Metallicity and $\alpha$-abundance for 48 million stars in low-extinction regions in the Milky Way

We estimate ([M/H], [$\alpha$/M]) for 48 million giants and dwarfs in low-dust extinction regions from the Gaia DR3 XP spectra by using tree-based machine-learning models trained on APOGEE DR17 and metal-poor star sample \revise{from} Li et al. The root mean square error of our estimation is 0.0890 dex for [M/H] and 0.0436 dex for [$\alpha$/M], when we evaluate our models \revise{on} the test data that are not used in training the models. Because the training data is dominated by giants, our estimation is most reliable for giants. The high-[$\alpha$/M] stars and low-[$\alpha$/M] stars selected by our ([M/H], [$\alpha$/M]) show different kinematical properties for giants and low-temperature dwarfs. We further investigate how our machine-learning models extract information on ([M/H], [$\alpha$/M]). Intriguingly, we find that our models seem to extract information on [$\alpha$/M] from Na D lines (589 nm) and Mg I line (516 nm). This result is understandable given the observed correlation between Na and Mg abundances in the literature. The catalog of ([M/H], [$\alpha$/M]) as well as their associated uncertainties are publicly available online.