  In this paper, we propose a learning rule based on a back-propagation (BP)
algorithm that can be applied to a hardware-based deep neural network (HW-DNN)
using electronic devices that exhibit discrete and limited conductance
characteristics. This adaptive learning rule, which enables forward, backward
propagation, as well as weight updates in hardware, is helpful during the
implementation of power-efficient and high-speed deep neural networks. In
simulations using a three-layer perceptron network, we evaluate the learning
performance according to various conductance responses of electronic synapse
devices and weight-updating methods. It is shown that the learning accuracy is
comparable to that obtained when using a software-based BP algorithm when the
electronic synapse device has a linear conductance response with a high dynamic
range. Furthermore, the proposed unidirectional weight-updating method is
suitable for electronic synapse devices which have nonlinear and finite
conductance responses. Because this weight-updating method can compensate the
demerit of asymmetric weight updates, we can obtain better accuracy compared to
other methods. This adaptive learning rule, which can be applied to full
hardware implementation, can also compensate the degradation of learning
accuracy due to the probable device-to-device variation in an actual electronic
synapse device.
