  Within the framework of natural orbital functional theory, having a
convenient representation of the occupation numbers and orbitals becomes
critical for the computational performance of the calculations. Recognizing
this, we propose an innovative parametrization of the occupation numbers that
takes advantage of the electron-pairing approach used in Piris natural orbital
functionals through the adoption of the softmax function, a pivotal component
in modern deep-learning models. Our approach not only ensures adherence to the
N-representability of the first-order reduced density matrix (1RDM) but also
significantly enhances the computational efficiency of 1RDM functional theory
calculations. The effectiveness of this alternative parameterization approach
was assessed using the W4-17-MR molecular set, which demonstrated faster and
more robust convergence compared to previous implementations.
