where || refers to the catenation operation, A is a learnable linear transformation, and a is a bias term. In the first EGAT layer, A has dimensions of 512x48, where 48 is the size of the catenated inputted node and edge features (Tables and) and 512 is the embedding dimension such that e ′ ij has dimensions of 512x1. In subsequent EGAT layers, A has dimensions of 512x1536, where 1536 is the size of the catenated embedded node and edge features, and e ′ ij has unchanged dimensions of 512x1. Recall that edges are defined based on the union of the bonds in the reactant and product graphs, such that an edge may exist in the reactant or product where no physical bond exists. The embedded edges are directional (i.e., e ′ ij ̸ = e ′ ji ) and so there are twice as many embedded edges as connected nodes.