Integrated photonic deep neural network with end-to-end on-chip backpropagation training

Integrated photonic neural networks (PNNs) have demonstrated significant potential to complement the digital electronic counterparts [1-3]. Nevertheless, robust and repeatable performance of scalable integrated PNNs is directly tied to the quality of their training. Error backpropagation (BP), which relies on nonlinear activation gradient computation, is the mainstream algorithm to train digital neural networks due to its scalability, versatility, and implementation efficiency [4]. Consequently, its adoption is highly desirable for the training of scalable PNNs. Despite such benefits and due to the lack of scalable on-chip activation gradient [5], PNNs have mostly been trained using a digital computer to run BP, which is inadequate in addressing device variations, or through gradient-free algorithms that do not fully benefit from the versatility of BP training. Here, we report the demonstration of an integrated photonic deep neural network with end-to-end on-chip gradient-descent BP training. All linear and nonlinear computations are performed on a single photonic chip, leading to scalable and robust training despite the considerable--but typical--fabrication-induced device variations. Two nonlinear data classification tasks are demonstrated in which the chip performance matches that of the ideal digital model, both in accuracy and robustness. Integrating the advantages of BP training with PNNs allows for generalization to various PNN architectures, paving the way for scalable and reliable next-generation photonic computing systems.