  Experimental observations of neuroscience suggest that the brain is working a
probabilistic way when computing information with uncertainty. This processing
could be modeled as Bayesian inference. However, it remains unclear how
Bayesian inference could be implemented at the level of neuronal circuits of
the brain. In this study, we propose a novel general-purpose neural
implementation of probabilistic inference based on a ubiquitous network of
cortical microcircuits, termed winner-take-all (WTA) circuit. We show that each
WTA circuit could encode the distribution of states defined on a variable. By
connecting multiple WTA circuits together, the joint distribution can be
represented for arbitrary probabilistic graphical models. Moreover, we prove
that the neural dynamics of WTA circuit is able to implement one of the most
powerful inference methods in probabilistic graphical models, mean-field
inference. We show that the synaptic drive of each spiking neuron in the WTA
circuit encodes the marginal probability of the variable in each state, and the
firing probability (or firing rate) of each neuron is proportional to the
marginal probability. Theoretical analysis and experimental results demonstrate
that the WTA circuits can get comparable inference result as mean-field
approximation. Taken together, our results suggest that the WTA circuit could
be seen as the minimal inference unit of neuronal circuits.
