Exact subset-order-preserving ('MAS') embeddings need dimension ≥|V| on finite ground sets and do not exist for infinite ground sets; the paper relaxes to weakly-MAS hat-activation models with Hölder-stability and probability-of-separation bounds.
Permutation invariant representations with applications to graph deep learning
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Monotone and Separable Set Functions: Characterizations and Neural Models
Exact subset-order-preserving ('MAS') embeddings need dimension ≥|V| on finite ground sets and do not exist for infinite ground sets; the paper relaxes to weakly-MAS hat-activation models with Hölder-stability and probability-of-separation bounds.