Fast prediction of torque density profiles driven by three-dimensional (3D) magnetic fields is required for accurate real-time control of plasma toroidal rotation. A toroidal torque spectral neural network (TORQSNet) is developed to enable rapid and accurate prediction of radial profiles of neoclassical toroidal viscosity (NTV) torque, electromagnetic torque, and Reynolds stress torque under the resonant magnetic perturbations (RMPs). TORQSNet is trained and validated using a numerical database of 3D equilibria computed using the MARS-F code for ASDEX Upgrade (AUG), DIII-D, MAST, and ITER. In oscillatory radial regions, torque density profiles are parameterized by Legendre polynomial expansion coefficients, which are predicted by the network and are used as interpretable features linked to resonant response characteristics in magnetohydrodynamic equilibria. Across all four devices and the investigated toroidal mode numbers, coefficients of determination of are obtained for reconstructed NTV torque density profiles. Strong cross-device generalization is demonstrated, with models trained on a single device accurately predicting radial torque profiles in the other three devices. The combined influence of plasma rotation and resistivity is captured by the trained TORQSNet. Core torque is reduced while edge torque is increased, which supports optimization of RMP-based edge localized mode suppression by promoting pedestal penetration and mitigating core flow damping.