  We analyze the global convergence of gradient descent for deep linear
residual networks by proposing a new initialization: zero-asymmetric (ZAS)
initialization. It is motivated by avoiding stable manifolds of saddle points.
We prove that under the ZAS initialization, for an arbitrary target matrix,
gradient descent converges to an $\varepsilon$-optimal point in $O(L^3
\log(1/\varepsilon))$ iterations, which scales polynomially with the network
depth $L$. Our result and the $\exp(\Omega(L))$ convergence time for the
standard initialization (Xavier or near-identity) [Shamir, 2018] together
demonstrate the importance of the residual structure and the initialization in
the optimization for deep linear neural networks, especially when $L$ is large.
