In this note, we show that over fields of any characteristic, exponential sums of Boolean instantiations of polynomials computed by multilinear circuits can be computed by multilinear circuits with polynomial blow-up in size. In particular, multilinear-VNP equals multilinear-VP. Our result showing closure under exponential sums also holds for other restricted multilinear classes - polynomials computed by multilinear (bounded-width) algebraic branching programs and formulas. Furthermore, it holds even if the circuit class is not fully multilinear but computes a polynomial that is multilinear in the summation variables. © 2015 Elsevier B.V.