Style snap computes interactions using the spectral neighbor analysis potential (SNAP) (Thompson). Like the GAP framework of Bartok et al. (Bartok2010), (Bartok2013) it uses bispectrum components to characterize the local neighborhood of each atom in a very general way. The mathematical definition of the bispectrum calculation used by SNAP is identical to that used of compute sna/atom. In SNAP, the total energy is decomposed into a sum over atom energies. The energy of atom i is expressed as a weighted sum over bispectrum components. See publication and LAMMPS doc page listed below for more information.
A. P. Thompson , L.P. Swiler, C.R. Trott, S.M. Foiles, and G.J. Tucker, "Spectral neighbor analysis method for automated generation of quantum-accurate interatomic potentials," J. Comp. Phys., 285 316 (2015) .
SNAP potential in LAMMPS: https://lammps.sandia.gov/doc/pair_snap.html