Year: 2019
Type: preprint
Abstract: 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 $\exp(Ω(L))$ 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.
Source: arXiv (Cornell University)
Authors: Wu, Lei, Wang, Qingcan, Ma, Chao
Institution: Princeton University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2984511682