Surprising properties of dropout in deep networks
This work provides foundational insights into dropout's mechanisms, benefiting researchers in deep learning by clarifying its properties and limitations.
The paper analyzes dropout in deep networks with ReLU activations and quadratic loss, revealing surprising differences from traditional regularizers like weight decay, such as dropout producing negative weights on simple datasets and its penalty growing exponentially with network depth.
We analyze dropout in deep networks with rectified linear units and the quadratic loss. Our results expose surprising differences between the behavior of dropout and more traditional regularizers like weight decay. For example, on some simple data sets dropout training produces negative weights even though the output is the sum of the inputs. This provides a counterpoint to the suggestion that dropout discourages co-adaptation of weights. We also show that the dropout penalty can grow exponentially in the depth of the network while the weight-decay penalty remains essentially linear, and that dropout is insensitive to various re-scalings of the input features, outputs, and network weights. This last insensitivity implies that there are no isolated local minima of the dropout training criterion. Our work uncovers new properties of dropout, extends our understanding of why dropout succeeds, and lays the foundation for further progress.