On the Computational Power of Circuits of Spiking Neurons

W. Maass and H. Markram


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 with—in fact benefit from—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.