  Optical machine learning offers advantages in terms of power efficiency,
scalability and computation speed. Recently, an optical machine learning method
based on Diffractive Deep Neural Networks (D2NNs) has been introduced to
execute a function as the input light diffracts through passive layers,
designed by deep learning using a computer. Here we introduce improvements to
D2NNs by changing the training loss function and reducing the impact of
vanishing gradients in the error back-propagation step. Using five phase-only
diffractive layers, we numerically achieved a classification accuracy of 97.18%
and 89.13% for optical recognition of handwritten digits and fashion products,
respectively; using both phase and amplitude modulation (complex-valued) at
each layer, our inference performance improved to 97.81% and 89.32%,
respectively. Furthermore, we report the integration of D2NNs with electronic
neural networks to create hybrid-classifiers that significantly reduce the
number of input pixels into an electronic network using an ultra-compact
front-end D2NN with a layer-to-layer distance of a few wavelengths, also
reducing the complexity of the successive electronic network. Using a 5-layer
phase-only D2NN jointly-optimized with a single fully-connected electronic
layer, we achieved a classification accuracy of 98.71% and 90.04% for the
recognition of handwritten digits and fashion products, respectively. Moreover,
the input to the electronic network was compressed by >7.8 times down to 10x10
pixels. Beyond creating low-power and high-frame rate machine learning
platforms, D2NN-based hybrid neural networks will find applications in smart
optical imager and sensor design.

Neural and Evolutionary Computing;Machine Learning;Optics