  In recent years, Convolutional Neural Networks (CNNs) have enabled ubiquitous
image processing applications. As such, CNNs require fast runtime (forward
propagation) to process high-resolution visual streams in real time. This is
still a challenging task even with state-of-the-art graphics and tensor
processing units. The bottleneck in computational efficiency primarily occurs
in the convolutional layers. Performing operations in the Fourier domain is a
promising way to accelerate forward propagation since it transforms
convolutions into elementwise multiplications, which are considerably faster to
compute for large kernels. Furthermore, such computation could be implemented
using an optical 4f system with orders of magnitude faster operation. However,
a major challenge in using this spectral approach, as well as in an optical
implementation of CNNs, is the inclusion of a nonlinearity between each
convolutional layer, without which CNN performance drops dramatically. Here, we
propose a Spectral CNN Linear Counterpart (SCLC) network architecture and
develop a Knowledge Distillation (KD) approach to circumvent the need for a
nonlinearity and successfully train such networks. While the KD approach is
known in machine learning as an effective process for network pruning, we adapt
the approach to transfer the knowledge from a nonlinear network (teacher) to a
linear counterpart (student). We show that the KD approach can achieve
performance that easily surpasses the standard linear version of a CNN and
could approach the performance of the nonlinear network. Our simulations show
that the possibility of increasing the resolution of the input image allows our
proposed 4f optical linear network to perform more efficiently than a nonlinear
network with the same accuracy on two fundamental image processing tasks: (i)
object classification and (ii) semantic segmentation.
