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Optical neural-network circuit to recognize BPSK labels for photonic label routing is proposed, whose neuron consists of optical amplitude amplifiers and phase shifters as weighting connections, a combiner and a nonlinear threshold device for an activation function. The parameters of these weighting connections are learned with back-propagation of teacher signals. The performance of the neural network circuits as recognition of two to four bit BPSK labels is clarified by computer simulation. For routing application, classification of routing labels into several groups corresponding to the output ports of the router is also discussed and is successfully simulated.