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In this paper, we aim to understand Residual Network (ResNet) in ascientifically sound way by providing a bridge between ResNet and Feynman pathintegral. In particular, we prove that the effect of residual block isequivalent to partial differential equation, and the ResNet transformingprocess can be equivalently converted to Feynman path integral. Theseconclusions greatly help us mathematically understand the advantage of ResNetin addressing the gradient vanishing issue. More importantly, our analysesoffer a path integral view of ResNet, and demonstrate that the output ofcertain network can be obtained by adding contributions of all paths. Moreover,the contribution of each path is proportional to e^{-S}, where S is the actiongiven by time integral of Lagrangian L. This lays the solid foundation in theunderstanding of ResNet, and provides insights in the future design ofconvolutional neural network architecture. Based on these results, we havedesigned the network using partial differential operators, which furthervalidates our theoritical analyses.

On the Mathematical Understanding of ResNet with Feynman Path Integral