Neural ordinary differential equations and their probabilistic extension

This paper describes the transition from neural net-work architecture to ordinary differential equationsand initial value problem. Two neural network architectures are compared: classical RNN and ODE-RNN, which uses neural ordinary differential equations. The paper proposes a new architecture ofp-ODE-RNN, which allows you to achieve a quality comparable to ODE-RNN, but is trained muchfaster. Furthermore, the derivation of the proposedarchitecture in terms of random process theory isdiscussed.