Robust training of MZI-based optical neural networks through phase discretization

Mach–Zehnder interferometer (MZI)-based optical neural networks (ONNs) offer high-speed and highly parallel optical computing, but their physical training is affected by finite-resolution phase control, thermal crosstalk, and stochastic phase fluctuations. While phase discretization induced by finite-resolution control is conventionally regarded as a source of quantization error, we reveal an overlooked beneficial effect: the finite spacing between accessible phases provides a sufficiently large probing distance for gradient estimation, thereby improving the robustness of ONN training against stochastic phase noise. To exploit this effect, we construct 2 Q quasi-uniform physical phases from D = Q + 1-bit digital-to-analog converter (DAC) control and develop an index-domain simultaneous perturbation stochastic approximation (SPSA) algorithm with latent continuous-variable updates. Numerical simulations under experimentally representative thermal crosstalk with μ th = 0.02 show that, on MNIST, the Q = 7 discrete-phase ONN maintains its training accuracy within 0.02 of the result without stochastic phase noise at the representative level σ st = 0.02, while exhibiting only an approximately 20% relative reduction even at the strong-noise level σ st = 0.06. Similar robustness trends are observed across different network configurations and on the more challenging Fashion-MNIST and KMNIST datasets. These results demonstrate the potential of phase-discretized training for robust physical optimization of MZI-based ONNs under realistic phase imperfections.