Architectural Relationship between Neural Cellular Automata and ConvLSTM

Abstract

Neural Cellular Automata (NCA) has emerged as a powerful deep learning framework capable of learning complex global behaviors that arise from purely local interactions. However, its architectural relationship with other established machine learning models remains unexplored, hindering the application of broader deep learning insights to NCA and complicating the identification of its intrinsic advantages over other models. This work situates NCA within the broader deep learning landscape, viewing it not primarily as a specialized extension of Cellular Automata, but rather as a distinct architecture within a common neural network paradigm. To achieve this, the present study focuses on the Convolutional Long Short-Term Memory (ConvLSTM) model, which is widely utilized as a backbone for spatio-temporal prediction and shares many architectural similarities with NCA. This paper first theoretically derives the NCA update rule by applying a specific series of transformations to the ConvLSTM formulation. Second, focusing on self-organizing tasks that converge to a single attractor state, it characterizes the inductive biases inherent in these architectural transformations through comparative experiments. These experiments reveal that the combination of an MLP-based update rule and a residual, fixed-gate structure is what enables high-fidelity pattern generation and strong resilience to damage in this regime. This research is expected to provide theoretical and experimental foundations for understanding NCA within the broader context of deep learning, offering concrete intuition for exploring future research directions. Code available at: https://doi.org/10.5281/zenodo.20790727 Supplementary Material available at: https://doi.org/10.5281/zenodo.20789928