Regression results for three stellar atmospheric parameters in the validation set: T_eff (left panel), log g (middle panel), and [Fe/H] (right panel). The top part of each panel show spectroscopic labels versus photometric predictions derived using the algorithm described in Sect. 3. The lower-left part of each panel displays the residuals between photometric predictions and spectroscopic labels, with the overall offset (μ) and standard deviation (σ) indicated in the top-left corner of the top plot. To enhance clarity and visualize trends, kernel density estimation (KDE) is used to model the probability densities of the results, represented as a color gradient ranging from purple (low density) to red (high density). The lower-right part of each panel shows the probability density of the residuals fitted using KDE. Black dashed lines denote the one-to-one relationship, while red dashed lines mark zero residuals.