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The Bayesian view of the brain hypothesizes that the brain constructs agenerative model of the world, and uses it to make inferences via Bayes' rule.Although many types of approximate inference schemes have been proposed forhierarchical Bayesian models of the brain, the questions of how these distinctinference procedures can be realized by hierarchical networks of spikingneurons remains largely unresolved. Based on a previously proposedmulti-compartment neuron model in which dendrites perform logarithmiccompression, and stochastic spiking winner-take-all (WTA) circuits in whichfiring probability of each neuron is normalized by activities of other neurons,here we construct Spiking Neural Networks that perform \emph{structured}mean-field variational inference and learning, on hierarchical directedprobabilistic graphical models with discrete random variables. In these models,we do away with symmetric synaptic weights previously assumed for\emph{unstructured} mean-field variational inference by learning both thefeedback and feedforward weights separately. The resulting online learningrules take the form of an error-modulated local Spike-Timing-DependentPlasticity rule. Importantly, we consider two types of WTA circuits in whichonly one neuron is allowed to fire at a time (hard WTA) or neurons can fireindependently (soft WTA), which makes neurons in these circuits operate inregimes of temporal and rate coding respectively. We show how the hard WTAcircuits can be used to perform Gibbs sampling whereas the soft WTA circuitscan be used to implement a message passing algorithm that computes themarginals approximately. Notably, a simple change in the amount of lateralinhibition realizes switching between the hard and soft WTA spiking regimes.Hence the proposed network provides a unified view of the two previouslydisparate modes of inference and coding by spiking neurons.

Structured Mean-field Variational Inference and Learning in Winner-take-all Spiking Neural Networks