25 years of criticality in neuroscience — established results, open controversies, novel concepts
Introduction
Twenty-five years ago, Dunkelmann and Radons [20] showed that neural networks can self-organize to a critical state. This critical state marks the transition between stable and unstable dynamics (Box 1 ): On average, the network conserves the number of spikes, thus every spike in one neuron on average causes one spike in all its postsynaptic neurons [54, 39, 70, 56••, 73]. At criticality, these networks are characterized by spatio-temporal cascades of activity, called avalanches, that typically are very small, but some span the entire network.
In the past decades, the criticality hypothesis, and in particular the experimental work by John Beggs and Dietmar Plenz (2003), has inspired numerous theoretical and experimental studies. Nonetheless, experimental results are still contradictory. How is it possible, that a hypothesis is at the same time so attractive and fascinating that it has prevailed for more than two decades, but also sparked heated debates and still remains controversial?
The hypothesis that the brain operates at a critical point is attractive for two reasons. On a conceptual level, criticality has been shown to maximize a number of properties that are considered favourable for computation. On an experimental level, there is considerable evidence in support of the criticality hypothesis. However, both of these points are sources of controversy. On the conceptual level, maximization of certain properties is unlikely to explain cortical function, and it is frequently neglected that criticality also maximizes properties that are likely adversarial to cortical function. On the experimental level, assessing criticality is more intricate than first thought, undermining the significance of the accumulated evidence. In the following, we discuss these two points in detail.
Section snippets
Conceptual appeal and controversies
In models of neural networks, criticality maximizes a number of properties considered favourable for computation [5,77]. Tuning models towards critical phase transitions has been shown to maximize the number of metastable states [31], the dynamic range [40,26], information transmission in terms of mutual information [84,78,79], active information storage [9•], and computational power in terms of input-output mappings [48,8,42]. Self-organized critical networks can also efficiently implement
Experimental evidence and challenges
Assessing criticality in experiments traditionally relies on identifying power-law distributions of avalanche sizes. Avalanches are spatio-temporal cascades of activity, whose sizes are expected to follow a power-law distribution [2] if networks are critical (see Box 2 ). The slope of this distribution depends on the universality class of the underlying dynamics [39,70] and is, e.g., expected to be −3/2 for critical branching processes [32].
Power-law distributions of avalanche sizes were indeed
Reverberating dynamics
This novel estimator suggests that cortical dynamics is not critical, but reverberating. We applied the estimator to in vivo spike recordings and identified a reverberating regime (0.94 < m < 0.998), consistently across brain areas, species, and tasks [92••, 93]. This reverberating regime has also been found by a complementary approach by Dahmen et al. [16], who inferred it from the distributions of spike covariances.
This reverberating regime may resolve many of the conceptual controversies [91,93
Open topics
It is unclear how different concepts of criticality relate to each other. The term criticality is not strictly defined, and it is used for multiple concepts in neuroscience [56••]. Besides the avalanche criticality discussed in this review, which is a transition between stability and instability, similar phenomena arise at different dynamical critical transitions, e.g. between ordered and chaotic, called the edge of chaos [8, 9•], or between non-oscillating and oscillating, called the edge of
Conflict of interests
The authors declare that there was no conflict of interests.
References and recommended reading
Papers of particular interest, published within the period of review, have been highlighted as:
• of special interest
•• of outstanding interest
Acknowledgments
JW and VP received financial support from the Max Planck Society.
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