Determining the means of soft labels. z_Q, z, and z* stand for the spectroscopic redshift of a given galaxy, the mean of its skewed scattering profile, and the determined mean of its soft label, respectively, also indicated by the vertical dotted blue, green, and red lines. The skewed scattering profile is assumed to be a bin-wise product of the initial Gaussian profile and the shape of the subsample distribution in the given magnitude bin. Ideally, if the subsample distribution is perfectly balanced (top row), the product profile remains a Gaussian function such that the mean Z of the profile and the mean z* of the soft label align with the spectroscopic redshift value z0. On the other hand, if the subsam-ple distribution has underpopulated regions (bottom row), the product profile is affected by nonflatness and deviates from a Gaussian function (i.e., it is skewed; shown as the green curve), which produces a shifted mean Z. The mean z* of the soft label in this case should be determined according to Eq. (8).