We propose all-optical neural networks characterized by very high energy efficiency and performance density of inference. We argue that the use of microcavity exciton-polaritons allows to take advantage of the properties of both photons and electrons in a seamless manner. This results in strong optical nonlinearity without the use of optoelectronic conversion. We propose a design of a realistic neural network and estimate energy cost to be at the level of attojoules per bit, also when including the optoelectronic conversion at the input and output of the network, several orders of magnitude below state-of-the-art hardware implementations. We propose two kinds of nonlinear binarized nodes based either on optical phase shifts and interferometry or on polariton spin rotations.
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