  In this work we propose a novel interpretation of residual networks showing
that they can be seen as a collection of many paths of differing length.
Moreover, residual networks seem to enable very deep networks by leveraging
only the short paths during training. To support this observation, we rewrite
residual networks as an explicit collection of paths. Unlike traditional
models, paths through residual networks vary in length. Further, a lesion study
reveals that these paths show ensemble-like behavior in the sense that they do
not strongly depend on each other. Finally, and most surprising, most paths are
shorter than one might expect, and only the short paths are needed during
training, as longer paths do not contribute any gradient. For example, most of
the gradient in a residual network with 110 layers comes from paths that are
only 10-34 layers deep. Our results reveal one of the key characteristics that
seem to enable the training of very deep networks: Residual networks avoid the
vanishing gradient problem by introducing short paths which can carry gradient
throughout the extent of very deep networks.
