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As a new emerging machine learning mechanism, optical diffractive deep neural network (OD2NN) has been intensively studied recently due to its incomparable advantages on speed and power efficiency. However, the training process of the OD2NN with traditional back-propagation (BP) method is always time-consuming. Here, we introduce the biologically plausible training methods without feedback to accelerate the training process of the hybrid OD2NN. Direct feedback alignment (DFA), error-sign-based DFA (sDFA) and direct random target projection (DRTP) are utilized and evaluated in the training process of the hybrid OD2NN respectively. For the hybrid OD2NN with 20 diffractive layers, about 160× (DFA; CPU), 30× (DFA; GPU), 170× (sDFA; CPU), 32× (sDFA; GPU), 158× (DRTP; CPU) and 32× (DRTP; GPU) accelerations are achieved respectively without significant loss of accuracy, compared with the training process using BP method on CPU or GPU.
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