  Memristor-based neuromorphic computing could overcome the limitations of
traditional von Neumann computing architectures -- in which data are shuffled
between separate memory and processing units -- and improve the performance of
deep neural networks. However, this will require accurate synaptic-like device
performance, and memristors typically suffer from poor yield and a limited
number of reliable conductance states. Here we report floating gate memristive
synaptic devices that are fabricated in a commercial complementary
metal-oxide-semiconductor (CMOS) process. These silicon synapses offer analogue
tunability, high endurance, long retention times, predictable cycling
degradation, moderate device-to-device variations, and high yield. They also
provide two orders of magnitude higher energy efficiency for
multiply-accumulate operations than graphics processing units. We use two
12-by-8 arrays of the memristive devices for in-situ training of a 19-by-8
memristive restricted Boltzmann machine for pattern recognition via a gradient
descent algorithm based on contrastive divergence. We then create a memristive
deep belief neural network consisting of three memristive restricted Boltzmann
machines. We test this on the modified National Institute of Standards and
Technology (MNIST) dataset, demonstrating recognition accuracy up to 97.05%.
