  This paper examines the assumptions of the derived equivalence between
dropout noise injection and $L_2$ regularisation for logistic regression with
negative log loss. We show that the approximation method is based on a
divergent Taylor expansion, making, subsequent work using this approximation to
compare the dropout trained logistic regression model with standard
regularisers unfortunately ill-founded to date. Moreover, the approximation
approach is shown to be invalid using any robust constraints. We show how this
finding extends to general neural network topologies that use a cross-entropy
prediction layer.
