(a) The Z_pred obtained using GPM-ResNet. (b and c) The predicted results obtained from second-order and third-order polynomials fit based on the color-metallicity relation, respectively. In all three subplots, the top panel represents the residual density plot, where the solid red line represents y = 0 and the dashed purple line represents y = ±0.1dex. The bottom panel illustrates the density distribution: the solid black line indicates the 1:1 relationship; the solid red line represents the median line of Z_pred, which varies with Z_true; and the dashed purple line denotes the 1 σ scatter around the median. Each point represents a galaxy sample, and color coding highlights the kernel density estimation of galaxy density.