Activity-difference training of deep neural networks using memristor crossbars

Artificial neural networks have rapidly progressed in recent years, but are limited by the high energy costs required to train them on digital hardware. Emerging analogue hardware, such as memristor arrays, could offer improved energy efficiencies. However, the widely used backpropagation training algorithms are generally incompatible with such hardware because of mismatches between the analytically calculated training information and the imprecision of actual analogue devices. Here we report activity-difference-based training on co-designed tantalum oxide analogue memristor crossbars. Our approach, which we term memristor activity-difference energy minimization, treats the network parameters as a constrained optimization problem, and numerically calculates local gradients via Hopfield-like energy minimization using behavioural differences in the hardware targeted by the training. We use the technique to train one-layer and multilayer neural networks that can classify Braille words with high accuracy. With modelling, we show that our approach can offer over four orders of magnitude energy advantage compared with digital approaches for scaled-up problem sizes. An activity-difference training approach, which employs 64 x 64 memristor arrays with integrated complementary metal-oxide-semiconductor control circuitry, can be used to train a deep neural network to efficiently classify Braille words.