标题： 频率直方图在元胞自动机和2D CA中的粗粒化 显示英文标题

标题： Frequency-Histogram Coarse Graining in Elementary Cellular Automata and 2D CA

摘要： 细胞自动机和其他离散动力系统长期以来一直被用作涌现复杂性的模型。 最近，神经细胞自动机被提出作为研究更通用的人工智能涌现的模型，这得益于它们支持自组织、涌现和开放性等特性的倾向。 然而，理解大规模系统中的涌现复杂性是一个开放性挑战。 如何识别导致涌现复杂结构和行为的重要计算？ 在本工作中，我们系统地研究了一种基于将宏观状态粗粒化为较小块的一维和二维细胞自动机的降维方法。 我们讨论了选定的示例，并在附录中提供了不同过滤级别下的粗粒化完整探索（也可通过此链接在线获取：https://s4nyam.github.io/eca88/）。 我们认为，能够捕捉人工智能系统中的涌现复杂性可能会为开放性进化铺平道路，这是实现人工通用智能的可行路径。 显示英文摘要

摘要： Cellular automata and other discrete dynamical systems have long been studied as models of emergent complexity. Recently, neural cellular automata have been proposed as models to investigate the emerge of a more general artificial intelligence, thanks to their propensity to support properties such as self-organization, emergence, and open-endedness. However, understanding emergent complexity in large scale systems is an open challenge. How can the important computations leading to emergent complex structures and behaviors be identified? In this work, we systematically investigate a form of dimensionality reduction for 1-dimensional and 2-dimensional cellular automata based on coarse-graining of macrostates into smaller blocks. We discuss selected examples and provide the entire exploration of coarse graining with different filtering levels in the appendix (available also digitally at this link: https://s4nyam.github.io/eca88/). We argue that being able to capture emergent complexity in AI systems may pave the way to open-ended evolution, a plausible path to reach artificial general intelligence.