  The technologically-relevant task of feature extraction from data performed
in deep-learning systems is routinely accomplished as repeated fast Fourier
transforms (FFT) electronically in prevalent domain-specific architectures such
as in graphics processing units (GPUs). However, electronics systems are
limited with respect to power dissipation and delay, both, due to wire-charging
challenges related to interconnect capacitance. Here we present a silicon
photonics-based architecture for convolutional neural networks that harnesses
the phase property of light to perform FFTs efficiently by executing the
convolution as a multiplication in the Fourier-domain. The algorithmic
executing time is determined by the time-of-flight of the signal through this
photonic reconfigurable passive FFT filter circuit and is on the order of 10s
of picosecond. A sensitivity analysis shows that this optical processor must be
thermally phase stabilized corresponding to a few degrees. Furthermore, we find
that for a small sample number, the obtainable number of convolutions per
{time-power-chip area) outperforms GPUs by about 2 orders of magnitude. Lastly,
we show that, conceptually, the optical FFT and convolution-processing
performance is indeed directly linked to optoelectronic device-level, and
improvements in plasmonics, metamaterials or nanophotonics are fueling next
generation densely interconnected intelligent photonic circuits with relevance
for edge-computing 5G networks.
