Neural sheet model with local inhibition for distributed Bayesian inference and self-organized learning.

<p>(A) The sampling hypothesis proposes that probability distributions are represented in the brain such that the time the network spends in state <i><b>z</b></i> is proportional to the probability <i>p</i>(<i><b>z</b></i>). (B) In [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0134356#pone.0134356.ref017" target="_blank">17</a>] it was shown that recurrent networks of stochastic spiking neurons can implement Markov chain Monte Carlo sampling in a well-defined graphical model (inset). Each neuron is identified with a binary random variable (RV). The state of the RV at time <i>t</i> encodes whether the neuron has fired shortly before (right). (C) In [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0134356#pone.0134356.ref025" target="_blank">25</a>] it was shown that a local population of neurons (orange), organized in a Winner-Take-All (WTA) architecture, can learn an implicit probabilistic model of spiking input (green) through STDP-type plasticity. In [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0134356#pone.0134356.ref025" target="_blank">25</a>], competition between the neurons was established via a global inhibitory current. Inset: Corresponding graphical mixture model. (D) We propose a spatially structured neural sheet model with lateral inhibition and recurrent excitation for distributed Bayesian computation and self-organized learning. The network model unites the benefits of [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0134356#pone.0134356.ref017" target="_blank">17</a>] and [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0134356#pone.0134356.ref025" target="_blank">25</a>]. Strong inhibitory connections (dashed blue) between nearby network neurons establish local competition. Sparse recurrent excitatory synapses (red) connect more distant neurons. In addition, each network neuron integrates spiking input from a local subset of input neurons (green). (E) Graphical model of the neural sheet in D. Nearby binary network RVs <i><b>z</b></i>_<i>k</i> (orange nodes) maintain competitive links (blue) while more distant variables can maintain associative links (red). Bottom-up input synapses in D give rise to generative downward arrows to the input RVs <i>y</i>_<i>i</i> (green nodes).