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).
- Mordvintsev, Alexander, Ettore Randazzo, Eyvind Niklasson, and Michael Levin. February 11, 2020. "Growing Neural Cellular Automata". Distill 5 (2):e23. DOI.
- Gilpin, William. September 9, 2018. “Cellular Automata as Convolutional Neural Networks”. arXiv:1809.02942 [Cond-Mat, Physics:Nlin, Physics:Physics]. http://arxiv.org/abs/1809.02942.