Deep Learning with Coherent Nanophotonic Circuits

 Used a series of MachZehnder interferometers with thermoelectric phaseshift elements to realize the unitary component of individual layer weightmatrix computation.
 Weight matrix was decomposed via SVD into UV*, which formed the unitary matrix (4x4, Special unitary 4 group, SU(4)), as well as $\Sigma$ diagonal matrix via amplitude modulators. See figure above / original paper.
 Note that interfereometric matrix multiplication can (theoretically) be zero energy with an optical system (modulo loss).
 In practice, you need to run the phasemoduator heaters.
 Nonlinearity was implemented electronically after the photodetector (e.g. they had only one photonic circuit; to get multiple layers, fed activations repeatedly through it. This was a demonstration!)
 Fed network FFT'd / banded recordings of consonants through the network to get nearsimulated vowel recognition.
 Claim that noise was from imperfect phase setting in the MZI + lower resolution photodiode readout.
 They note that the network can more easily (??) be trained via the finite difference algorithm (e.g. test out an incremental change per weight / parameter) since running the network forward is so (relatively) lowenergy and fast.
 Well, that's not totally true  you need to update multiple weights at once in a large / deep network to descend any highdimensional valleys.
