Equivariant message-passing networks get a universal approximation theorem: a layer cutoff shorter than the physical range still captures atomic energies
For a class of equivariant graph-neural-network interatomic potentials, a universal approximation theorem now covers atomic energies: provided every atom's neighbors are reached within a common number of layers and no more than a given number of neighbors sit at a common distance inside the layer cutoff, a multilayer network whose layer cutoff is shorter than the physical range still approximates the atomic energy over that range, with spherical harmonic filter degrees no larger than that neighbor bound. The production DPA4 architecture inherits the result by simulating the constructed layers and realizing the bilinear readout.