  Gated recurrent units (GRUs) are specialized memory elements for building
recurrent neural networks. Despite their incredible success on various tasks,
including extracting dynamics underlying neural data, little is understood
about the specific dynamics representable in a GRU network. As a result, it is
both difficult to know a priori how successful a GRU network will perform on a
given task, and also their capacity to mimic the underlying behavior of their
biological counterparts. Using a continuous time analysis, we gain intuition on
the inner workings of GRU networks. We restrict our presentation to low
dimensions, allowing for a comprehensive visualization. We found a surprisingly
rich repertoire of dynamical features that includes stable limit cycles
(nonlinear oscillations), multi-stable dynamics with various topologies, and
homoclinic bifurcations. At the same time we were unable to train GRU networks
to produce continuous attractors, which are hypothesized to exist in biological
neural networks. We contextualize the usefulness of different kinds of observed
dynamics and support our claims experimentally.
