  An optical neural network is proposed and demonstrated with programmable
matrix transformation and nonlinear activation function of photodetection
(square-law detection). Based on discrete phase-coherent spatial modes, the
dimensionality of programmable optical matrix operations is 30~37, which is
implemented by spatial light modulators. With this architecture, all-optical
classification tasks of handwritten digits, objects and depth images are
performed on the same platform with high accuracy. Due to the parallel nature
of matrix multiplication, the processing speed of our proposed architecture is
potentially as high as7.4T~74T FLOPs per second (with 10~100GHz detector)
