article
The simplest maximum entropy model for collective behavior in a neural network
published
yes
Gasper
Tkacik
author 3D494DCA-F248-11E8-B48F-1D18A9856A870000-0002-6699-1455
Olivier
Marre
author
Thierry
Mora
author
Dario
Amodei
author
Michael
Berry
author
William
Bialek
author
GaTk
department
Recent work emphasizes that the maximum entropy principle provides a bridge between statistical mechanics models for collective behavior in neural networks and experiments on networks of real neurons. Most of this work has focused on capturing the measured correlations among pairs of neurons. Here we suggest an alternative, constructing models that are consistent with the distribution of global network activity, i.e. the probability that K out of N cells in the network generate action potentials in the same small time bin. The inverse problem that we need to solve in constructing the model is analytically tractable, and provides a natural 'thermodynamics' for the network in the limit of large N. We analyze the responses of neurons in a small patch of the retina to naturalistic stimuli, and find that the implied thermodynamics is very close to an unusual critical point, in which the entropy (in proper units) is exactly equal to the energy. © 2013 IOP Publishing Ltd and SISSA Medialab srl.
IOP Publishing Ltd.2013
eng
Journal of Statistical Mechanics Theory and Experiment
1207.631910.1088/1742-5468/2013/03/P03011
20133
Tkačik G, Marre O, Mora T, Amodei D, Berry M, Bialek W. The simplest maximum entropy model for collective behavior in a neural network. <i>Journal of Statistical Mechanics Theory and Experiment</i>. 2013;2013(3). doi:<a href="https://doi.org/10.1088/1742-5468/2013/03/P03011">10.1088/1742-5468/2013/03/P03011</a>
G. Tkačik, O. Marre, T. Mora, D. Amodei, M. Berry, and W. Bialek, “The simplest maximum entropy model for collective behavior in a neural network,” <i>Journal of Statistical Mechanics Theory and Experiment</i>, vol. 2013, no. 3. IOP Publishing Ltd., 2013.
Tkačik, G., Marre, O., Mora, T., Amodei, D., Berry, M., & Bialek, W. (2013). The simplest maximum entropy model for collective behavior in a neural network. <i>Journal of Statistical Mechanics Theory and Experiment</i>. IOP Publishing Ltd. <a href="https://doi.org/10.1088/1742-5468/2013/03/P03011">https://doi.org/10.1088/1742-5468/2013/03/P03011</a>
Tkačik, Gašper, et al. “The Simplest Maximum Entropy Model for Collective Behavior in a Neural Network.” <i>Journal of Statistical Mechanics Theory and Experiment</i>, vol. 2013, no. 3, P03011, IOP Publishing Ltd., 2013, doi:<a href="https://doi.org/10.1088/1742-5468/2013/03/P03011">10.1088/1742-5468/2013/03/P03011</a>.
Tkačik G, Marre O, Mora T, Amodei D, Berry M, Bialek W. 2013. The simplest maximum entropy model for collective behavior in a neural network. Journal of Statistical Mechanics Theory and Experiment. 2013(3), P03011.
G. Tkačik, O. Marre, T. Mora, D. Amodei, M. Berry, W. Bialek, Journal of Statistical Mechanics Theory and Experiment 2013 (2013).
Tkačik, Gašper, Olivier Marre, Thierry Mora, Dario Amodei, Michael Berry, and William Bialek. “The Simplest Maximum Entropy Model for Collective Behavior in a Neural Network.” <i>Journal of Statistical Mechanics Theory and Experiment</i>. IOP Publishing Ltd., 2013. <a href="https://doi.org/10.1088/1742-5468/2013/03/P03011">https://doi.org/10.1088/1742-5468/2013/03/P03011</a>.
28502018-12-11T11:59:55Z2021-01-12T07:00:14Z