Steimer A., Maass W., Douglas R. Belief Propagation in Networks of Spiking Neurons

Neural Computation 21, 2502–2523 (2009)From a theoretical point of view, statistical inference is an attractivemodel
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. Each
of the various output messages to be transmitted over the edges of the
graph is 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, drawn from coding theory, models
the transmission of signals through an unreliable channel and demonstrates
the principles and generality of ournetwork approach.The second,
more applied example is of a psychophysicalmechanism 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, demonstrate good agreement between the performance of our
networks and the direct numerical evaluation of belief propagation.