These modified NACs, referred to as smoothed NACs ( Cij , 'smooth_nacs') are pre-computed and stored in the database. This can be achieved by enabling the smooth_nacs=True option when using the GenerateDB or ConvertDB classes of spainn.asetools to create a SpaiNN database. Moreover, training of NACs and other properties arising from the interaction of two electronic states is further complicated by the arbitrary phase inherent in the wavefunction, resulting in these properties bearing an arbitrary sign. Numerous strategies have been proposed to confront this challenge, including phase correction of the data prior to fitting , and a phase-free training algorithm enabling the training of raw data. While the former approach is often applicable only within limited conformational re-gions of a molecule, the latter is constrained by the escalating training complexity as the number of electronically excited states increases. SpaiNN incorporates two classes of phase-free loss functions, namely PhaseLossAtomistic and PhysPhaseLossAtomistic, enhancing computational efficiency and simplicity compared to the original approach of SchNarc. The different loss functions implemented are explained in detail in the SI in section S1. 4.