In this paper, we will consider the deep learning systems that can learn fundamental physics theory based on cellular automaton interpretation (CAI). First, assuming that we can map quantum states to cellular automaton (CA) and calculate the time-evolved CA for any initial CA by knowing the time-evolution law of the given system, we will show that there exists a convolutional neural network (CNN) architecture that can learn the time-evolution law of this system with only the calculated data set for a time-reversible CA. Mathematically, finding a CNN architecture that can learn CA rule is equivalent to showing that a time-evolution operator can be approximated as a finite composition of time-independent linear functions and ReLU type non-linear functions, as the possible associated generator of approximation may absorbs the information about the dynamics. Going one step further, we will discuss the correspondence between the quantum system and deep learning architecture and relate the concept of moduli space of Riemann surfaces to deep learning parameters when considering interactions. Finally, for the CA model in which the dimensional reduction in quantum gravity was first presented, we will discuss the CNN architecture that can find the non-trivial evolution law for holographic direction in a deductive way without the label. It is suggested that the limits to this effort can be improved through AdS/CFT correspondance.

翻译：本文探讨能够基于细胞自动机解释学习基础物理理论的深度学习系统。首先，假设我们可以将量子态映射到细胞自动机，并通过已知系统的时间演化律计算任意初始细胞自动机的时间演化状态，我们将证明存在一种卷积神经网络架构，能够仅利用时间可逆细胞自动机的计算数据集学习该系统的演化律。数学上，寻找可学习细胞自动机规则的卷积神经网络架构等价于证明时间演化算子可近似为时间无关线性函数与ReLU型非线性函数的有限复合，其潜在的近似生成元可能吸收动力学信息。进一步地，我们将讨论量子系统与深度学习架构之间的对应关系，并在考虑相互作用时将黎曼曲面模空间的概念与深度学习参数相关联。最后，针对首次提出量子引力维度约简的细胞自动机模型，我们将探讨能够以演绎方式无标签地发现全息方向非平凡演化律的卷积神经网络架构，并指出通过AdS/CFT对应可改进该研究的局限性。