Layer-wise supervised incremental training of residual networks
Due to their structure, it may be that residual modules  could be trained incrementally, starting from a previous, shallower net learned with full supervision. At each step, the network would learn an additional residual module, which would be an additional non-linear feature representation of the input that is fed into the previous module — the classifier. A very useful reading to help intuition of this effect is , which gives an ensemble-like interpretation of residual networks. The re-use of the previously trained layers should save computational time. Moreover, it is possible to show that at each step we are learning in a strictly larger model space, of which network learned in the previous step is the optimal model when we zero-out the weights of the new residual units just added.
Some approaches for incremental learning have been recently investigated [3, 4]. They share some intuition with this one. Although they try to solve the more general problem of transfer learning and they are not tailored to residual networks specifically.
Efficient layer-wise training of deep networks could allow to significantly speed up training of large models. It is one of the long-standing "dreams" of deep learning, but has proven elusive so far. If such a method were to be devised and performed competitively with end-to-end trained models while providing computational benefits, it would quickly be adopted across the entire field.