 It renders the algorithm invariant to monotonous formula_3-transformations.Let

such that formula_171 is the density of the multivariate normal distribution formula_172.Then, we have an explicit expression for the inverse of the Fisher information matrix where formula_65 is fixed

and for

and, after some calculations, the updates in the CMA-ES turn out as



and



where mat forms the proper matrix from the respective natural gradient sub-vector.