The recent DM21 functional has received substantial attention in the DFT development community, as it demonstrated that extensively data-driven approaches can provide an important way to incorporate also important physical limits, such as a simultaneous reduction of delocalization errors and static correlation errors. The main disadvantage of such a deep neural-network functional is its complete black-box character. Here we have applied a much smaller neural network in a much more tailored way to a flexible but well-defined human-designed functional form. Only the LMF has been trained by a neural network. As the LMF is a simple real-space function with a small value range determining the EXX admixture of an LH, graphical evaluations for different molecules provide important insights into the LMF properties required for accurate thermochemistry and reaction barriers. For example, we find that the presence or absence of unphysical repulsive NDC contributions to noncovalent interactions seems to be related to the behavior of the LMF in the small-density region between the weakly interacting atoms. t-LMFs, which have been the most widely used ones so far, go to small values in such regions and thereby promote undesirable artefacts that have to be removed by a suitable calibration function. The new n-LMF and the recently proposed x-LMF of LH24x exhibit different behaviors in such regions. This can now be linked to the successful suppression of gauge-related artefacts by these LMFs. We note that, while the recent x-LMF had been constructed specifically to reduce the gauge problem, the n-LMF shares the favorable behavior even though the current training data do not contain any obvious connection to the gauge problem.