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

J. Wilting, V. Priesemann

arXiv:1903.05129v1q-bio.NC

TL;DR

Despite decades of research, experimental findings on neural criticality remain contradictory; this paper reviews the controversy and applies an estimator to in-vivo recordings. It reports reverberating cortical dynamics across brain areas, species, and tasks, alongside criticality in in-vitro networks.

  • Problem

    Experimental findings on neural criticality remain contradictory despite decades of active research, leaving the hypothesis controversial.

    Source: Introduction · p. 1

  • Method

    The paper reviews experimental and conceptual controversies and applies an ongoing-activity estimator of distance from criticality to in-vivo spike recordings.

    Source: Experimental evidence and challenges · p. 3, Reverberating dynamics · p. 3

  • Results

    0.94 < m < 0.998 characterized reverberating in-vivo dynamics across brain areas, species, and tasks, while in-vitro neuronal networks self-organized to criticality.

    Source: Highlights · p. 1, Reverberating dynamics · p. 3

  • Takeaways & Limitations

    Sufficient task performance, rather than maximizing one network property, is a more likely design principle for network function.

    Source: Conceptual appeal and controversies · p. 1

    The term criticality is underspecified across distinct dynamical concepts, and the literature lacks definite justification for treating them as interchangeable.

    Source: Open topics · p. 5

Abstract

from arXiv · show

Twenty-five years ago, Dunkelmann and Radons (1994) proposed that neural networks should self-organize to a critical state. In models, criticality 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.

Highlights

The paper revisits experimental and conceptual controversies over criticality, reports that in vitro neuronal networks self-organize to a critical state, and proposes reverberating, subcritical cortical dynamics as a way to resolve many controversies.

  • The paper revises and discusses experimental and conceptual controversies surrounding criticality.Source: Highlights · p. 1
  • The paper proposes that cortical dynamics are reverberating and subcritical.Source: Highlights · p. 1
  • In vitro neuronal networks self-organize to a critical state.Source: Highlights · p. 1
  • The proposed account resolves many of the controversies.Source: Highlights · p. 1

Introduction

The criticality hypothesis has inspired decades of research yet remains controversial, with disputes over both its computational appeal and the interpretation of experimental evidence.

  • Twenty-five years ago, proposed that neural networks might self-organize to criticality, a transition between stable and unstable dynamics where activity cascades called avalanches occur.On average, the network conserves spike numbers, so one spike causes one spike across its postsynaptic neurons.Source: Introduction · p. 1
  • Despite thousands of studies, experimental results on the criticality hypothesis remain contradictory and debates persist more than two decades after Beggs and Plenz (2003).Source: Introduction · p. 1
  • Criticality is attractive for computational properties it can maximize and supporting experimental evidence, but these arguments are contested and criticality may also maximize properties adversarial to cortical function.Assessing criticality is more intricate than initially thought, which undermines the significance of accumulated evidence.Source: Introduction · p. 1

Conceptual appeal and controversies

Models make criticality attractive by associating it with favorable computational properties, but criticality can also impair response specificity, reliability, and speed [23]. The paper proposes that networks should balance competing properties to achieve sufficient task performance, which may not occur at criticality [23].

Conceptual appeal and controversies

  • Models associate criticality with maxima in metastable states, dynamic range, mutual information, active information storage, and computational power, as well as efficient non-convex optimization [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22].Source: Conceptual appeal and controversies · p. 1
  • At criticality, response variability diverges, reducing specificity and reliability, while critical slowing down can delay readiness for new stimuli [23].Source: Conceptual appeal and controversies · p. 1
  • Criticality may not be optimal: network function may instead require balancing competing properties to achieve sufficient performance for a task [23].The proposed balances include sensitivity versus specificity, representation quality versus integration time, and stimulus detection versus discrimination.Source: Conceptual appeal and controversies · pp. 1, 3
  • Near criticality, small control-parameter changes can adjust network properties more rapidly than when networks are poised farther from criticality.The properties described include sensitivity, response variance, correlation length, and autocorrelation time.Source: Figure 1 · p. 2

Experimental evidence and challenges

Experimental avalanche evidence is ambiguous: distributions depend on how avalanches are extracted and analyzed, and power laws alone do not establish criticality. A recent estimator instead quantifies distance from criticality continuously and is subsampling-invariant.

Experimental evidence and challenges

  • Power laws may arise without criticality through time-varying network input, logarithmic representations, or thresholding, so power-law statistics alone do not establish self-organized criticality.Source: Experimental evidence and challenges · p. 3
  • Power-law avalanche sizes, the traditional criticality indicator, were reported in cultured preparations and diverse in-vivo signals.Reports include cultured preparations, animal recordings, and human recordings. The expected slope depends on the universality class, and is −3/2 for critical branching processes.Source: Experimental evidence and challenges · p. 3
  • Awake-animal spiking avalanches typically lacked power laws, and approximate power laws should persist under random subsampling, indicating deviations from critical dynamics.The authors attribute these deviations not to subsampling, but to deviations from critical dynamics.Source: Experimental evidence and challenges · p. 3
  • Avalanches cannot be unambiguously separated from spike recordings because neural activity lacks clear pauses, while bin size, thresholding, and sample size alter the resulting distributions.Continuous activity can cause cascades to merge and split; avalanches may also appear when bin size tends to zero, under heavy subsampling, or with thresholding.Source: Experimental evidence and challenges · p. 3
  • An ongoing-activity estimator quantifies distance from criticality continuously and is subsampling-invariant, requiring only tens of multi-unit spike recordings without spike sorting or timescale separation.The estimator is presented as a practical tool for investigating cortical network dynamics and their changes.Source: Experimental evidence and challenges · p. 3

Reverberating dynamics

In vivo cortical dynamics consistently occupy a reverberating regime rather than a critical state, which may reconcile experimental and conceptual controversies. This regime can balance computational demands, adapt to tasks, and avoid requiring criticality as an ideal target.

Reverberating dynamics

  • The estimator identified reverberating cortical dynamics (0.94 < m < 0.998) across brain areas, species, and tasks, consistent with an independent covariance-based approach [60].The study describes cortical dynamics as reverberating rather than critical.Source: Reverberating dynamics · p. 3
  • The reverberating regime may balance competing demands, enable rapid task adaptation, amplify small stimuli while avoiding supercritical instability, and support tunable short-term memory [23].Small parameter changes can rapidly alter computational properties, termed dynamic adaptive computation; memory spans range from a few hundred milliseconds to a few seconds.Source: Reverberating dynamics · p. 3
  • Cortical networks may self-organize to different points in the reverberating regime, gaining flexibility and balancing competing requirements rather than aiming to be as close to critical as possible.This offers a way beyond the view of criticality as the ideal target.Source: Reverberating dynamics · pp. 3, 5
  • Overlapping populations sampled by human and awake-animal electrodes can produce apparent power laws in coarse signals despite reverberating dynamics, while in vivo spike recordings typically lack them.This account does not contradict evidence for criticality, including spiking activity, in vitro; differences in topology or absent external input may explain the distinct states [9].Source: Reverberating dynamics · p. 5

Open topics

Open questions concern how distinct forms of neural criticality relate and whether observed brain dynamics reflect a single self-organized critical state or adaptation among different states. Future experiments must link changes in network dynamics to specific tasks.

Open topics

  • Criticality describes distinct transitions—stability to instability, order to chaos, and non-oscillation to oscillation —whose interchangeable use remains unjustified.These concepts share features such as avalanche-size distributions and critical slowing down.Source: Open topics · p. 5
  • Statistical criticality, identified by diverging specific heat in maximum-entropy models, may occur in neural networks, but its relation to dynamical criticality remains open.Source: Open topics · p. 5
  • A hierarchy of distances to criticality and network timescales across visual and sensory pathways may specialize to network function, motivating predictions of modulation by vigilance and task.Source: Open topics · p. 5
  • Avalanche-size power laws vary with cognitive state, including sleep-wake transitions and changes in consciousness.Source: Open topics · p. 5
  • Criticality markers also change transiently with behavioral state, attention, and stimuli, suggesting self-organization to different states; linking reverberating-regime changes to specific tasks remains challenging.Source: Open topics · p. 5

Annotated references

The references cover foundational reviews and experimental evidence, methods and models of criticality, and studies of information processing, self-organization, and computational trade-offs. They also include work on hierarchical processing and thermodynamic criticality in neuronal networks.

Annotated references

  • [5] reviews concepts of criticality in biological systems, including neural networks, and [33] provides the first experimental evidence for criticality in neural systems.Source: Annotated references · p. 5
  • [30] introduced a method to gauge criticality beyond avalanche size distributions, while [8] built the first model that self-organizes to criticality across a large parameter range.Source: Annotated references · p. 5
  • [18] found different characterizations of information processing maximized at criticality, whereas [91] found transfer entropy is not maximized there but in a subcritical regime.Source: Annotated references · p. 5
  • [81] used a model poised close to a phase transition for hierarchical processing, while [9] showed homeostatic plasticity can self-organize diverse dynamical states depending on network input.Source: Annotated references · p. 5
  • [27] demonstrated a trade-off at criticality between stimulus detection and discrimination, and [75] recently reviewed thermodynamic criticality in neuronal networks.Source: Annotated references · p. 5
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