Supplement to ' Autoencoders that don't overfit towards the Identity '

Eq. 1 in the paper (re-stated in Eq. 2 below), and show that it is equal to the objective function in the Theorem in the paper (see Eq. 8 below) up to the factor In the following, we provide the detailed steps. We start by re-stating Eq. 1 in the paper 1 n null null nullA The details are outlined in Sections 2.2 and 2.3 below. See Eq. 1 above for the definitions of X, multiplied by the dropout-probability p, and q = 1 p. In line 6, we change the sum over the m columns back to matrix notation. Finally, in line 8, we used the substitutions from Eq. 1 as to obtain In lines 11 and 12, the squared loss is expanded into its four terms.