where ϕ e (x) and φe (x) are gated multi-layer perceptrons, ⊕ is the concatenation operator, N v is the number of atoms, and e 0 ij are the distance-expanded basis functions with values. In this work, we do not update the global state u. For the models that do not use the angle featurization in making the updates to nodes and edges, Equations 2 and 3 are not used, making these models fairly equivalent to MEGNet.