Permutation Equivariant Layers for Higher Order Interactions

Recent work on permutation equivariant neural networks has mostly focused on the first order case (sets) and second order case (graphs). We describe the machinery for generalizing permutation equivariance to arbitrary k-ary interactions between entities for any value of k. We demonstrate the effectiveness of higher order permutation equivariant models on several real world applications and find that our results compare favorably to existing permutation invariant/equivariant baselines.