Edge of chaos and prediction of computational power for neural microcircuit models
What makes a neural microcircuit computationally powerful? Or more precisely, which measurable quantities could explain why one microcircuit C is better suited for a particular family of computational tasks than another microcircuit C0? One potential answer comes from results on cellular automata and random Boolean networks, where some evidence was provided that their computational power for offline computations is largest at the edge of chaos, i.e. at the transition boundary between order and chaos. We analyse in this article the significance of the edge of chaos for real time computations in neural microcircuit models consisting of spiking neurons and dynamic synapses. We find that the edge of chaos predicts quite well those values of circuit parameters that yield maximal computational power. But obviously it makes no prediction of their computational power for other parameter values. Therefore, we propose a new method for predicting the computational power of neural microcircuit models. The new measure estimates directly the kernel property and the generalization capability of a neural microcircuit. We validate the proposed measure by comparing its prediction with direct evaluations of the computational performance of various neural microcircuit models. This procedure is applied first to microcircuit models that differ with regard to the spatial range of synaptic connections and their strength, and then to microcircuit models that differ with regard to the level of background input currents, the conductance, and the level of noise on the membrane potential of neurons. In the latter case the proposed method allows us to quantify differences in the computational power and generalization capability of neural circuits in different dynamic regimes (UP- and DOWN-states) that have been demonstrated through intracellular recordings in vivo.