  Neural-ODE parameterize a differential equation using continuous depth neural
network and solve it using numerical ODE-integrator. These models offer a
constant memory cost compared to models with discrete sequence of hidden layers
in which memory cost increases linearly with the number of layers. In addition
to memory efficiency, other benefits of neural-ode include adaptability of
evaluation approach to input, and flexibility to choose numerical precision or
fast training. However, despite having all these benefits, it still has some
limitations. We identify the ODE-integrator (also called ODE-solver) as the
weakest link in the chain as it may have stability, consistency and convergence
(CCS) issues and may suffer from slower convergence or may not converge at all.
We propose a first-order Nesterov's accelerated gradient (NAG) based ODE-solver
which is proven to be tuned vis-a-vis CCS conditions. We empirically
demonstrate the efficacy of our approach by training faster, while achieving
better or comparable performance against neural-ode employing other fixed-step
explicit ODE-solvers as well discrete depth models such as ResNet in three
different tasks including supervised classification, density estimation, and
time-series modelling.
