  Deep neural networks achieve state-of-the-art performance for a range of
classification and inference tasks. However, the use of stochastic gradient
descent combined with the nonconvexity of the underlying optimization problems
renders parameter learning susceptible to initialization. To address this
issue, a variety of methods that rely on random parameter initialization or
knowledge distillation have been proposed in the past. In this paper, we
propose FuseInit, a novel method to initialize shallower networks by fusing
neighboring layers of deeper networks that are trained with random
initialization. We develop theoretical results and efficient algorithms for
mean-square error (MSE)-optimal fusion of neighboring dense-dense,
convolutional-dense, and convolutional-convolutional layers. We show
experiments for a range of classification and regression datasets, which
suggest that deeper neural networks are less sensitive to initialization and
shallower networks can perform better (sometimes as well as their deeper
counterparts) if initialized with FuseInit.
