Matrix eigenvalue solver based on reconfigurable photonic neural network

Abstract

The solution of matrix eigenvalues has always been a research hotspot in the field of modern numerical analysis, which has important value in practical application of engineering technology and scientific research. Despite the fact that currently existing algorithms for solving the eigenvalues of matrices are well-developed to try to satisfy both in terms of computational accuracy and efficiency, few of them have been able to be realized on photonic platform. The photonic neural network not only has strong judgment in solving inference tasks due to the superior learning ability, but also makes full use of the advantages of photonic computing with ultrahigh speed and ultralow energy consumption. Here, we propose a strategy of an eigenvalue solver for real-value symmetric matrices based on reconfigurable photonic neural networks. The strategy shows the feasibility of solving the eigenvalues of real-value symmetric matrices of n × n matrices with locally connected networks. Experimentally, we demonstrate the task of solving the eigenvalues of 2 × 2, 3 × 3, and 4 × 4 real-value symmetric matrices based on graphene/Si thermo-optical modulated reconfigurable photonic neural networks with saturated absorption nonlinear activation layer. The theoretically predicted test set accuracy of the 2 × 2 matrices is 93.6% with the measured accuracy of 78.8% in the experiment by the standard defined for simplicity of comparison. This work not only provides a feasible solution for the on-chip integrated photonic realization of eigenvalue solving of real-value symmetric matrices, but also lays the foundation for a new generation of intelligent on-chip integrated all-optical computing.

Integrated Photonic Neural Networks: Opportunities and Challenges

“…(e) Optical micrograph of the locally connected IPNNs with nine input ports ( i 1 – i 9 ) and four output ports ( o 1 – o 4 ). Reprinted with permission from ref . Copyright 2022 De Gruyter.…”

“…This scheme has a large operating bandwidth with the response frequency of 70 MHz, a low loss of 4.28 dB, and a low threshold power of 5.1 mW. In 2022, Hu’s group proposed and experimentally verified the performance of a single-layer graphene with optical nonlinear saturable absorption effect covered on a silicon waveguide as a nonlinear activation layer in an on-chip integrated locally connected photonic neural network (Figure c) . Compared with the configuration without the proposed nonlinear layer, there is about 30% improvement in accuracy in the task of solving the eigenvalues of second-order real symmetric matrices.…”

“…The transmission curve with fitting parameters of saturated absorption effect of α S = 0.088, α NS = 0.852, and I s = 5.446. Reprinted with permission from ref . Copyright 2022 De Gruyter.…”

“…Details about integrated optical activation functions will be further discussed in the later section. But it is worth noting that in 2022, Hu et al demonstrated a five-layer integrated locally connected photonic neural network with an all-optical saturated absorption nonlinear activation layer, 57 as shown in Figure 1e. This network contains an activation layer after the second linear layer, allowing it to deal with complex tasks such as solving for the eigenvalues of a matrix.…”

“…In 2022, Hu's group proposed and experimentally verified the performance of a single-layer graphene with optical nonlinear saturable absorption effect covered on a silicon waveguide as a nonlinear activation layer in an on-chip integrated locally connected photonic neural network (Figure 4c). 57 Compared with the configuration without the proposed nonlinear layer, there is about 30% improvement in accuracy in the task of solving the eigenvalues of second-order real symmetric matrices. This work lays the foundation for a new generation of intelligent onchip integrated all-optical computing.…”