where  \(F\)\(S\) represent the rank matrix of the property relation map and the transfer learning for all forty-two property tasks, \(F^r\)\(S^r\) represent the rank sequence for the \(r\)-th task in \(F\) and \(S\)\(R\) represent the total number of tasks (actually \(R=42\)).
In summary, the approximation degree of the rank matrix \(F\) and \(S\), \(Similarity(F,S)\), demonstrates the reliability of our proposed property relation map. The higher \(Similarity(F,S)\) means that the property relation map more confidently reveals the inner relationship between property tasks.
Model architecture. The backbone network is based on the normal GCN model [32\cite{bib30}], which consists of two GCN feature extractor layers and one MLP predictor layer. To combine the input atom features and bond features, we add an atom linear layer and bond linear layer before the two GCN layers to unify the dimension between the two features. Then, after feature extraction, we use the max-pooling layer to integrate atom and bond features into one fragment feature.
Training and evaluation settings. The Adam optimizer is used to train the imputation models with the following parameters on a graphics processing unit (GPU) server: learning rate 0.001, weight decay 0.0, eps 1e-8, beta (0.9, 0.99), amsgrad false. The Binary Cross Entropy loss function is employed to measure model performance in both the training and validation stages. The loss formula (4) is as follows: