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Hopfield neural networks tolerating weight faults are presented. The network training is made on condition some faults occur. Statuses of such faults are evoked by intentionally injecting faults into the network. The learning using the single-fault injection is shown first. Learning schemes, which are based on the double-fault injection for a couple of weights within a neuron, are then proposed to improve the fault tolerance further. Experimental results show that the learning using the random-double-fault injection allows us to complete the reasonably dependable network with the acceptable length of the learning time. In addition, the proposed schemes make the network robust against the input noise.