The Data Movement Bottleneck: Theoretical Shortcomings of Analog Optical Fourier Transform and Convolution Computing Accelerators

Modern computing tasks are constrained to having digital electronic input and output data. Due to these constraints imposed by the user, any analog computing accelerator must perform an analog-to-digital conversion on its input data and a subsequent digital-to-analog conversion on its output data. To avoid this the analog hardware would need to completely replace the full functionality of traditional digital electronic computer hardware. Using 27 empirically-measured benchmarks we estimate that an ideal optical accelerator that accelerates Fourier transforms and convolutions can produce an average speedup of 9.4 times, and a median speedup of 1.9 times for the set of benchmarks. The maximum speedups achieved were 45.3 times for a pure Fourier transform and 159.4 times for a pure convolution. These results show that an optical accelerator only produces significant speedup for applications consisting exclusively of Fourier transforms and convolutions. In addition to the theoretical results we quantify the data movement bottleneck which causes a 23.8 times slowdown in a prototype optical Fourier transform accelerator which we built from widely-available off-the-shelf parts.