Monotone and Separable Set Functions: Characterizations and Neural Models
Quick summary
arXiv:2510.23634v4 Announce Type: replace-cross Abstract: Motivated by applications for set containment problems, we consider the following fundamental problem: can we design set-to-vector functions so that the natural partial order on sets is preserved, namely $S\subseteq T \text{ if and only if } F(S)\leq F(T) $. We call functions satisfying this property Monotone and Separating (MAS) set functions. % We establish lower and upper bounds for the vector dimension necessary to obtain MAS functions, as a function of the cardinality of the multisets and the underlying ground set. In the important
Key takeaways
- arXiv:2510.23634v4 Announce Type: replace-cross Abstract: Motivated by applications for set containment problems, we consider the following fundamental problem: can we design set-to-vector functions so that the natural partial order on sets is preserved, namely $S\subseteq T \text{ if and only if } F(S)\leq F(T) $.
- We call functions satisfying this property Monotone and Separating (MAS) set functions.
- % We establish lower and upper bounds for the vector dimension necessary to obtain MAS functions, as a function of the cardinality of the multisets and the underlying ground set.
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