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Dropout is a widely-used regularization technique, often required to obtainstate-of-the-art for a number of architectures. This work demonstrates thatdropout introduces two distinct but entangled regularization effects: anexplicit effect (also studied in prior work) which occurs since dropoutmodifies the expected training objective, and, perhaps surprisingly, anadditional implicit effect from the stochasticity in the dropout trainingupdate. This implicit regularization effect is analogous to the effect ofstochasticity in small mini-batch stochastic gradient descent. We disentanglethese two effects through controlled experiments. We then derive analyticsimplifications which characterize each effect in terms of the derivatives ofthe model and the loss, for deep neural networks. We demonstrate thesesimplified, analytic regularizers accurately capture the important aspects ofdropout, showing they faithfully replace dropout in practice.

The Implicit and Explicit Regularization Effects of Dropout