  We investigate the application of deep learning to the retrieval of the
internuclear distance in the two-dimensional H$_2^{+}$ molecule from the
momentum distribution of photoelectrons produced by strong-field ionization. We
study the effect of the carrier-envelope phase on the prediction of the
internuclear distance with a convolutional neural network. We apply the
transfer learning technique to make our convolutional neural network applicable
to distributions obtained for parameters outside the ranges of the training
data. The convolutional neural network is compared with alternative approaches
to this problem, including the direct comparison of momentum distributions,
support-vector machines, and decision trees. These alternative methods are
found to possess very limited transferability. Finally, we use the
occlusion-sensitivity technique to extract the features that allow a neural
network to take its decisions.
