We observed that when O approaches O2, the 9th, 10th, and 11th PES exhibit a rapid change in character when O2 bond length is in the range of 1.0~1.2 Å which can be seen in panel a of Figure . This rapid change of electronic structure is due to interaction with higher states in this short O2 bond length region. States beyond the first 14 are not included in our adiabaticequivalent diabatic representation. With all data weighted equally in 2023 version of the surface, the NN gives unsmooth low-lying PESs; these were not uncovered in our trial dynamics calculations prior to publishing the 2023 surfaces, but they became clear in subsequent dynamics calculations with those surfaces, for which some of the trajectories are unphysical. This problem persisted in the early fts for the present improved surfaces. We finally found that we could make the potential energy surfaces of the low-lying states smoother and reduce the impact of this nonsmoothness by using higher weights for the first 8 states during training. Specifically, the first and last terms in the cost function as described in eq (14) -which account for adiabatic potential energies and permutational restraints -were modified as follows: