Elsevier

Current Opinion in Neurobiology

Volume 58, October 2019, Pages 105-111
Current Opinion in Neurobiology

25 years of criticality in neuroscience — established results, open controversies, novel concepts

https://doi.org/10.1016/j.conb.2019.08.002Get rights and content

Highlights

  • The criticality hypothesis has received major attention in the past 25 years.

  • We revise and discuss the experimental and conceptual controversies.

  • We propose that cortical dynamics is reverberating, subcritical.

  • In vitro neuronal networks indeed self-organize to a critical state.

  • This picture overcomes apparent contradictions of past work.

Twenty-five years ago, Dunkelmann and Radons (1994) showed that neural networks can self-organize to a critical state. In models, the critical state offers a number of computational advantages. Thus this hypothesis, and in particular the experimental work by Beggs and Plenz (2003), has triggered an avalanche of research, with thousands of studies referring to it. Nonetheless, experimental results are still contradictory. How is it possible, that a hypothesis has attracted active research for decades, but nonetheless remains controversial? We discuss the experimental and conceptual controversy, and then present a parsimonious solution that (i) unifies the contradictory experimental results, (ii) avoids disadvantages of a critical state, and (iii) enables rapid, adaptive tuning of network properties to task requirements.

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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