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We define and explicitly construct schemes evinced by generalized additivedecompositions (GADs) of a given $d$-homogeneous polynomial $F$. We employ GADsto investigate the regularity of $0$-dimensional schemes apolar to $F$,focusing on those satisfying some minimality conditions. We show thatirredundant schemes to $F$ need not be $d$-regular, unless they are evinced byspecial GADs of $F$. Instead, we prove that tangential decompositions ofminimal length are always $d$-regular, as well as irredundant apolar schemes oflength at most $2d+1$.

On schemes evinced by generalized additive decompositions and their regularity