To put this performance into perspective, we compare these models to two recent kernel ML models that are specifically tailored to predicting dipole moments, namely the operator ML approach of Christensen, Faber and Lilienfeld and the aforementioned MuML model of Veit et al.. (see Fig. ). The former uses a modified variant of the Faber-Christensen-Huang-Lilienfeld (FCHL) representation (FCHL ), which can incorporate the response of the ML model to applied electric fields and thus provides a physically rigorous and equivariant route to predicting dipole moments. Meanwhile, the latter uses a decomposition of the total molecular dipole into atomic monopole and dipole contributions, using the equivariant λ-SOAP approach. For reference we also include the learning curve of a naive FCHL model, which simply predicts the total dipole moment as a scalar (taken from ref. [49]). As already discussed in reference [49], the FCHL model is a significant improvement over the scalar approach. It also significantly outperforms conventional QEq for all but the smallest training sets. Meanwhile the MuML and kQEq models display remarkably similar learning curves and represent a further improvement over FCHL . Note that for consistency the QEq and kQEq models in Fig. were trained on the same reference data (calculated at the B3LYP level) as the MuML model from ref. [20].