# Belief-propagation in networks of spiking neurons

**A. Steimer, W. Maass, and R. Douglas**

### Abstract:

From a theoretical point of view, statistical inference is an attractive model
of brain operation. However, it is unclear how to implement these inferential
processes in neuronal networks. We offer a solution to this problem by
showing in detailed simulations how the Belief-Propagation algorithm on a
factor graph can be embedded in a network of spiking neurons. We use pools of
spiking neurons as the function nodes of the factor graph. Each pool gathers
'messages' in the form of population activities from its input nodes and
combines them through its network dynamics. The various output messages to be
transmitted over the edges of the graph are each computed by a group of
readout neurons that feed in their respective destination pools. We use this
approach to implement two examples of factor graphs. The first example is
drawn from coding theory. It models the transmission of signals through an
unreliable channel and demonstrates the principles and generality of our
network approach. The second, more applied example, is of a psychophysical
mechanism in which visual cues are used to resolve hypotheses about the
interpretation of an object's shape and illumination. These two examples, and
also a statistical analysis, all demonstrate good agreement between the
performance of our networks and the direct numerical evaluation of
beliefpropagation.

**Reference:** A. Steimer, W. Maass, and R. Douglas.
Belief-propagation in networks of spiking neurons.
*Neural Computation*, 21:2502-2523, 2009.