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Neural networks are widely deployed models across many scientific disciplinesand commercial endeavors ranging from edge computing and sensing to large-scalesignal processing in data centers. The most efficient and well-entrenchedmethod to train such networks is backpropagation, or reverse-mode automaticdifferentiation. To counter an exponentially increasing energy budget in theartificial intelligence sector, there has been recent interest in analogimplementations of neural networks, specifically nanophotonic neural networksfor which no analog backpropagation demonstration exists. We designmass-manufacturable silicon photonic neural networks that alternately cascadeour custom designed "photonic mesh" accelerator with digitally implementednonlinearities. These reconfigurable photonic meshes program computationallyintensive arbitrary matrix multiplication by setting physical voltages thattune the interference of optically encoded input data propagating throughintegrated Mach-Zehnder interferometer networks. Here, using our packagedphotonic chip, we demonstrate in situ backpropagation for the first time tosolve classification tasks and evaluate a new protocol to keep the entiregradient measurement and update of physical device voltages in the analogdomain, improving on past theoretical proposals. Our method is made possible byintroducing three changes to typical photonic meshes: (1) measurements atoptical "grating tap" monitors, (2) bidirectional optical signal propagationautomated by fiber switch, and (3) universal generation and readout of opticalamplitude and phase. After training, our classification achieves accuraciessimilar to digital equivalents even in presence of systematic error. Ourfindings suggest a new training paradigm for photonics-accelerated artificialintelligence based entirely on a physical analog of the popular backpropagationtechnique.

Experimentally realized in situ backpropagation for deep learning in nanophotonic neural networks