The parallel updating scheme of RRAM-based analog neuromorphic systems based on sign stochastic gradient descent (SGD) can dramatically accelerate the training of neural networks. However, sign SGD can decrease accuracy. Also, some non-ideal factors of RRAM devices, such as intrinsic variations and the quantity of intermediate states, may significantly damage their convergence. In this paper, we analyzed the effects of these issues on the parallel updating scheme and found that it performed poorly on the task of MNIST recognition when the number of intermediate states was limited or the variation was too large. Thus, we propose a weighted synapse method to optimize the parallel updating scheme. Weighted synapses consist of major and minor synapses with different gain factors. Such a method can be widely used in RRAM-based analog neuromorphic systems to increase the number of equivalent intermediate states exponentially. The proposed method also generates a more suitable Δ W , diminishing the distortion caused by sign SGD. Unlike when several RRAM cells are combined to achieve higher resolution, there are no carry operations for weighted synapses, even if a saturation on the minor synapses occurs. The proposed method also simplifies the circuit overhead, rendering it highly suitable to the parallel updating scheme. With the aid of weighted synapses, convergence is highly optimized, and the error rate decreases significantly. Weighted synapses are also robust against the intrinsic variations of RRAM devices.
Keywords: neural networks; online learning; resistive random-access memory (RRAM); sign stochastic gradient descent; weighted synapses.