Bayesian computation emerges in generic cortical microcircuits through spike-timing-dependent plasticity.

Wolfgang Maass,Michael Pfeiffer,Lars Buesing,Bernhard Nessler

doi:10.1371/journal.pcbi.1003037

Abstract

The principles by which networks of neurons compute, and how spike-timing dependent plasticity (STDP) of synaptic weights generates and maintains their computational function, are unknown. Preceding work has shown that soft winner-take-all (WTA) circuits, where pyramidal neurons inhibit each other via interneurons, are a common motif of cortical microcircuits. We show through theoretical analysis and computer simulations that Bayesian computation is induced in these network motifs through STDP in combination with activity-dependent changes in the excitability of neurons. The fundamental components of this emergent Bayesian computation are priors that result from adaptation of neuronal excitability and implicit generative models for hidden causes that are created in the synaptic weights through STDP. In fact, a surprising result is that STDP is able to approximate a powerful principle for fitting such implicit generative models to high-dimensional spike inputs: Expectation Maximization. Our results suggest that the experimentally observed spontaneous activity and trial-to-trial variability of cortical neurons are essential features of their information processing capability, since their functional role is to represent probability distributions rather than static neural codes. Furthermore it suggests networks of Bayesian computation modules as a new model for distributed information processing in the cortex.

Highlights

Numerous experimental data show that the brain applies principles of Bayesian inference for analyzing sensory stimuli, for reasoning and for producing adequate motor outputs [1,2,3,4,5]
How do neurons learn to extract information from their inputs, and perform meaningful computations? Neurons receive inputs as continuous streams of action potentials or ‘‘spikes’’ that arrive at thousands of synapses. The strength of these synapses - the synaptic weight undergoes constant modification. It has been demonstrated in numerous experiments that this modification depends on the temporal order of spikes in the pre- and postsynaptic neuron, a rule known as spike-timing dependent plasticity (STDP), but it has remained unclear, how this contributes to higher level functions in neural network architectures
We show that STDP approximates one of the most powerful learning methods in machine learning, Expectation-Maximization (EM)

Summary

Introduction

Numerous experimental data show that the brain applies principles of Bayesian inference for analyzing sensory stimuli, for reasoning and for producing adequate motor outputs [1,2,3,4,5]. Bayesian inference has been suggested as a mechanism for the important task of probabilistic perception [6], in which hidden causes (e.g. the categories of objects) that explain noisy and potentially ambiguous sensory inputs have to be inferred. This process requires the combination of prior beliefs about the availability of causes in the environment, and probabilistic generative models of likely sensory observations that result from any given cause. In spite of the existing evidence that Bayesian computation is a primary information processing step in the brain, it has remained open how networks of neurons can acquire these priors and likelihood models, and how they combine them to arrive at posterior distributions of hidden causes

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