Molecule Graph Networks with Many-body Equivariant Interactions

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 $l = 1$ equivariant many-body interactions to enhance directional symmetric information in the message passing scheme. We provided a mathematical analysis demonstrating the necessity of incorporating many-body equivariant interactions and generalized the formulation to $N$-body interactions. Experiments indicate that integrating many-body equivariant representations enhances prediction accuracy across diverse scalar and tensorial quantum chemical properties.