Abstract
There are indications that for optimizing neural computation, neural networks may operate at criticality. Previous approaches have used distinct fingerprints of criticality, leaving open the question whether the different notions would necessarily reflect different aspects of one and the same instance of criticality, or whether they could potentially refer to distinct instances of criticality. In this work, we choose avalanche criticality and edge-of-chaos criticality and demonstrate for a recurrent spiking neural network that avalanche criticality does not necessarily entrain dynamical edge-of-chaos criticality. This suggests that the different fingerprints may pertain to distinct phenomena.
Highlights
In the endeavor of understanding the functioning of the brain, the hypothesis has emerged that biological neural networks might operate at criticality.1–3 The promise of this hypothesis is that at the critical point, the particular details of the system’s individual elements, and their interaction laws cease to have importance.4 In this case, the phase transition itself dominates the behavior of the system and many astounding anatomical and biophysical details of neural circuits would surrender to some very generic network properties, which would permit to describe the fundamentals of the ongoing information processing and computation—at least for this case—in a simple way
Based on a realistic paradigm of neural networks, we show that a positive largest Lyapunov exponent—indicating chaotic dynamics of the network— is conserved as we tune the network from subcritical to critical and to supercritical avalanche behavior
This demonstrates that avalanche criticality does not necessarily co-occur with edge-of-chaos criticality
Summary
In the endeavor of understanding the functioning of the brain, the hypothesis has emerged that biological neural networks might operate at criticality. The promise of this hypothesis is that at the critical point, the particular details of the system’s individual elements, and their interaction laws cease to have importance. In this case, the phase transition itself dominates the behavior of the system and many astounding anatomical and biophysical details of neural circuits would surrender to some very generic network properties, which would permit to describe the fundamentals of the ongoing information processing and computation—at least for this case—in a simple way. A fingerprint of criticality is power law distributions of the properties exhibited by local descriptors when evaluated across the ensemble Such distributions were found in the statistics of spontaneous avalanches in cortical tissue recorded with multi-electrode arrays and, more recently, in the auditory system.. For best task performance (in the edge-ofchaos sense of “computation”), a network requires properties somewhat analogous to the ones ascribed to avalanche criticality: Flexibility to represent spatiotemporally diverse inputs, while essentially preserving distance relationships (i.e., similar inputs should trigger similar responses). This is the case at the system’s transition from stable to chaotic dynamics, which is characterized by a vanishing largest.
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