implemented as linear transformations that are combined with convolutional layers satisfying rotational invariance. DimeNet formulates the task as a message passing exercise, while also introducing directionality by considering the angles between atoms. Instead of atom embeddings, DimeNet computes directional embeddings between pairs of atoms j, i that incorporate atomic distances and angles by aggregating other embeddings directed towards the source atom j. The construction also guarantees invariance to rotations. Furthermore, instead of using raw angles, DimeNet represents distances and angles through a spherical 2D Fourier-Bessel basis, a physics-inspired decision that was also empirically found to be preferable. The original DimeNet architecture was subsequently updated to a faster and more accurate model denoted DimeNet++ by replacing costly operations with fast and expressive alternatives .