# On the Computational Power of Circuits of Spiking Neurons

### Abstract:

Complex real-time computations on multi-modal time-varying input streams are
carried out by generic cortical microcircuits. Obstacles for the development
of adequate theoretical models that could explain the seemingly universal
power of cortical microcircuits for real-time computing are the complexity
and diversity of their computational units (neurons and synapses), as well as
the traditional emphasis on offline computing in almost all theoretical
approaches towards neural computation. In this article, we initiate a
rigorous mathematical analysis of the real-time computing capabilities of a
new generation of models for neural computation, liquid state machines, that
can be implemented withÂ—in fact benefit fromÂ—diverse computational units.
Hence, realistic models for cortical microcircuits represent special
instances of such liquid state machines, without any need to simplify or
homogenize their diverse computational units. We present proofs of two
theorems about the potential computational power of such models for real-time
computing, bothon analog input streams and for spike trains as inputs.

**Reference:** W. Maass and H. Markram.
On the computational power of circuits of spiking neurons.
*Journal of Computer and System Sciences*, 69(4):593-616, 2004.