This is one of the only attempt to represent a CA rule as a CNN I have come across. The author uses a deep CNN to learn a rule and studies various information-theoretic quantities in the activation patterns to evaluate the complexity of the rules.
I am personally very interested by the paper since it is an interesting direction for creating neural-network based rules that can be sampled and efficiently stored and applied. This work is also cited in (Mordvintsev et al. 2020).
- William Gilpin. . "Cellular Automata as Convolutional Neural Networks". Arxiv:1809.02942 [cond-mat, Physics:nlin, Physics:physics]. http://arxiv.org/abs/1809.02942.
- Alexander Mordvintsev, Ettore Randazzo, Eyvind Niklasson, Michael Levin. . "Growing Neural Cellular Automata". Distill 5 (2):e23. DOI. See notes