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Dropout and its extensions (eg. DropBlock and DropConnect) are popularheuristics for training neural networks, which have been shown to improvegeneralization performance in practice. However, a theoretical understanding oftheir optimization and regularization properties remains elusive. Recent workshows that in the case of single hidden-layer linear networks, Dropout is astochastic gradient descent method for minimizing a regularized loss, and thatthe regularizer induces solutions that are low-rank and balanced. In this workwe show that for single hidden-layer linear networks, DropBlock inducesspectral k-support norm regularization, and promotes solutions that arelow-rank and have factors with equal norm. We also show that the globalminimizer for DropBlock can be computed in closed form, and that DropConnect isequivalent to Dropout. We then show that some of these results can be extendedto a general class of Dropout-strategies, and, with some assumptions, to deepnon-linear networks when Dropout is applied to the last layer. We verify ourtheoretical claims and assumptions experimentally with commonly used networkarchitectures.

On the Regularization Properties of Structured Dropout