New lower bounds establish that Deep Sets need embedding dimension linear in the number of points (up to constants) for d>1, and give the first non-trivial bounds for higher-order Janossy pooling.
Dimension and superposition of continuous functions.Israel Journal of Mathematics, 70(2):205–218
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Embedding Dimension Lower Bounds for Universality of Deep Sets and Janossy Pooling
New lower bounds establish that Deep Sets need embedding dimension linear in the number of points (up to constants) for d>1, and give the first non-trivial bounds for higher-order Janossy pooling.