To test MLS2, we start with 96 total correlation energies from the W4-11 database that are not included in the training set (see Sec. S8 in the SI for a full list and how we obtain the underlying reference total correlation energies). In Fig. , we show the relative absolute correlation energy errors for κMP2, MP2 and MLS2. Note the log-scale in the y-axis and the dashed lines representing mean absolute relative errors (MAREs). Going from MP2 to κMP2 (from magenta circles to blue squares), we can see that the introduction of the κ regularization slightly increases the MP2 errors. On the other hand, our MLS2 model (green diamonds) yields here far more accurate correlation energies than MP2, with MArE reduced by ∼10 (from ∼10% to 1%).