Differentiable Logic Cellular Automata: From Game of Life to Pattern Generation with Learned Recurrent Circuits
This paper introduces DiffLogic CA, a novel neural cellular automata (NCA) architecture using a fully discrete cell state updated via a learned, recurrent binary circuit. Replacing neural network components with Deep Differentiable Logic Networks allows differentiable training of discrete logic gates. The success of applying differentiable logic gates to cellular automata is demonstrated by replicating Conway's Game of Life and generating patterns through learned discrete dynamics. This highlights the potential of integrating discrete logic within NCAs and proves differentiable logic gate networks can be effectively learned in recurrent architectures. While promising, training for complex shapes remains a challenge, suggesting future work on hierarchical architectures and specialized gates for improved state management.
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