  The ability to record activities from hundreds of neurons simultaneously in
the brain has placed an increasing demand for developing appropriate
statistical techniques to analyze such data. Recently, deep generative models
have been proposed to fit neural population responses. While these methods are
flexible and expressive, the downside is that they can be difficult to
interpret and identify. To address this problem, we propose a method that
integrates key ingredients from latent models and traditional neural encoding
models. Our method, pi-VAE, is inspired by recent progress on identifiable
variational auto-encoder, which we adapt to make appropriate for neuroscience
applications. Specifically, we propose to construct latent variable models of
neural activity while simultaneously modeling the relation between the latent
and task variables (non-neural variables, e.g. sensory, motor, and other
externally observable states). The incorporation of task variables results in
models that are not only more constrained, but also show qualitative
improvements in interpretability and identifiability. We validate pi-VAE using
synthetic data, and apply it to analyze neurophysiological datasets from rat
hippocampus and macaque motor cortex. We demonstrate that pi-VAE not only fits
the data better, but also provides unexpected novel insights into the structure
of the neural codes.
