Tkacik, GasperIST Austria ; Mora, Thierry; Marre, Olivier; Amodei, Dario; Palmer, Stephanie; Berry Ii, Michael; Bialek, William
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.
Research was supported in part by National Science Foundation Grants PHY-1305525, PHY-1451171, and CCF-0939370, by National Institutes of Health Grant R01 EY14196, and by Austrian Science Foundation Grant FWF P25651. Additional support was provided by the Fannie and John Hertz Foundation, by the Swartz Foundation, by the W. M. Keck Foundation, and by the Simons Foundation.
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Tkacik G, Mora T, Marre O, et al. Thermodynamics and signatures of criticality in a network of neurons. PNAS. 2015;112(37):11508-11513. doi:10.1073/pnas.1514188112
Tkacik, G., Mora, T., Marre, O., Amodei, D., Palmer, S., Berry Ii, M., & Bialek, W. (2015). Thermodynamics and signatures of criticality in a network of neurons. PNAS, 112(37), 11508–11513. https://doi.org/10.1073/pnas.1514188112
Tkacik, Gasper, Thierry Mora, Olivier Marre, Dario Amodei, Stephanie Palmer, Michael Berry Ii, and William Bialek. “Thermodynamics and Signatures of Criticality in a Network of Neurons.” PNAS 112, no. 37 (2015): 11508–13. https://doi.org/10.1073/pnas.1514188112.
G. Tkacik et al., “Thermodynamics and signatures of criticality in a network of neurons,” PNAS, vol. 112, no. 37, pp. 11508–11513, 2015.
Tkacik G, Mora T, Marre O, Amodei D, Palmer S, Berry Ii M, Bialek W. 2015. Thermodynamics and signatures of criticality in a network of neurons. PNAS. 112(37), 11508–11513.
Tkacik, Gasper, et al. “Thermodynamics and Signatures of Criticality in a Network of Neurons.” PNAS, vol. 112, no. 37, National Academy of Sciences, 2015, pp. 11508–13, doi:10.1073/pnas.1514188112.
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