  Recordings of complex neural population responses provide a unique
opportunity for advancing our understanding of neural information processing at
multiple scales and improving performance of brain computer interfaces.
However, most existing analytical techniques fall short of capturing the
complexity of interactions within the concerted population activity. Vine
copula-based approaches have shown to be successful at addressing complex
high-order dependencies within the population, disentangled from the
single-neuron statistics. However, most applications have focused on parametric
copulas which bear the risk of misspecifying dependence structures. In order to
avoid this risk, we adopted a fully non-parametric approach for the
single-neuron margins and copulas by using Neural Spline Flows (NSF). We
validated the NSF framework on simulated data of continuous and discrete type
with various forms of dependency structures and with different dimensionality.
Overall, NSFs performed similarly to existing non-parametric estimators, while
allowing for considerably faster and more flexible sampling which also enables
faster Monte Carlo estimation of copula entropy. Moreover, our framework was
able to capture low and higher order heavy tail dependencies in neuronal
responses recorded in the mouse primary visual cortex during a visual learning
task while the animal was navigating a virtual reality environment. These
findings highlight an often ignored aspect of complexity in coordinated
neuronal activity which can be important for understanding and deciphering
collective neural dynamics for neurotechnological applications.

Neurons and Cognition