将细胞自动机与神经网络结合，实现自组织生成系统建模。
A New Kind of Network? Review and Reference Implementation of Neural Cellular Automata
- 用可学习的神经网络替代传统规则，让细胞自动机从数据中自主演化。
- 提出统一框架与开源实现，支持多种复杂系统的生成建模。
- 适合对生成模型、自组织系统感兴趣的科研人员和开发者。
Stephen Wolfram 在2003年的开创性著作《一种新科学》中指出，以细胞自动机（CA）为代表的简单递归程序，是替代现有数学形式（如微分方程）来建模复杂系统的一种有前景方法。尽管过去二十多年间细胞自动机在科学应用上尚未取得突破性进展，但近期研究展示了将沃尔弗拉姆思想与可学习的人工神经网络相结合的新路径：神经细胞自动机（NCA）能够从数据样本中学习复杂的更新规则，从而建模自组织的生成系统。本文旨在综述现有的NCA研究工作，提供统一的模块化框架与符号表示，并发布基于开源库NCAtorch的参考实现。补充材料、视频及代码可在项目网站 https://www.neural-cellular-automata.org/ 获取。
原文摘要 · Abstract (English)
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/
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