## 5 Discussion
Results are shown in Table 8, and, as the reader can notice, four properties, \(\gamma\), UV, \(-\chi\)\(\cdot\)10\({}^{6}\), and El, do not show up due to poor modeling, while for properties d, FP, and \(\mu\), only one index was deleted. We also notice that the dipole moment, \(\mu\), does not obey the lowest sensibility rule (see Table 5) as following this rule we should have deleted T\({}_{\Sigma/M}\) index. Now, deletion of this index gives rise to a poor modeling for the dipole moment. This confirms that sensibility values change from run to run, like the weights, and they are not guidance for the absolute importance of an index, but only for its importance within a given model. The statistics here are usually not as good as in the MLS case (Table 4), with a clear and amazing exception, the modeling of the whole set of compounds for the dielectric constant, \(\varepsilon\). Looking only at the training plus test modeling, we would simply discarded thismodeling. Nevertheless, the very good modeling of the evaluated compounds helps to improve the overall model for this property. Thus, (i) before throwing away some training plus test ANN or MLS results, re-evaluate and do not forget that (ii) a very good ANN modeling may hiding somewhere. All this comes back to the random assigning of the initial weights in ANN computations, which renders it difficult to reproduce values that seem to show up by chance. Tables 5-8 tell also that there is no fixed preferential value for the parameter Ntr (numbers of networks to train). Usually, different Ntr values give rise to rather similar statistical parameters. Generally, the addition of the EV set does not greatly affect the overall quality of the models, showing their robustness in most cases. The differences in \(\mathbf{r}^{2}\) are not greater than 0.5, as a rule. Some exceptions are the MLS models for FP and \(\upmu\), and the ANN ones for \(\varepsilon\), \(\upgamma\), and \(\upmu\). Concerning the most used values for \(\delta^{\mathrm{v}}\), Tables 4-7 show that the \(\delta^{\mathrm{v}}_{\mathrm{PPO}}\) configuration is preferred, especially throughout the nHN cases (Tables 6 and 7). This choice means a strong dependence on the core electrons for higher row atoms (see Appendix A). Regarding the exponent of the fractional term in \(\delta^{\mathrm{v}}\) (see Appendix A), the most used values are 1, \(-\)0.5; i.e., strong hydrogen atom dependence--and 50; i.e., no hydrogen atom dependence. The strong hydrogen dependence of \(\delta^{\mathrm{v}}\) tells us that the hydrogen atoms should not be neglected. Plots of Figures 3-6 exemplify the best models obtained from the given properties. These four properties, \(\mathrm{T_{b}}\), d, RI, and \(\upeta\) (Vis) show the best statistics for the set of points evaluated. The residual plots, nevertheless, remind us that the models achieved could be further improved since the evaluated points are not placed symmetrically around the zero line, as required in a perfect model. In the graphs of Figures 4 and 5 a point appears away from the remaining points, which could anchor the regression line. However, the corresponding residual plots show that this is not the case, since their residuals are not insignificant. This is due to the  
One of the great advantages of MLS computation is that its statistical results are reproducible, no matter how many times the calculations are repeated with the same indices, the same results are obtained. The ANN-MLP results can seem, instead, as non-reproducible since the weights of the ANN-MLP calculations start with random values, and the minimization procedure usually ends up with different values from run to run. Furthermore, as a rule, different ANN-MLP computations end up in different local minima. However, it must be pointed out that repeating the training process by setting up the same procedure, by using the same seed, randomization the algorithm and precision, with the same data sets, the resulting model would be the same.