  Message passing neural networks have demonstrated significant efficacy in
predicting molecular interactions. Introducing equivariant vectorial
representations augments expressivity by capturing geometric data symmetries,
thereby improving model accuracy. However, two-body bond vectors in opposition
may cancel each other out during message passing, leading to the loss of
directional information on their shared node. In this study, we develop
Equivariant N-body Interaction Networks (ENINet) that explicitly integrates
equivariant many-body interactions to preserve directional information in the
message passing scheme. Experiments indicate that integrating many-body
equivariant representations enhances prediction accuracy across diverse scalar
and tensorial quantum chemical properties. Ablation studies show an average
performance improvement of 7.9% across 11 out of 12 properties in QM9, 27.9% in
forces in MD17, and 11.3% in polarizabilities (CCSD) in QM7b.
