Fig. 1. Integrated self-monitored all-optical neuronal circuit.

a The architecture diagram of the proposed SM-AONN. X and Y are input and output optical signals in vectors, respectively. W_i, f_i and M_i represent linear transformation, nonlinear activation function and electrical monitoring signals for the i-th hidden layer, respectively. b Reconfigurable Si-based MZI mesh for optical linear operations. Any real matrix, corresponding to any linear transformation, can be decomposed into the product of unitary matrix and diagonal matrix through singular value decomposition. The unitary matrices can be equivalent to MZI networks in triangular or rectangular meshes⁵⁶. The diagonal matrix can be equivalent to MZI arrays. The figure shows the rectangular mesh connected by 6 MZIs, equivalent to any 4 × 4 unitary matrixes. c The detailed structure of a tunable Mach-Zehnder interferometer. An MZI consists of two optical phase shifters and two splitters. Any 2 × 2 unitary matrixes can be configured. The MZI network integrated in a photonic chip interconnects with the DAC through wire bonding. Al, aluminum. d The Ge-Si all-optical nonlinear block for optical nonlinear activation and electrical monitoring. Four AONUs are included. e From light-splitting-and-detection to non-intrusive monitoring. f The detailed structure of the AONU. The Ge film coats on the Si waveguide and interacts with light.