  Circuits of biological neurons, such as in the functional parts of the brain
can be modeled as networks of coupled oscillators. Inspired by the ability of
these systems to express a rich set of outputs while keeping (gradients of)
state variables bounded, we propose a novel architecture for recurrent neural
networks. Our proposed RNN is based on a time-discretization of a system of
second-order ordinary differential equations, modeling networks of controlled
nonlinear oscillators. We prove precise bounds on the gradients of the hidden
states, leading to the mitigation of the exploding and vanishing gradient
problem for this RNN. Experiments show that the proposed RNN is comparable in
performance to the state of the art on a variety of benchmarks, demonstrating
the potential of this architecture to provide stable and accurate RNNs for
processing complex sequential data.
