We study deterministic polynomial identity testing (PIT) and reconstruction algorithms for depth-$4$ arithmetic circuits of the form
\[
\Sigma^{[r]}\!\wedge^{[d]}\!\Sigma^{[s]}\!\Pi^{[\delta]}.
\]
This model generalizes Waring decompositions and diagonal circuits, and captures sums of powers of low-degree sparse polynomials. Specifically, each circuit computes a sum of $r$ terms, where each term is ... more >>>