For an atom target, the input size of FFNN is equal to the hidden size (i.e. the dimension of the embedding). However, for bond property prediction, the input size is twice the hidden size because r r r β,ij and r r r β,ji are two distinct vectors as a result of using directed bonds during message passing, but both latent representations are connected to the same bond target that does not depend on direction. Therefore, we concatenate the embeddings of the same bond into concat(r r r β,ij , r r r β,ji ) and concat(r r r β,ji , r r r β,ij ), and subsequently pass both into the same FFNN and average the two outputs to ensure that the concatenation of forward and backward bonds is order-invariant.