Abstract: We obtain non-trivial bounds for bilinear sums of traces functions well be-low the Pólya-Vinogradov range assuming only, natural, easy to check assumptions on thegeometric monodromy group of the underlying ℓ-adic sheaf. In particular, most of the Kloosterman and hypergeometric sheaves studied by N. Katz in his PUP books satisfy these assumptions. Our approach builds on a general stratification theorem for sums of products of trace functions, obtained via the method of moments (à la Xu), using joint Sato-Tate equidistribution theorems obtained by a robust version of the Goursat-Kolchin-Ribet criterion.