Artificial neural networks (ANNs) have now been widely used for industry applications and also played more important roles in fundamental researches. Although most ANN hardware systems are electronically based, optical implementation is particularly attractive because of its intrinsic parallelism and low energy consumption. Here, we propose and demonstrate fully-functioned all optical neural networks (AONNs), in which linear operations are programmed by spatial light modulators and Fourier lenses, and optical nonlinear activation functions are realized with electromagnetically induced transparency in laser-cooled atoms. Moreover, all the errors from different optical neurons here are independent, thus the AONN could scale up to a larger system size with final error still maintaining in a similar level of a single neuron. We confirm its capability and feasibility in machine learning by successfully classifying the order and disorder phases of a typical statistic Ising model. The demonstrated AONN scheme can be used to construct various ANNs of different architectures with the intrinsic parallel computation at the speed of light.
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