Towards Understanding the Importance of Shortcut Connections in Residual Networks
This work provides theoretical insights into the training dynamics of ResNets, which is an incremental contribution to understanding deep learning architectures.
The paper tackles the problem of understanding why residual networks train efficiently by analyzing a two-layer convolutional ResNet with non-convex optimization, showing that gradient descent with proper normalization avoids spurious local optima and converges to a global optimum in polynomial time under specific initialization conditions.
Residual Network (ResNet) is undoubtedly a milestone in deep learning. ResNet is equipped with shortcut connections between layers, and exhibits efficient training using simple first order algorithms. Despite of the great empirical success, the reason behind is far from being well understood. In this paper, we study a two-layer non-overlapping convolutional ResNet. Training such a network requires solving a non-convex optimization problem with a spurious local optimum. We show, however, that gradient descent combined with proper normalization, avoids being trapped by the spurious local optimum, and converges to a global optimum in polynomial time, when the weight of the first layer is initialized at 0, and that of the second layer is initialized arbitrarily in a ball. Numerical experiments are provided to support our theory.