SpecDis: Value added distance catalogue for 4 million stars from DESI Year-1 data

We present the SpecDis value added stellar distance catalog accompanying DESI DR1. SpecDis trains a feed-forward Neural Network (NN) with Gaia parallaxes and gets the distance estimates. To build up unbiased training sample, we do not apply selections on parallax error or signal-to-noise (S/N) of the stellar spectra, and instead we incorporate parallax error into the loss function. Moreover, we employ Principal Component Analysis (PCA) to reduce the noise and dimensionality of stellar spectra. Validated by independent external samples of member stars with precise distances from globular clusters (GCs), dwarf galaxies, stellar streams, combined with blue horizontal branch (BHB) stars, we demonstrate that our distance measurements show no significant bias up to 100kpc, and are much more precise than Gaia parallax beyond 7kpc. The median distance uncertainties are 23%, 19%, 11% and 7% for S/N $<$ 20, 20 $\leq$ S/N$<$ 60, 60 $\leq$ S/N $<$ 100 and S/N $\geq$ 100. Selecting stars with $\log g<3.8$ and distance uncertainties smaller than 25%, we have more than 74,000 giant candidates within 50kpc to the Galactic center and 1,500 candidates beyond this distance. Additionally, we develop a Gaussian mixture model to identify unresolvable equal-mass binaries by modeling the discrepancy between the NN-predicted and the geometric absolute magnitudes from Gaia parallaxes and identify 120,000 equal-mass binary candidates. Our final catalog provides distances and distance uncertainties for $>$ 4 million stars, offering a valuable resource for Galactic astronomy.