In this series of notes, we try to model neural networks as as discretizations of continuous flows on the space of data, which can be called flow model. The idea comes from an observation of their similarity in mathematical structures. This conceptual analogy has not been proven useful yet, but it seems interesting to explore. In this part, we start with a linear transport equation (with nonlinear transport velocity field) and obtain a class of residual type neural networks. If the transport velocity field has a special form, the obtained network is found similar to the original ResNet. This neural network can be regarded as a discretization of the continuous flow defined by the transport flow. In the end, a summary of the correspondence between neural networks and transport equations is presented, followed by some general discussions. Notes: A Continuous Model of Neural Networks. Part I: Residual Networks

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