Neural criticality from effective latent variables

Joint Public Review:

This paper shows that signatures of criticality -- in particular, power law behavior and "crackling" (the latter referring to a particular relationship among critical exponents) -- emerge from a biologically reasonable model that has nothing to do with criticality. Instead, the firing rate of a population of "neurons" (taken to be binary units) varies slowly in time. Importantly, conditioned on firing rate, the activity of each neuron (whether or not it emits a "spike") is independent of the activity of all the other neurons.

To put this result in broader context, we need to be clear what critically is and is not. Critically is a very specific set of phenomena in physics in which fundamentally local interactions produce unexpected long-range behavior. The model in this paper has no such local interactions. Instead, each neuron is coupled to a small number of latent dynamical modes (which in turn produce slowly varying firing rates). Thus, signatures of criticality emerge through fundamentally non-critical mechanisms. Consequently, such signatures of criticality observed in the brain can be misleading: they might not be evidence that the brain is critical at all; instead, they might just be evidence that neural activity is mirroring a small number of dynamical latent variables.

While this does not rule out criticality in the brain, it decidedly weakens the evidence for it, which was based on the following logic: critical systems give rise to power law behavior; power law behavior is observed in cortical networks; therefore, cortical networks operate near a critical point. Given, as shown in this paper, that power laws can arise from non-critical processes, the logic breaks. Moreover, the authors show that criticality does not imply optimal information transmission (one of its proposed functions). This highlights the necessity for more rigorous analyses to affirm criticality in the brain. In particular, it suggests that attention should be focused on the question "does the brain implement a dynamical latent variable model?".

These authors are not the first to show that slowly varying firing rates can give rise to power law behavior (see, for example, Touboul and Destexhe, 2017; Priesemann and Shriki, 2018). However, to our knowledge they are the first to show crackling, and to compute information transmission in the critical state.

Major comments:

1. For many readers, the essential messages of the paper may not be immediately clear. For example, is the paper criticizing the criticality hypothesis of cortical networks, or does the criticism extend deeper, to the theoretical predictions of "crackling" relationships in physical systems as they can emerge without criticality? Statements like "We show that a system coupled to one or many dynamical latent variables can generate avalanche criticality ..." could be misinterpreted as affirming criticality. A more accurate language is needed; for instance, the paper could state that the model generates relationships observed in critical systems. The paper should provide a clearer conclusion and interpretation of the findings in the context of the criticality hypothesis of cortical dynamics.

2. On lines 97-99, the authors state that "We are agnostic as to the origin of these inputs: they may be externally driven from other brain areas, or they may arise from recurrent dynamics locally". This idea is also repeated at the beginning of the Summary section. Perhaps being agnostic isn't such a good idea: it's possible that the recurrent dynamics is in a critical regime, which would just push the problem upstream. Presumably you're thinking of recurrent dynamics with slow timescales that's not critical? Or are you happy if it's in the critical regime? This should be clarified.

3. Even though the model in Equation 2 has been described in a previous publication and the Methods section, more details regarding the origin and justification of this model in the context of cortical networks would be helpful in the Results section. Was it chosen just for simplicity, or was there a deeper reason?

4. The Methods section (paragraph starting on lie 340) connects the time scale to actual time scales in neuronal systems, stating that "The timescales of latent variables examined range from about 3 seconds to 3000 seconds, assuming 3-ms bins". While bins of 3 ms are relevant for electrophysiological data from LFPs or high-density EEG/MEG, time scales above 10 seconds are difficult to generate through biophysically clear processes like ionic channels and synaptic transmission. The paper suggests that slow time scales of the latent variables are crucial for obtaining power law behavior resembling criticality. Yet, one way to generate such slow time scales is via critical slowing down, implying that some brain areas providing input to the network under study may operate near criticality. This pushes the problem toward explaining the criticality of those external networks. Hence, discussing potential sources for slow time scales in latent variables is crucial. One possibility you might want to consider is sources external to the organism, which could easily have time scales in the 1-24 hour range.

5. It is common in neuronal avalanche analysis to calculate the branching parameter using the ratio of events in consecutive bins. Near-critical systems should display values close to 1, especially in simulations without subsampling. Including the estimated values of the branching parameter for the different cases investigated in this study could provide more comprehensive data. While the paper acknowledges that the obtained exponents in the model differ from those in a critical branching process, it would still be beneficial to offer the branching parameter of the observed avalanches for comparison.

6. In the Discussion (l 269), the paper suggests potential differences between networks cultured in vitro and in vivo. While significant differences indeed exist, it's worth noting that exponents consistent with a critical branching process have also been observed in vivo (Petermann et al 2009; Hahn et al. 2010), as well as in large-scale human data.

References:

Touboul and Destexhe, 2017: Touboul J, Destexhe A. Power-law statistics and universal scaling in the absence of criticality. Phys Rev E. 2017 95:012413, 2017.

Priesemann and Shriki, 2018: Priesemann V, Shriki O. PLOS Comp. Bio. 14:1-29, 2018.

Petermann et al 2009: Oetermann, T., Thiagarajan, T. C., Lebedev, M. A., Nicolelis, M. A., Chialvo, D. R., and Plenz, D. PNAS 106:15921-15926, 2009.

Hahn et al. 2010: Hahn, G., Petermann, T., Havenith, M. N., Yu, S., Singer, W., Plenz, D., and Nikolic, D. J. Neurophys. 104:3312-3322, 2010.

Minor comments:

1. The term 'latent variable' should be rigorously explained, as it is likely to be unfamiliar to some readers.

2. There's a relatively important typo in the equations: Eq. 2 and Eq. 6 differ by a minus sign in the exponent. Eqs. 3 and 4 use the plus sign, but epsilon_0 on line 198 uses the minus sign. All very confusing until we figured out what was going on. But easy to fix.

3. In Eq. 7, the left hand side is zeta'/zeta', which is equal to 1. Maybe it should be zeta'/zeta?