  We characterize a prevalent weakness of deep neural networks
(DNNs)---overthinking---which occurs when a DNN can reach correct predictions
before its final layer. Overthinking is computationally wasteful, and it can
also be destructive when, by the final layer, a correct prediction changes into
a misclassification. Understanding overthinking requires studying how each
prediction evolves during a DNN's forward pass, which conventionally is opaque.
For prediction transparency, we propose the Shallow-Deep Network (SDN), a
generic modification to off-the-shelf DNNs that introduces internal
classifiers. We apply SDN to four modern architectures, trained on three image
classification tasks, to characterize the overthinking problem. We show that
SDNs can mitigate the wasteful effect of overthinking with confidence-based
early exits, which reduce the average inference cost by more than 50% and
preserve the accuracy. We also find that the destructive effect occurs for 50%
of misclassifications on natural inputs and that it can be induced,
adversarially, with a recent backdooring attack. To mitigate this effect, we
propose a new confusion metric to quantify the internal disagreements that will
likely lead to misclassifications.
