Interpretable-machine-learning-enabled discretized antireflective multilayer design outperforms traditional continuous graded-index coatings

. These simulations revealed that at a 150 nm total thickness, the mean reflectance of the binary design can rise to 5.6%, whereas the octal design remains near 1%, indicating that richer index bases enhance the robustness to fabrication perturbations. We further introduced a phasor-based interpretation to illustrate the justification of second-order factorization machines in navigating the complex design space and identifying near-global optima. These findings highlight the promise of a discrete optimization framework in machine learning to surpass analytical multilayer design rules, enabling fast, interpretable, and fabrication-tolerance inverse design of high-performance multilayer coatings.