  Due to their high degree of parallelism, fast processing speeds and low power
consumption, analog optical functional elements offer interesting routes for
realizing neuro-morphic computer hardware. For instance, convolutional neural
networks lend themselves to analog optical implementations by exploiting the
Fourier-transform characteristics of suitable designed optical setups. However,
the efficient implementation of optical nonlinearities for such neural networks
still represents challenges. In this work, we report on the realization and
characterization of a three-layer optical convolutional neural network where
the linear part is based on a 4f-imaging system and the optical nonlinearity is
realized via the absorption profile of a cesium atomic vapor cell. This system
classifies the handwritten digital dataset MNIST with 83.96% accuracy, which
agrees well with corresponding simulations. Our results thus demonstrate the
viability of utilizing atomic nonlinearities in neural network architectures
with low power consumption.
