1f9f9d8ff75205aa73ec83e543d8b571-Supplemental.pdf

We repeat the theorems presented in Sec. 3 and provide their proofs below. The theorems hold for Neumann boundary conditions, which we use in our implementation--this is achieved by the construction of the differential operators. The proofs follow the ones presented in [22]. If the activation function σ() is monotonically non-decreasing and sign-preserving, then the forward propagation through the diffusive PDE in (1) for t [0,) yields a non-increasing feature norm, that is, t kfk2 0. Proof. Let us examine the following inner product following Eq.