  We introduce a new class of time-continuous recurrent neural network models.
Instead of declaring a learning system's dynamics by implicit nonlinearities,
we construct networks of linear first-order dynamical systems modulated via
nonlinear interlinked gates. The resulting models represent dynamical systems
with varying (i.e., liquid) time-constants coupled to their hidden state, with
outputs being computed by numerical differential equation solvers. These neural
networks exhibit stable and bounded behavior, yield superior expressivity
within the family of neural ordinary differential equations, and give rise to
improved performance on time-series prediction tasks. To demonstrate these
properties, we first take a theoretical approach to find bounds over their
dynamics and compute their expressive power by the trajectory length measure in
latent trajectory space. We then conduct a series of time-series prediction
experiments to manifest the approximation capability of Liquid Time-Constant
Networks (LTCs) compared to classical and modern RNNs. Code and data are
available at https://github.com/raminmh/liquid_time_constant_networks
