been iterated for between 64 and 200 steps (the actual number of steps is randomly picked each time). The damage caused to the organism is clearly seen in the three rightmost NCAs of the regenerating example. Horizontal lines added to help distinguish the two examples.
• Figure 4: Structure of the NCA seed cell (a) for internal signals, and (b) for reacting to external signals. In (a), we have 4 genome channels, but this could be increased or decreased by adjusting the number of remaining hidden channels accordingly. In no experiments were more than 12 hidden channels used.
• Figure 5: Growth of two meditation emoji from a single NCA trained to produce one of two organisms depending on a single change in the seed cell. The only difference between the two is $c_4 = 0$ for the top example, $c_4 = 1$ for the bottom example. The NCA is trained to produce the organism within 200 timesteps. Snapshots are shown from times $t = 10, 20, 30, 50, 100, 400$.