A Theoretical View of Linear Backpropagation and Its Convergence
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Backpropagation is widely used for calculating gradients in deep neural networks (DNNs). Applied often along with stochastic gradient descent (SGD) or its variants, backpropagation is considered as a de-facto choice in a variety of machine learning tasks including DNN training and adversarial attack/defense. Recently, a linear variant of BP named LinBP was introduced for generating more transferable adversarial examples for black-box adversarial attacks, by Guo et al. Yet, it has not been theoretically studied and the convergence analysis of such a method is lacking. This paper serves as a complement and somewhat an extension to Guo et al.'s paper, by providing theoretical analyses on LinBP in neural-network-involved learning tasks including adversarial attack and model training. We demonstrate that, somewhat surprisingly, LinBP can lead to faster convergence in these tasks in the same hyper-parameter settings, compared to BP. We confirm our theoretical results with extensive experiments.
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