Approach to the cellular automaton interpretation using deep learning

Recently, there has been significant research on the connection between physics theory and machine learning. As a way to approach physics theory from machine learning, there has been a study on the universe that learns its own laws based on the fact that quantum field theory and learning system are expressed as a matrix model in much the same way. In the opposite position, certain familiar symmetries have been required for conventional convolutional neural networks (CNNs) for performance improvement, and as a result, CNNs have come to be expressed in a covariant form that physics theory must satisfy. These positive signals can be a driving force for studying physics theory using machine learning, but in reality, there are several difficulties in implementing a working system. First of all, just because the convolution can be expressed in covariant form, it is not obvious to implement the algorithm corresponding to that expression. At the beginning of this paper, we show that it is possible to reach covariant CNNs through the proposed method without implementing the specific algorithm. However, the more serious problem is that there is still insufficient discussion on how to collect a well-defined data set corresponding to the law to be learned. Therefore, in the current situation, it would be best to simplify the problem to satisfy some physical requirements and then see if it is possible to learn with the corresponding neural-networks architecture. In this point of view, we demonstrate to learning process of cellular automata (CA) that could satisfy locality, time-reversibility through CNNs. With simple rules that satisfy the above two conditions and an arbitrary dataset that satisfies those rules, CNNs architecture that can learn rules were proposed and it was confirmed that accurate inference, that is, an approximation of the equation was made for simple examples.