Recurrent circuit based neural population codes for stimulus representation and inference

A large part of the synaptic input received by cortical neurons comes from local cortico-cortical connectivity. Despite their abundance, the role of local recurrent connections in cortical function is unclear, and in simple coding schemes it is often the case that a circuit with no recurrent connections performs optimally. We consider a recurrent excitatory-inhibitory circuit model of a cortical hypercolumn which performs sampling-based Bayesian inference to infer latent hierarchical stimulus features. We show that local recurrent connections can store an internal model of the correlations between stimulus features that are present in the external world. When the resulting recurrent input is combined with feedforward input it produces a population code from which the posterior over the stimulus features can be linearly read out. Internal Poisson spiking variability provides the proper fluctuations for the population to sample stimulus features, yet the resultant population variability is aligned along the stimulus feature direction, producing differential correlations. Importantly, the amplitude of these internally generated differential correlations is determined by the associative prior in the model stored in the recurrent connections. This provides experimentally testable predictions for how population connectivity and response variability are related to the structure of latent external stimuli.