Here we show some of known benefits of the critical state for a neural
network or any other information processing system.

Optimal dynamical range, thus optimal
information transmission.

This property was shown in the number of publications [5,9,11,17].
For example, Kinouchi and Copelli showed, that if the network is near
the critical value of the branching parameter, then it can
differentiate between more input signals than in any other regime.

Figure 3: Networks
constructed with branching ratios close to one maintain, on average,
the input activity (green, followed by yellow and red), thus optimizing
the dynamic range. Instead, supercritical networks explode with
activity, whereas subcritical ones are unable to sustain any input
pattern. Pictures are taken: (left) from [9], news and views article about [17] and (right) original
article [17]

Information storage.

When a recurrent network based on a branching process is tuned to the
critical point, the number of significantly repeating avalanche
patterns is maximized [15]
. At the critical point, there is a mixture of strong and weak
connections, allowing for a variety of independently stable patterns of
activity.

Computational power.

By changing the variance in synaptic weights in a spiking network
model, Bertschinger and Natschlager [7] were able to produce
networks that showed damped, sustained, and expanding activity. These
regimes correspond to subcritical, critical, and supercritical dynamics
respectively. They found that networks tuned to the critical point
performed more effectively on a broad range of computational tasks than
networks that were tuned to have either subcritical or supercritical
dynamics. Their study was continued in the series of publications by
Legenstein and Maass [18,19].

Figure: The network mediated
separation and computational performance
for a 3-bit parity task with different settings of parameters. Darker
symbols corresponds to a better performance. a) The network mediated
separation peaks at the critical line. b) High performance is achieved
near
the critical line. The performance is measured in terms of the memory
capacity. Pictures are taken from [19]