  This document, as the title stated, is meant to provide a vectorized
implementation of adjoint dynamics calculation for Graph Convolutional Neural
Ordinary Differential Equations (GCDE). The adjoint sensitivity method is the
gradient approximation method for neural ODEs that replaces the back
propagation. When implemented on libraries such as PyTorch or Tensorflow, the
adjoint can be calculated by autograd functions without the need for a
hand-derived formula. In applications such as edge computing and in memristor
crossbars, however, autograds are not available, and therefore we need a
vectorized derivation of adjoint dynamics to efficiently map the system on
hardware. This document will go over the basics, then move on to derive the
vectorized adjoint dynamics for GCDE.
