  The large amounts of astrophysical data being provided by existing and future
instrumentation require efficient and fast analysis tools. Transfer learning is
a new technique promising higher accuracy in the derived data products, with
information from one domain being transferred to improve the accuracy of a
neural network model in another domain. In this work, we demonstrate the
feasibility of applying the deep transfer learning (DTL) approach to
high-resolution spectra in the framework of photospheric stellar parameter
determination. To this end, we used 14 stars of the CARMENES survey sample with
interferometric angular diameters to calculate the effective temperature, as
well as six M dwarfs that are common proper motion companions to FGK-type
primaries with known metallicity. After training a deep learning (DL) neural
network model on synthetic PHOENIX-ACES spectra, we used the internal feature
representations together with those 14+6 stars with independent parameter
measurements as a new input for the transfer process. We compare the derived
stellar parameters of a small sample of M dwarfs kept out of the training phase
with results from other methods in the literature. Assuming that temperatures
from bolometric luminosities and interferometric radii and metallicities from
FGK+M binaries are sufficiently accurate, DTL provides a higher accuracy than
our previous state-of-the-art DL method (mean absolute differences improve by
20 K for temperature and 0.2 dex for metallicity from DL to DTL when compared
with reference values from interferometry and FGK+M binaries). Furthermore, the
machine learning (internal) precision of DTL also improves as uncertainties are
five times smaller on average. These results indicate that DTL is a robust tool
for obtaining M-dwarf stellar parameters comparable to those obtained from
independent estimations for well-known stars.
