  While most classic studies of function in experimental neuroscience have
focused on the coding properties of individual neurons, recent developments in
recording technologies have resulted in an increasing emphasis on the dynamics
of neural populations. This has given rise to a wide variety of models for
analyzing population activity in relation to experimental variables, but direct
testing of many neural population hypotheses requires intervening in the system
based on current neural state, necessitating models capable of inferring neural
state online. Existing approaches, primarily based on dynamical systems,
require strong parametric assumptions that are easily violated in the
noise-dominated regime and do not scale well to the thousands of data channels
in modern experiments. To address this problem, we propose a method that
combines fast, stable dimensionality reduction with a soft tiling of the
resulting neural manifold, allowing dynamics to be approximated as a
probability flow between tiles. This method can be fit efficiently using online
expectation maximization, scales to tens of thousands of tiles, and outperforms
existing methods when dynamics are noise-dominated or feature multi-modal
transition probabilities. The resulting model can be trained at kiloHertz data
rates, produces accurate approximations of neural dynamics within minutes, and
generates predictions on submillisecond time scales. It retains predictive
performance throughout many time steps into the future and is fast enough to
serve as a component of closed-loop causal experiments.
