Efficient on-chip training of large-scale optical neural network through block adjoint training algorithm

MZI-based block optical neural networks (BONNs), which utilize block matrix multiplication to achieve large-scale network models, have garnered significant attention but still lack efficient training algorithms. In this article, by calculating the original field and adjoint field for the block matrices in BONNs and directly updating the phase values of all phase shifters within the optical mesh, we propose an on-chip block adjoint training (BAT) algorithm for large-scale BONNs. To demonstrate the effectiveness of our proposed algorithm, the trained BONNs are applied in image classification tasks for MNIST and SVHN datasets. The calculated results demonstrate that the performance of the BAT algorithm (95.915% for the MNIST dataset and 82.64% for the SVHN dataset) is competitive with the traditional gradient algorithm based on artificial neural networks (96.238% and 84.182%), but the BONNs can infer 1.5 times and 1.3 times faster than artificial neural networks, respectively. By studying the influence of the block size and the inputted position of the padded zero signals, we demonstrate that the BAT algorithm based on the BONNs with 12 block sizes can achieve higher performance by adding the padded zero signals to the same side beside the normal inputted signals. Additionally, we demonstrate that substituting the complete weight matrices with unitary matrices to construct BONNs is an efficient way to reduce both the system area and the required trainable parameters. Finally, we demonstrate the relatively good robustness of the BAT algorithm and the imprecision alleviation method by using on-chip retraining. Notably, our proposed BAT algorithm shows excellent potential for more complex tasks and network models.