Thermodynamics and signatures of criticality in a network of neurons

The activity of a neural network is defined by patterns of spiking and silence from the individual neurons. Because spikes are (relatively) sparse, patterns of activity with increasing numbers of spikes are less probable, but, with more spikes, the number of possible patterns increases. This tradeof...

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Published in:Proceedings of the National Academy of Sciences - PNAS Vol. 112; no. 37; p. 11508
Main Authors: Tkačik, Gašper, Mora, Thierry, Marre, Olivier, Amodei, Dario, Palmer, Stephanie E, Berry, 2nd, Michael J, Bialek, William
Format: Journal Article
Language:English
Published: United States 15.09.2015
Subjects:
Algorithms
Animals
Brain - physiology
Caudata
Entropy
Hot Temperature
Models, Neurological
Models, Statistical
Monte Carlo Method
Nerve Net
Neurons - physiology
Probability
Reproducibility of Results
Retina - physiology
Thermodynamics
information
entropy
Monte Carlo
correlation
neural networks
ISSN:1091-6490, 1091-6490
Online Access:Get more information
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Summary:The activity of a neural network is defined by patterns of spiking and silence from the individual neurons. Because spikes are (relatively) sparse, patterns of activity with increasing numbers of spikes are less probable, but, with more spikes, the number of possible patterns increases. This tradeoff between probability and numerosity is mathematically equivalent to the relationship between entropy and energy in statistical physics. We construct this relationship for populations of up to N = 160 neurons in a small patch of the vertebrate retina, using a combination of direct and model-based analyses of experiments on the response of this network to naturalistic movies. We see signs of a thermodynamic limit, where the entropy per neuron approaches a smooth function of the energy per neuron as N increases. The form of this function corresponds to the distribution of activity being poised near an unusual kind of critical point. We suggest further tests of criticality, and give a brief discussion of its functional significance.
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ISSN:1091-6490
1091-6490
DOI:10.1073/pnas.1514188112