  Neural networks are a popular tool for modeling sequential data but they
generally do not treat time as a continuous variable. Neural ODEs represent an
important exception: they parameterize the time derivative of a hidden state
with a neural network and then integrate over arbitrary amounts of time. But
these parameterizations, which have arbitrary curvature, can be hard to
integrate and thus train and evaluate. In this paper, we propose making a
piecewise-constant approximation to Neural ODEs to mitigate these issues. Our
model can be integrated exactly via Euler integration and can generate
autoregressive samples in 3-20 times fewer steps than comparable RNN and
ODE-RNN models. We evaluate our model on several synthetic physics tasks and a
planning task inspired by the game of billiards. We find that it matches the
performance of baseline approaches while requiring less time to train and
evaluate.
