<p>This study investigates the Kairat-X equation, a nonlinear model that plays a crucial role in describing complex wave phenomena. A novel neural network-based approach, inspired by analytical expansion strategies, is proposed WAS Neural Network Method to derive exact soliton solutions of the equation. Several new families of solutions are obtained, including dark solitons, kink-type solitons, and singular periodic waves, which have not been previously reported in the literature. The stability analysis of these solutions demonstrates their physical feasibility, ensuring that they can represent realistic dynamical behaviors in optical fibers, plasma waves, and fluid systems which show novelty and significance. These findings not only expand the catalog of known solutions for the Kairat-X equation but also highlight the broader potential of neural network-assisted analytical methods in exploring nonlinear wave models across applied sciences.</p>