  This tutorial paper surveys provably optimal alternatives to end-to-end
backpropagation (E2EBP) -- the de facto standard for training deep
architectures. Modular training refers to strictly local training without both
the forward and the backward pass, i.e., dividing a deep architecture into
several nonoverlapping modules and training them separately without any
end-to-end operation. Between the fully global E2EBP and the strictly local
modular training, there are weakly modular hybrids performing training without
the backward pass only. These alternatives can match or surpass the performance
of E2EBP on challenging datasets such as ImageNet, and are gaining increasing
attention primarily because they offer practical advantages over E2EBP, which
will be enumerated herein. In particular, they allow for greater modularity and
transparency in deep learning workflows, aligning deep learning with the
mainstream computer science engineering that heavily exploits modularization
for scalability. Modular training has also revealed novel insights about
learning and has further implications on other important research domains.
Specifically, it induces natural and effective solutions to some important
practical problems such as data efficiency and transferability estimation.
