On approximating dropout noise injection

Abstract

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.

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Reproductions