  Deep learning (DL) techniques are a promising approach among the set of
methods used in the ever-challenging determination of stellar parameters in M
dwarfs. In this context, transfer learning could play an important role in
mitigating uncertainties in the results due to the synthetic gap (i.e.
difference in feature distributions between observed and synthetic data). We
propose a feature-based deep transfer learning (DTL) approach based on
autoencoders to determine stellar parameters from high-resolution spectra.
Using this methodology, we provide new estimations for the effective
temperature, surface gravity, metallicity, and projected rotational velocity
for 286 M dwarfs observed by the CARMENES survey. Using autoencoder
architectures, we projected synthetic PHOENIX-ACES spectra and observed
CARMENES spectra onto a new feature space of lower dimensionality in which the
differences between the two domains are reduced. We used this low-dimensional
new feature space as input for a convolutional neural network to obtain the
stellar parameter determinations. We performed an extensive analysis of our
estimated stellar parameters, ranging from 3050 to 4300 K, 4.7 to 5.1 dex, and
-0.53 to 0.25 dex for Teff, logg, and [Fe/H], respectively. Our results are
broadly consistent with those of recent studies using CARMENES data, with a
systematic deviation in our Teff scale towards hotter values for estimations
above 3750 K. Furthermore, our methodology mitigates the deviations in
metallicity found in previous DL techniques due to the synthetic gap. We
consolidated a DTL-based methodology to determine stellar parameters in M
dwarfs from synthetic spectra, with no need for high-quality measurements
involved in the knowledge transfer. These results suggest the great potential
of DTL to mitigate the differences in feature distributions between the
observations and the PHOENIX-ACES spectra.
