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Benefits of the critical state

Benefits of the critical state


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

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]
Image dynamical_range Image dynamical_range
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. 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]
Image edge_of_chaos

Anna Levina and J. Michael Herrmann