Organizations: The University of Tokyo · Atomi University · Alternative Machine Inc.
Abstract
Growing Neural Cellular Automata (GNCA) are capable of robust self-maintenance and self-repair, yet the internal dynamical mechanisms that support these capabilities remain poorly understood. Here, we investigate the role of internal fluctuations--temporal micro-variability of hidden channel states--in a trained GNCA model, challenging the assumption that such variability is merely residual stochastic noise. Through systematic analysis spanning update-rate sweeps, spatial correlation measurements, dimensionality reduction of collective state trajectories, localized damage experiments, transfer entropy vector field estimation, and partial information decomposition, we show that internal fluctuations are spatially structured, dynamically coupled to an attracting collective state, and associated with distributed small-magnitude updates that contribute to damage recovery. Damage induces a global deviation in latent state space followed by gradual re-convergence, and suppressing distributed small-magnitude updates associated with baseline fluctuation dynamics outside a permissive radius that encompasses the majority of the cells significantly impairs recovery. Transfer entropy analysis characterizes a spatially differentiated repair response: corrective inward flow near the damage site coexists with outward perturbation propagation at greater distances. Partial information decomposition further suggests a regime shift from synergy-dominant resting computation to redundancy-increased coordination during recovery. These findings indicate that GNCA self-repair emerges from high-dimensional nonlinear collective dynamics in which internal fluctuations serve as a functional component supporting information flow, coordination, and return toward an attracting recurrent state.
Growing Neural Cellular Automata (GNCA) develop complex morphologies from a single seed cell through shared local rules, yet the internal dynamics of this process remain poorly understood. To investigate how GNCA grows, the full developmental trajectory of trained GNCA models was traced. The trajectory of cell state development revealed that morphological convergence often proceeds non-monotonically through transient intermediate configurations. In addition, channel-wise analysis showed that the hidden channels self-organize into modular groups in parallel with the visible form. Furthermore, geometric analysis of the cell state space indicated that cell states diversify within a low-dimensional, smooth manifold. To examine cell development in more detail, community detection on an ε-neighbour network of cells was conducted. This analysis successfully extracted discrete cell types from this continuous space, and identified transient cell-type communities during early development and stable, finer-grained types corresponding to spatially coherent regions of the mature morphology. The temporal coordination of these phenomena across multiple independent measures indicates that the developmental process of GNCA is a reorganization of transient states rather than incremental refinement.
This study significantly advances multi-texture synthesis using Neural Cellular Automata (NCAs) by introducing a novel training methodology that enables robust self-regeneration of textures in damaged regions. This inherent healing mechanism, essential for dynamic and adaptive systems, extends beyond traditional computer graphics applications, highlighting the fundamental self-organizing properties of NCAs. Furthermore, we present a versatile grafting technique, enabling the seamless combination of distinct textures. This is achieved efficiently during the inference phase, without requiring specialized retraining, through precise initialization of the NCA's genome channels. Our findings demonstrate the generation of high-quality, complex textures with fluid transitions, showcasing a powerful and efficient paradigm for dynamic texture composition and self-repair in autonomous systems.
Mirela-Magdalena Catrina, Ioana Cristina Plajer, Alexandra Băicoianu
Stephen Wolfram proclaimed in his 2003 seminal work "A New Kind Of Science" that simple recursive programs in the form of Cellular Automata (CA) are a promising approach to replace currently used mathematical formalizations, e.g. differential equations, to improve the modeling of complex systems. Over two decades later, while Cellular Automata have still been waiting for a substantial breakthrough in scientific applications, recent research showed new and promising approaches which combine Wolfram's ideas with learnable Artificial Neural Networks: So-called Neural Cellular Automata (NCA) are able to learn the complex update rules of CA from data samples, allowing them to model complex, self-organizing generative systems. The aim of this paper is to review the existing work on NCA and provide a unified modular framework and notation, as well as a reference implementation in the open-source library NCAtorch. Supplementary materials, videos, and code are available at the project website: https://www.neural-cellular-automata.org/