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Backpropagation (BP) is widely used for calculating gradients in deep neuralnetworks (DNNs). Applied often along with stochastic gradient descent (SGD) orits variants, BP is considered as a de-facto choice in a variety of machinelearning tasks including DNN training and adversarial attack/defense. Recently,a linear variant of BP named LinBP was introduced for generating moretransferable adversarial examples for performing black-box attacks, by Guo etal. Although it has been shown empirically effective in black-box attacks,theoretical studies and convergence analyses of such a method is lacking. Thispaper serves as a complement and somewhat an extension to Guo et al.'s paper,by providing theoretical analyses on LinBP in neural-network-involved learningtasks, including adversarial attack and model training. We demonstrate that,somewhat surprisingly, LinBP can lead to faster convergence in these tasks inthe same hyper-parameter settings, compared to BP. We confirm our theoreticalresults with extensive experiments.

A Theoretical View of Linear Backpropagation and Its Convergence