Understand the Effectiveness of Shortcuts through the Lens of DCA
This work provides a theoretical explanation for a key architectural feature in deep learning, which is incremental as it builds on existing optimization frameworks.
The paper tackles the problem of understanding why shortcut connections in neural networks are effective by showing that their gradient can be derived using the Difference-of-Convex Algorithm (DCA) applied to vanilla networks, and it introduces NegNet, a new architecture that performs comparably to ResNet within this framework.
Difference-of-Convex Algorithm (DCA) is a well-known nonconvex optimization algorithm for minimizing a nonconvex function that can be expressed as the difference of two convex ones. Many famous existing optimization algorithms, such as SGD and proximal point methods, can be viewed as special DCAs with specific DC decompositions, making it a powerful framework for optimization. On the other hand, shortcuts are a key architectural feature in modern deep neural networks, facilitating both training and optimization. We showed that the shortcut neural network gradient can be obtained by applying DCA to vanilla neural networks, networks without shortcut connections. Therefore, from the perspective of DCA, we can better understand the effectiveness of networks with shortcuts. Moreover, we proposed a new architecture called NegNet that does not fit the previous interpretation but performs on par with ResNet and can be included in the DCA framework.