The only difference now is that we no longer rely on using the average neighbor-type embedding but rather here, x j are the results of the previous perturbational update which took into account the direct neighborhood. Since the direct neighboring atoms also incorporated their own neighborhood from the first order perturbation, then the atom-embedding for atom i is now recognizing the indirect neighborhood layer that is two bonds away. If repeated one more time, for the third order perturbational replicate, then atom i is indirectly incorporating the neighborhood layer that is three bonds away, and so on. Again, this is repeated for each atom in the molecule to get all of their embeddings replicates based on the third layer of neighborhood composition. Note that at each update, the number of features being used is the same, D embedding × D elements , and only involves the embedding of the direct neighbors, either from the previous replicate or the initial average. However, in contrast to the true GNN which produces the embeddings, the replicates effectively reduce that model's correlations to be based purely on neighborhood composition. While this does mean that the exact graph layout of the neighborhood is ignored from our feature space, it provides us with the majority of the embedding space.