  Intrinsic colors (ICs) of stars are essential for the studies on both stellar
physics and dust reddening. In this work, we developed an XGBoost model to
predict the ICs with the atmospheric parameters $T_{\rm eff}$, ${\rm log}\,g$,
and $\rm [M/H]$. The model was trained and tested for three colors at Gaia and
2MASS bands with 1,040,446 low-reddening sources. The atmospheric parameters
were determined by the Gaia DR3 GSP-phot module and were validated by comparing
with APOGEE and LAMOST. We further confirmed that the biases in GSP-phot
parameters, especially for $\rm [M/H]$, do not present a significant impact on
the IC prediction. The generalization error of the model estimated by the test
set is 0.014 mag for $(G_{\rm BP}\,{-}\,G_{\rm RP})_0$, 0.050 mag for $(G_{\rm
BP}\,{-}\,K_{\rm S})_0$, and 0.040 mag for $(J\,{-}\,K_{\rm S})_0$. The model
was applied to a sample containing 5,714,528 reddened stars with stellar
parameters from Andrae et al. (2023) to calculate ICs and reddenings. The high
consistency in the comparison of $E(J\,{-}\,K_{\rm S})$ between our results and
literature values further validates the accuracy of the XGBoost model. The
variation of $E(G_{\rm BP}\,{-}\,K_{\rm S})/E(G_{\rm BP}\,{-}\,G_{\rm RP})$, a
representation of the extinction law, with Galactic longitude is found on large
scales. This work preliminarily presents the feasibility and the accuracy of
the machine-learning approach for IC and dust reddening calculation, whose
products could be widely applied to spectro-photometric data. The data sets and
trained model can be accessed via
\url{https://doi.org/10.5281/zenodo.12787594}. The models for more bands will
be completed in the following works.
