We construct an individual convolutional neural network architecture for each of the four stellar parameters effective temperature (Teff), surface gravity (log g), metallicity [M/H], and rotational velocity (v sin i). The networks are trained on synthetic PHOENIX-ACES spectra, showing small training and validation errors. We apply the trained networks to the observed spectra of 283 M dwarfs observed with CARMENES. Although the network models do very well on synthetic spectra, we find large deviations from literature values especially for metallicity, due to the synthetic gap.