Fig. 2: Working principle and experimental implementation of the Photonic Neural Cellular automata.

a Working principle of neural cellular automata. Each pixel/cell interacts with its neighboring cells with a set of weights, trained with gradient descent. The final values of these cells represent an individual local decision about the global distribution. b The local interaction scheme behaves as a perceptron, whose output becomes the value of the cell in the next step. While the weighted sum is performed in photonics by the combination of the outputs of variable optical attenuators, c the pump depletion in a periodically poled lithium niobate waveguide, d serves as the nonlinear activation