The proposition makes use of the following observation: For the discriminator defined in(1), the normofgradientforwt isupperboundedby k wtDθ(x)k F kxk LY

As lw(x) is a linear transformation, we havelcw(x) = c lw(x), and lw(cx) = c lw(x). A, we know that w0tDθ(x) F, otl(x)Dθ(x), and kotl(x)k have upper bounds. Proposition 3 (Upper bound of Hessian's spectral norm). Consider the discriminator defined in Eq.(1). The proof is in App.