SupplementaryMaterials

We first prove the direction Z T SI(Z;T) = 0, which is equivalent to prove I(Z;T) = 0 SI(Z;T) = 0. We prove the contrapositive, i.e. rather than show LHS = RHS, we show that RHS = LHS. Now assume that supwi,vj ρ(w i Z i,v j T j) > ϵ for some i,j. Then by setting those elements in w,v unrelated to Z i,T j to zero, and those related to Z i,T j exactlythesameaswi,vj,weknowthatsupw,vρ(w Z,v T) > ϵ. All neural networks are trained by Adam with its default settings and a learning rate η = 0.001. Early stopping is an useful technique for avoiding overfitting, however it needs to be carefully considered when applied to adversarial methods.