Convolutional neural networks and Stokes response functions

In this work, we study the information content learned by a convolutional neural network (CNN) when trained to carry out the inverse mapping between a database of synthetic Ca ii intensity spectra and the vertical stratification of the temperature of the atmospheres used to generate such spectra. In particular, we evaluate the ability of the neural network to extract information about the sensitivity of the spectral line to temperature as a function of height. By training the CNN on sufficiently narrow wavelength intervals across the Ca ii spectral profiles, we find that the error in the temperature prediction shows an inverse relationship to the response function of the spectral line to temperature, that is, different regions of the spectrum yield a better temperature prediction at their expected regions of formation. This work shows that the function that the CNN learns during the training process contains a physically meaningful mapping between wavelength and atmospheric height.