Fig. 1. Schematic diagram of 2×2 Mach-Zehnder interferometer

Fig. 2. Forward-propagating MZI mesh structures. (a) Triangular mesh structure^[10]; (b) rectangular mesh structure^[10]

Fig. 3. Cyclic MZI mesh structures^[10]. (a) Quadrilateral topological mesh structure; (b) hexagonal topological mesh structure; (c) triangular topological mesh structure

Fig. 4. MZI meshes of other topological structures. (a) Vertically parallel waveguide mesh structure^[52]; (b) 2D coupled microring mesh structure^[56]

Fig. 5. Schematic diagrams of gradient-optimization-based self-configuration approaches. (a) Architecture of online backpropagation-based configuration^[76]; (b) experimental setup for numerical gradient descent algorithm^[77]; (c) experimental setup combining Adam algorithm with gradient descent algorithm^[78]; (d) architecture using direct derivative computation method^[79]

Fig. 6. Biological-inspired self-configuration algorithm. (a) Hardware control flow^[81]; (b) software control flow^[82]

Fig. 7. Configuration flow of hybrid mutation strategy based genetic algorithm^[83]

Fig. 8. Reference path-assisted self-configuration algorithm. (a) Self-configuration schematic based on Kramers-Kronig relations^[8]; (b) self-configuration schematic based on universal reference path assistance technology^[84]

Fig. 9. Self-configuration algorithm based on backpropagation and stochastic gradient descent^[31]. (a) Schematic diagram of two-layer optical neural network experiment; (b) feedback and control loop used in experiment; (c) optical micrograph illustration of experimentally demonstrated OIU; (d) schematic diagram of single phase shifter in MZI and transmission curve for tuning internal phase shifter

Fig. 10. Structure calibration and error-compensated self-configuration algorithms. (a) Graph-topology framework flow for network construction^[85]; (b) schematic of pre-calibration error compensation method^[86]; (c) optimized error compensation configuration approach^[88]; (d) 3 dB splitter error compensation strategy for symmetric MZI structure^[89]

Fig. 11. Noise-robust self-configuration algorithms. (a) Noise-aware quantization (ROQ) and protected group lasso (PGL) regularization flow^[91]; (b) MZI mesh noise optimization framework^[92]

Fig. 12. Genetic algorithm configuration workflow^[93]