Mixtures of Neural Cellular Automata: A Stochastic Framework for Growth Modelling and Self-Organization

TL;DR

This paper introduces Mixture of Neural Cellular Automata (MNCA), a stochastic framework that enhances traditional NCAs by modeling diverse behaviors and capturing biological variability, improving robustness and interpretability in growth and segmentation tasks.

Contribution

The paper presents a novel MNCA framework that integrates probabilistic rules and noise into NCAs, enabling modeling of stochastic biological processes.

Findings

MNCAs outperform deterministic NCAs in robustness to perturbations

MNCAs better replicate biological growth patterns

MNCAs provide interpretable rule segmentation

Abstract

Neural Cellular Automata (NCAs) are a promising new approach to model self-organizing processes, with potential applications in life science. However, their deterministic nature limits their ability to capture the stochasticity of real-world biological and physical systems. We propose the Mixture of Neural Cellular Automata (MNCA), a novel framework incorporating the idea of mixture models into the NCA paradigm. By combining probabilistic rule assignments with intrinsic noise, MNCAs can model diverse local behaviors and reproduce the stochastic dynamics observed in biological processes. We evaluate the effectiveness of MNCAs in three key domains: (1) synthetic simulations of tissue growth and differentiation, (2) image morphogenesis robustness, and (3) microscopy image segmentation. Results show that MNCAs achieve superior robustness to perturbations, better recapitulate real biological growth patterns, and provide interpretable rule segmentation. These findings position MNCAs as a promising tool for modeling stochastic dynamical systems and studying self-growth processes.