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Analog computing paradigms are promising solutions to the growing computational demands of machine learning applications. Despite being susceptible to errors, analog and mixed-signal platforms have the potential to achieve higher speed and power efficiency for artificial neural network (ANN) applications than digital computers. Driven by the development of digital fixed-point ANN accelerators, low-precision ANN models have proven to be successful in compressing the size of ANNs and conforming the models to the data format of digital accelerators. While the inputs and weights of these digital, fixed-point ANN models can have low bit widths, the intermediate results (e.g., activations) must be preserved in high precision. As a result, these digital fixed-point models and training algorithms cannot be migrated easily to analog accelerators, because the analog intermediate results typically suffer from reduced precision due to noises and device imperfections. Here, we report on a training method for mixed-signal ANNs that considers two types of analog impairments, namely, random noise and distortion (deterministic in nature). The results show that mixed-signal ANN trained with our method can achieve the same classification accuracy as the digital fixed-point model with noise levels up to 50% of the ideal quantization step size. We demonstrate our training method on a mixed-signal, convolutional neural network based on diffractive optics.

Training of Mixed-Signal Optical Convolutional Neural Networks With Reduced Quantization Levels