---
_id: '2850'
abstract:
- lang: eng
  text: "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.\r\n"
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.\r\n"
article_number: P03011
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Gasper
  full_name: Tkacik, Gasper
  id: 3D494DCA-F248-11E8-B48F-1D18A9856A87
  last_name: Tkacik
  orcid: 0000-0002-6699-1455
- first_name: Olivier
  full_name: Marre, Olivier
  last_name: Marre
- first_name: Thierry
  full_name: Mora, Thierry
  last_name: Mora
- first_name: Dario
  full_name: Amodei, Dario
  last_name: Amodei
- first_name: Michael
  full_name: Berry, Michael
  last_name: Berry
- first_name: William
  full_name: Bialek, William
  last_name: Bialek
citation:
  ama: 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>
  apa: Tkačik, G., Marre, O., Mora, T., Amodei, D., Berry, M., &#38; 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.
    <a href="https://doi.org/10.1088/1742-5468/2013/03/P03011">https://doi.org/10.1088/1742-5468/2013/03/P03011</a>
  chicago: 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, 2013. <a href="https://doi.org/10.1088/1742-5468/2013/03/P03011">https://doi.org/10.1088/1742-5468/2013/03/P03011</a>.
  ieee: 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,
    2013.
  ista: 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.
  mla: 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, 2013, doi:<a href="https://doi.org/10.1088/1742-5468/2013/03/P03011">10.1088/1742-5468/2013/03/P03011</a>.
  short: G. Tkačik, O. Marre, T. Mora, D. Amodei, M. Berry, W. Bialek, Journal of
    Statistical Mechanics Theory and Experiment 2013 (2013).
date_created: 2018-12-11T11:59:55Z
date_published: 2013-03-12T00:00:00Z
date_updated: 2025-09-29T13:42:18Z
day: '12'
department:
- _id: GaTk
doi: 10.1088/1742-5468/2013/03/P03011
external_id:
  arxiv:
  - '1207.6319'
  isi:
  - '000316056900011'
intvolume: '      2013'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/1207.6319
month: '03'
oa: 1
oa_version: Preprint
publication: Journal of Statistical Mechanics Theory and Experiment
publication_status: published
publisher: IOP Publishing
publist_id: '3942'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The simplest maximum entropy model for collective behavior in a neural network
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 2013
year: '2013'
...