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Methods and systems for training a neural network are provided. In one example, an apparatus comprises a memory that stores instructions; and a hardware processor configured to execute the instructions to: control a neural network processor to perform a loss gradient operation to generate data gradients; after the loss gradient operation completes, control the neural network processor to perform a forward propagation operation to generate intermediate outputs; control the neural network processor to perform a backward propagation operation based on the data gradients and the intermediate outputs to generate weight gradients; receive the weight gradients from the neural network processor; and update weights of a neural network based on the weight gradients.