The robust and repeatable performance of scalable integrated photonic neural networks (PNNs)1–3 strongly depends on the quality of their training. Gradient-based backpropagation is the mainstream algorithm for training digital neural networks thanks to its scalability, versatility and implementation efficiency4. Consequently, there is an interest in implementing it within a photonic platform in an all-optical manner. At present, owing to the lack of a scalable on-chip activation gradient5, training PNNs has relied on digital computers to run backpropagation, whose performance is reduced in the presence of inevitable device-to-device and environmental variations, or on gradient-free algorithms that do not fully benefit from the versatility of backpropagation training. Here we report the demonstration of an integrated photonic deep neural network, trained end-to-end with on-chip gradient-descent backpropagation. All linear and nonlinear computations are performed on a single photonic chip, leading to scalable and robust training, despite the considerable yet typical fabrication-induced device variations. In two nonlinear data classification tasks, chip performance matches that of the reference digital model in accuracy (over 90%) and robustness without using a digital computer. Integrating the advantages of backpropagation training with PNNs allows for generalization to various PNN architectures for future scalable and reliable photonic computing systems.
