3) an aggregation function to join atomic embeddings into molecular embeddings, and 4) a standard feed-forward neural network (FFN) for the transformation of molecular embeddings to target properties, summarized in Fig. . The D-MPNN is a class of graph-convolutional neural network (GCNN), which updates hidden representations of the vertices V and edges E of a graph G based on the local environment. In the following, we will use bold lower case to denote vectors, bold upper case to denote matrices, and italic light font for scalars and objects.