Permutation Equivariant Layers for Higher Order Interactions

Recent work on permutation equivariant neural networkshas 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 orderpermutation equivariant models on several real world applications and find that our resultscompare favorably to existing permutation invariant/equivariant baselines.