Structured Fluctuations and the Information Dynamics of Self-Maintenance in Growing Neural Cellular Automata.

Overview

1. Graduate School of Arts and Sciences, The University of Tokyo, Tokyo 153-8902, Japan
2. Atomi Information Science and Arts Center, Atomi University, Tokyo 112-8687, Japan
3. Alternative Machine Inc., Tokyo 150-0001, Japan

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, hypothesizing that they constitute a functional component of the dynamics rather than merely residual stochastic noise. We analyzed the trained model through dynamical-systems analysis (low-dimensional embedding and recurrence analysis of collective state trajectories) and information-theoretic analysis (transfer entropy and partial information decomposition), including its response to localized damage and to suppression of small-magnitude updates. These analyses 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-maintenance and self-repair emerge 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.

Reproduced under the paper's license (CC BY), from the paper cited above.

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Data

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Data Availability Statement

The code and trained model checkpoints used in this study are available on a dedicated GitHub repository upon request to Atsushi Masumori.

Reproduced under the paper's license (CC BY), from the paper cited above.

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Version 1, 27 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 3 authors, 8 keywords, 1 funder, 30 references.

Cite

This paper

Masumori, A., Sato, H., & Ikegami, T. (2026). Structured Fluctuations and the Information Dynamics of Self-Maintenance in Growing Neural Cellular Automata. Entropy (Basel, Switzerland), 28(8), 893. https://doi.org/10.3390/e28080893

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