Not yet reviewed by Pith; the record is open.

Photonic integrated circuits are emerging as a promising platform for accelerating matrix multiplications in deep learning, leveraging the inherent parallel nature of light. Although various schemes have been proposed and demonstrated to realize such photonic matrix accelerators, the in-situ training of artificial neural networks using photonic accelerators remains challenging due to the difficulty of direct on-chip backpropagation on a photonic chip. In this work, we propose a silicon microring resonator (MRR) optical crossbar array with a symmetric structure that allows for simple on-chip backpropagation, potentially enabling the acceleration of both the inference and training phases of deep learning. We demonstrate a $4 \times 4$ circuit on a Si-on-insulator (SOI) platform and use it to perform inference tasks of a simple neural network for classifying Iris flowers, achieving a classification accuracy of 93.3%. Subsequently, we train the neural network using simulated on-chip backpropagation and achieve an accuracy of 91.1% in the same inference task after training. Furthermore, we simulate a convolutional neural network (CNN) for handwritten digit recognition, using a $9 \times 9$ MRR crossbar array to perform the convolution operations. This work contributes to the realization of compact and energy-efficient photonic accelerators for deep learning.