Machine learning has been successfully applied in varied field but whether it
is a viable tool for determining the distance to molecular clouds in the Galaxy
is an open question. In the Galaxy, the kinematic distance is commonly employed
as the distance to a molecular cloud. However, there is a problem in that for
the inner Galaxy, two different solutions, the ``Near'' solution, and the
``Far'' solution, can be derived simultaneously. We attempted to construct a
two-class (``Near'' or ``Far'') inference model using a Convolutional Neural
Network (CNN), a form of deep learning that can capture spatial features
generally. In this study, we used the CO dataset toward the 1st quadrant of the
Galactic plane obtained with the Nobeyama 45-m radio telescope (l = 62-10
degree, |b| < 1 degree). In the model, we applied the three-dimensional
distribution (position-position-velocity) of the 12CO (J=1-0) emissions as the
main input. The dataset with ``Near'' or ``Far'' annotation was made from the
HII region catalog of the infrared astronomy satellite WISE to train the model.
As a result, we could construct a CNN model with a 76% accuracy rate on the
training dataset. By using the model, we determined the distance to molecular
clouds identified by the CLUMPFIND algorithm. We found that the mass of the
molecular clouds with a distance of < 8.15 kpc identified in the 12CO data
follows a power-law distribution with an index of about -2.3 in the mass range
of M >10^3 Msun. Also, the detailed molecular gas distribution of the Galaxy as
seen from the Galactic North pole was determined.Comment: 29 pages, 12 figure