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Furthermore, the branching correction is found to be especially important when dealing with strongly repulsive potential energy surfaces, which are common in realistic systems, thus promising for general applications.The message passing neural network (MPNN) framework is a promising tool for modeling atomic properties but is, until recently, incompatible with directional properties, such as Cartesian tensors. We propose a modified Cartesian MPNN (CMPNN) suitable for predicting atom-centered multipoles, an essential component of ab init