## 2 Materials and Methods
### ANN Datasets and General Workflow  
Figure 1 shows the workflow for the Net-Net AutoML method applied to BCNs. Our goal was to find a tool that would be able to predict BCN node connectivity (communications between brain regions). This task can be solved by training an ANN classifier using as dataset the previous known node connections (output) with any type of node descriptors (inputs). This solution involves intensive training of ANNs. Net-Net AutoML proposed a shortcut: The creation of another classifier with any ML method that can evaluate whether an ANN is able to predict with accuracy the node connectivity in BCNs, without any ANN training. In order to obtain this classifier, one should previously train different ANNs to predict BCN connectivity. Thus, this Net-Net AutoML classifier is a relationship between the ANN topologies trained for BCN prediction and the ability of these ANNs to provide good predictions. In order to build ANNs for BCN prediction and Net-Net AutoML classifiers for the best ANN, both types of networks (BCNs and ANNs) should provide numerical descriptors. Therefore, for each BCN pair of nodes (brain regions), we knew the experimental connectivity (connected or not) and we could calculate the node descriptors such as Sh\({}_{\text{k}}\). This dataset was used to train different ANN topologies for the BCN prediction. In order to include information about ANNs to build a Net-Net AutoML classifier, we needed to include ANN information such as Sh\({}_{\text{k}}\) of the entire ANN. Thus, we combined two types of descriptors in order to mix information about the BCN connectivity and ANN topology: We mixed Sh\({}_{\text{k}}\) of BCN nodes (A\({}_{\text{i}}\)-B\({}_{\text{j}}\) pairs) with Sh\({}_{\text{k}}\) for an ANN (S\({}_{\text{hk}}\)(ANN)). We took into account the Shannon entropy from both types of networks but for different quantification: For nodes in BCN and for the entire network in ANN. The output of the Net-Net AutoML best classifier is the ability of S\({}_{\text{hk}}\)(ANN) to predict connectivity between BCN nodes A\({}_{\text{i}}\) and B\({}_{\text{j}}\). We calculated the values of entropy Sh\({}_{\text{k}}\)(A\({}_{\text{i}}\)) and Sh\({}_{\text{k}}\)(B\({}_{\text{j}}\)) for a large number of pair of nodes in the BCN of the CoCoMac experiment [47]. The values Sh\({}_{\text{k}}\)(A\({}_{\text{i}}\)) are for the activated brain regions and the values Sh\({}_{\text{k}}\)(B\({}_{\text{i}}\)) for the co-activated brain regions. With these values we created a large dataset with output values L\({}_{\text{ij}}\) = 1 (BCN links) or L\({}_{\text{ij}}\) = 0 (absence of region co-activation), and input values Sh\({}_{\text{k}}\)(A\({}_{\text{i}}\)) and Sh\({}_{\text{k}}\)(B\({}_{\text{i}}\)). The dataset was used to train 10 different ANNs with the STATISTICA software [48]. This work is a proof-of-concept method, so at this point we applied the default behavior of STATISTICA that used an automatic algorithm to calculate the best ANN by means of feature selection and topology modification. Future studies should include more ANNs. In the second step, we created the final dataset to find a Net-Net AutoML classifier: We used the outputs of 10 previously trained ANNs to predict BCN connections for 52,690 pairs of BCN nodes (500,740 examples after pre-processing). Figure 1: Proposed workflow. Thus, the final dataset had the output as the ability of a specific ANN to predict the type of connection between BCN nodes, and the inputs as different entropies for BCN nodes and entire ANNs. In the next step, linear and nonlinear ML methods were tested to find the best Net-Net AutoML classifier to evaluate the ANN topology for BCN predictions. Net-Net AutoML algorithm (Figure 1) has the following steps:  
(1) For each BCN:  
(1.1) Extract the connectivity matrix. (1.2) Add weights for the BCN connections (if present). (1.3) For each node A\({}_{i}\):  
(1.3.1) Calculate Shannon entropies for nodes using MI-NODES: Sh\({}_{\text{k}}\)(A\({}_{i}\)).