The local ansatz was also explored previously in the Local-type model, where the total χ is written as the sum of atomic contribution χ i and χ i was constructed using the tensor product of pairwise interaction 1 I ij . In PiNet2-χ, all flavors including the EEM-type, the EtaInvtype, the ACKS2-type and the Local-type have been upgraded thanks to the inclusion of vectorial features 3 P i into 1 P i and 1 I ij via Eq. 4 and Eq. 1 respectively.