Deep learning with coherent nanophotonic circuits
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...Although we focus our discussion on one particular recently proposed hardware implementation [3], our conclusions are derived starting from Maxwell’s equations, and the ideas could therefore extend to other photonic neural network platforms, as well as to other applications....
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...[3], we assume that the matrix-vector multiplications are implemented using an Optical Interference Unit (OIU), consisting of a mesh of reconfigurable Mach-Zehnder interferometers....
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...The computational resolution of ONNs is limited by practical non-idealities, including (1) thermal crosstalk between phase shifters in interferometers, (2) optical coupling drift, (3) the finite precision with which an optical phase can be set (16 bits in our case), (4) photodetection noise and (5) finite photodetection dynamic range (30 dB in our case)....
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...(3) Once a neural network is trained, the architecture can be passive, and computation on the optical signals will be performed without additional energy input....
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...We used four instances of the OIU to realize the following matrix transformations in the spatial-mode basis: (1) U((1))Σ((1)), (2) V((1)), (3) U((2))Σ((2)) and (4) V((2))....
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...Transformations (1) and (2) realize the first matrix M((1)), and (3) and (4) implement M((2))....
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...ANNs can be trained by feeding training data into the input layer and then computing the output by forward propagation; weighting parameters in each matrix are subsequently optimized using back propagation [16]....
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