As a result, most models cannot describe the spin effect in magnetic materials. Though several methods for magnetic materials are developed very recently, there is not a complete approach that can include time-reversal symmetry for both collinear and noncollinear magnetic moments cases with spin-orbit coupling to be considered or not. Ivan et al. first presented magnetic Moment Tensor Potentials (mMTPs) which add the contributions of collinear magnetic moments on Moment Tensor Potentials (MTPS) to include collinear magnetic degrees of freedom in ML potential without considering the time-reversal symmetry. Marco et al. then developed magnetic high dimensional neural network potential (mHDNNP) based on the ACSFs to spin-dependent ACSFs (sACSFs) . As mMTPS, mHDNNP can only deal with collinear magnetic moments while the noncollinear magnetic states such as spirals, skyrmions, and bimerons can not be handled. Meanwhile, it is not feasible for calculating magnetic transition temperature with Monte Carlo simulation and perform spin-molecular dynamics . As a result, the ML model with noncollinear magnetic degrees of freedom is significant. M. Domina et al. present machine learning potentials including spin with a spectral neighbor representation for the vector field . The spin is treated as a vector transformed with the bond vector and achieves SE(3) invariant local representation. Nevertheless, the time-reversal and parity symmetry are not kept invariant in its representation causing a symmetry broken in potentials while it should conserve. It's demanding for a model as a general framework for the magnetic material that can not only considers the symmetry of time-reversal and E(3) but can also bring in or out spin-orbit coupling for both collinear and non-collinear cases.