# The simplest maximum entropy model for collective behavior in a neural network

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.

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Author

Tkacik, Gasper

^{ISTA}^{}; Marre, Olivier; Mora, Thierry; Amodei, Dario; Berry, Michael; Bialek, WilliamDepartment

Abstract

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.

Publishing Year

Date Published

2013-03-12

Journal Title

Journal of Statistical Mechanics Theory and Experiment

Acknowledgement

his work was supported in part by NSF Grants IIS-0613435 and PHY-0957573, by NIH Grants R01 EY14196 and P50 GM071508, by the Fannie and John Hertz Foundation, by the Human Frontiers Science Program, by the Swartz Foundation, and by the WM Keck Foundation.

Volume

2013

Issue

3

Article Number

P03011

IST-REx-ID

### Cite this

Tkačik G, Marre O, Mora T, Amodei D, Berry M, Bialek W. The simplest maximum entropy model for collective behavior in a neural network.

*Journal of Statistical Mechanics Theory and Experiment*. 2013;2013(3). doi:10.1088/1742-5468/2013/03/P03011Tkačik, 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*. IOP Publishing Ltd. https://doi.org/10.1088/1742-5468/2013/03/P03011Tkačik, Gašper, Olivier Marre, Thierry Mora, Dario Amodei, Michael Berry, and William Bialek. “The Simplest Maximum Entropy Model for Collective Behavior in a Neural Network.”

*Journal of Statistical Mechanics Theory and Experiment*. IOP Publishing Ltd., 2013. https://doi.org/10.1088/1742-5468/2013/03/P03011.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,”

*Journal of Statistical Mechanics Theory and Experiment*, vol. 2013, no. 3. IOP Publishing Ltd., 2013.Tkačik, Gašper, et al. “The Simplest Maximum Entropy Model for Collective Behavior in a Neural Network.”

*Journal of Statistical Mechanics Theory and Experiment*, vol. 2013, no. 3, P03011, IOP Publishing Ltd., 2013, doi:10.1088/1742-5468/2013/03/P03011.**All files available under the following license(s):**

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arXiv 1207.6319