Abstract
<jats:p>Equivariant interatomic potentials construct and reweight expressive edge messages, but typically combine them through a linear neighbour sum, leaving downstream neighbour-pair interactions governed by separable edge-wise weights. We introduce CHORUS (Cross-neighbour Hermitian O(3) Representations with U(1)-Structured aggregation), a residual operator that learns density formation itself. It lifts real O(3)-equivariant edge messages into auxiliary U(1)-charged doublets and Hermitian-contracts their neighbourhood sum into a real, U(1)-neutral O(3) residual. The diagonal sector learns edge self-density; relative phase supplies signed cross-neighbour coupling and hence reinforcement and cancellation. CHORUS requires no change to the spatial irreducible representations or energy readout. Independent implementations improve six of seven test force endpoints in MACE-ICTC and all seven in spherical-harmonic NequIP. Matched ablations show that cross-neighbour terms improve every diagonal control and that persistent charged-state propagation gains importance with depth. MACE-CHORUS also outperforms similar-scale DPA-4 C32 on five of seven force endpoints and the larger TECE on six, while remaining faster than TECE across the measured A100 scaling range. These results establish learnable Hermitian density formation as a transferable accuracy–efficiency axis for equivariant interatomic potentials.</jats:p>