# Solving constraint satisfaction problems with networks of spiking
neurons

**Z. Jonke, S. Habenschuss, and W. Maass**

### Abstract:

Network of neurons in the brain apply unlike processors in our current
generation of computer hardware an event-based processing strategy, where
short pulses (spikes) are emitted sparsely by neurons to signal the
occurrence of an event at a particular point in time. Such spike-based
computations promise to be substantially more power-efficient than
traditional clocked processing schemes. However it turns out to be
surprisingly difficult to design networks of spiking neurons that can solve
difficult computational problems on the level of single spikes, rather than
rates of spikes. We present here a new method for designing networks of
spiking neurons via an energy function. Furthermore we show how the energy
function of a network of stochastically firing neurons can be shaped in a
transparent manner by composing the networks of simple stereotypical network
motifs. We show that this design approach enables networks of spiking neurons
to produce approximate solutions to difficult (NP-hard) constraint
satisfaction problems from the domains of planning/optimization and
verification/logical inference. The resulting networks employ noise as a
computational resource. Nevertheless the timing of spikes plays an essential
role in their computations. Furthermore, networks of spiking neurons carry
out for the Traveling Salesman Problem a more efficient stochastic search for
good solutions compared with stochastic artificial neural networks (Boltzmann
machines) and Gibbs sampling.

**Reference:** Z. Jonke, S. Habenschuss, and W. Maass.
Solving constraint satisfaction problems with networks of spiking neurons.
*Front. Neurosci., 30 March*, 2016.