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Differentiable Logic Cellular Automata
We use Differentiable Logic Gate Networks to create end-to-end differentiable, self-organizing discrete cellular automata powered by recurrent circuits, capable of playing the Game of Life as well as producing patterns à la Neural Cellular Automata.
We again find strong kinship with the the work Programmable Matter and Computronium by Toffoli and Margolus, who proposed the CAM-8 , a computer architecture based on cellular automata which is similar to the system above where each cell uses a DRAM chips for state variables and an SRAM for processing. In contrast to traditional computing, which relies on precise, error-free components, robust systems are designed to remain functional even in the face of hardware failures, environmental interference, unexpected inputs, or manufacturing variations. The successful application of differentiable logic gates to cellular automata is demonstrated through two key results: replicating the rules of Conway's Game of Life and generating patterns via learned discrete dynamics.
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