Phase-Aware Training of a Dynamical Photonic Network: A Stable Real-Imaginary Parameterization

Photonic and wave-based computing architectures offer the promise of massively parallel computation via interference and phase dynamics. However, training such systems with gradient-based methods remains challenging due to phase discontinuities, unstable complex-valued gradients, and mismatches between simulation and learning dynamics. In this work, we present a phase-aware training method for a dynamical photonic network that explicitly parameterizes connectivity in real-imaginary form, avoiding angle-based representations. We demonstrate stable end-to-end training of a recurrent, interference-driven photonic substrate on the MNIST classification task, achieving ~95% test accuracy without convolutional structure or digital depth. Our results show that (i) phase degrees of freedom materially increase learnable capacity, (ii) dynamical rollouts must be matched between training and evaluation, and (iii) modest classification performance is sufficient to validate the feasibility of learning interference-based computation. This work establishes a practical bridge between photonic simulation and gradient-based optimization.