## 1 Introduction  
Recently [1], the mean molecular connectivity indices (MMCI) were introduced to model eleven properties of organic solvents. The multilinear least-squares (MLS) used to derive the quantitative structure-property relationships (QSPR) showed that three out of eleven properties, the refractive index (RI), the flash points (FP), and the ultraviolet cutoff values (UV), were modeled with the MMCI while the remaining properties were modeled with the well-known molecular connectivity indices (MCI). The MMCI indices are also centered on the basic concepts of the delta, valence delta, I- and S-indices that go back to the origins of the molecular connectivity theory [2; 3; 4; 5; 6; 7]. Results from two other recent studies that used semiempirical sets of descriptors [8; 9] showed that the artificial neural network (ANN) model with a variable number of hidden neurons chosen by the software improves the quality of a QSPR obtained with the aid of the multilinear least-squares (MLS) methodology, also known as multilinear regression (MLR). Nevertheless, this improvement is somewhat artificial as the ANN computations for the eleven properties employed a number of weights, due to the presence of more than one hidden neuron, much greater than the number of weights or regression coefficients in the MLS procedure. This fact can provide poor results when new data are to be predicted. This is called overfitting, and it can be avoided by guiding the training process after the predictions in a test set, by more general regularization techniques, or by dropout of the hidden neurons.  
A scheme of the work is depicted in Figure 1. Data consisting of eleven physicochemical properties of solvents were randomly split into train (TR) and evaluation (EV) sets. Molecular descriptors were calculated, as explained in section Materials and Methods, for every molecule. MLS computations performed with the train set ended up choosing the best descriptors among the set of given descriptors. These best descriptors were used to perform the Multilayer Perceptron ANN (ANN-MLP) computations. To avoid overfitting, during its training process the ANN randomly selects test sets (TE) within the original TR set. Finally, the models obtained by each method are applied, for external validation, to the evaluation (EV) set. It should be underlined that the evaluation set is common to every type of computation.  
The aim of the present work is to pin down the real advantages and the drawbacks of the ANN methodology, and apply it to the model of the eleven properties of [1] where either MCI or MMCI are used as the descriptors. Four different types of ANN computations are here performed to detect the level of achieved improvement, if any, (a) with one hidden neuron, (b) with a pre-fixed number of hidden neurons, (c) with a variable number of hidden neurons chosen by the software, and (d) with a minor number of descriptors for the one hidden neuron case. This last case attempted to render the number of ANN weights equal to the number of MLS weights. It also monitored if ANN computations preferred either MCIs or MMCIs for modeling purposes. The descriptors for the eleven properties are those of [1]; however, whenever a property was not satisfactorily modeled by the given MCI (or MMCI) the second or third best MCI (or MMCI) was chosen. The domain of applicability of the models presented here includes substances that have been used as solvents without any other chemical restrictions.