  Neural manifolds are an attractive theoretical framework for characterizing
the complex behaviors of neural populations. However, many of the tools for
identifying these low-dimensional subspaces are correlational and provide
limited insight into the underlying dynamics. The ability to precisely control
this latent activity would allow researchers to investigate the structure and
function of neural manifolds. Employing techniques from the field of optimal
control, we simulate controlling the latent dynamics of a neural population
using closed-loop, dynamically generated sensory inputs. Using a spiking neural
network (SNN) as a model of a neural circuit, we find low-dimensional
representations of both the network activity (the neural manifold) and a set of
salient visual stimuli. With a data-driven latent dynamics model, we apply
model predictive control (MPC) to provide anticipatory, optimal control over
the trajectory of the circuit in a latent space. We are able to control the
latent dynamics of the SNN to follow several reference trajectories despite
observing only a subset of neurons and with a substantial amount of unknown
noise injected into the network. These results provide a framework to
experimentally test for causal relationships between manifold dynamics and
other variables of interest such as organismal behavior and BCI performance.
