Learnable and time-reversible cellular automata with holography principle
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Recently, there are active studies to extend the concept of convolutional neural networks(CNNs) to non-Euclidean space. In particular, there have been a study on how to implement CNNs for data in non-Euclidean space that are invariant under a certain transformation. During this process, the concept of symmetry came in and convolution was described as a covariant form after considering gauge symmetry. Therefore, the covariant CNNs might be suitable framework for learning physical transformations, and conventional CNNs can be seen as a approximations of the framework. In this point of view, we demonstrate to learning process of cellular automata(CA) that could satisfy locality,time-reversibility and the holographic principle through CNNs. After choosing a rules that satisfy the above three conditions for cells, CNNs architecture that can learn rules were proposed and it was confirmed that accurate inferences were made for simple examples.
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