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Title: Cusps enable line attractors for neural computation

Abstract

Here, line attractors in neuronal networks have been suggested to be the basis of many brain functions, such as working memory, oculomotor control, head movement, locomotion, and sensory processing. In this paper, we make the connection between line attractors and pulse gating in feed-forward neuronal networks. In this context, because of their neutral stability along a one-dimensional manifold, line attractors are associated with a time-translational invariance that allows graded information to be propagated from one neuronal population to the next. To understand how pulse-gating manifests itself in a high-dimensional, nonlinear, feedforward integrate-and-fire network, we use a Fokker-Planck approach to analyze system dynamics. We make a connection between pulse-gated propagation in the Fokker-Planck and population-averaged mean-field (firing rate) models, and then identify an approximate line attractor in state space as the essential structure underlying graded information propagation. An analysis of the line attractor shows that it consists of three fixed points: a central saddle with an unstable manifold along the line and stable manifolds orthogonal to the line, which is surrounded on either side by stable fixed points. Along the manifold defined by the fixed points, slow dynamics give rise to a ghost. We show that this line attractor arises atmore » a cusp catastrophe, where a fold bifurcation develops as a function of synaptic noise; and that the ghost dynamics near the fold of the cusp underly the robustness of the line attractor. Understanding the dynamical aspects of this cusp catastrophe allows us to show how line attractors can persist in biologically realistic neuronal networks and how the interplay of pulse gating, synaptic coupling, and neuronal stochasticity can be used to enable attracting one-dimensional manifolds and, thus, dynamically control the processing of graded information.« less

Authors:
 [1];  [2]; ORCiD logo [3];  [4]
  1. Univ. of Arizona, Tucson, AZ (United States); Peking Univ., Beijing (China)
  2. Beijing Computational Science Research Center, Beijing (China)
  3. Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of California, Davis, CA (United States)
  4. Peking Univ., Beijing (China)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
National Institutes of Health (NIH); USDOE
OSTI Identifier:
1411361
Report Number(s):
LA-UR-17-28766
Journal ID: ISSN 2470-0045; PLEEE8; TRN: US1800226
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review E
Additional Journal Information:
Journal Volume: 96; Journal Issue: 5; Journal ID: ISSN 2470-0045
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
59 BASIC BIOLOGICAL SCIENCES; 60 APPLIED LIFE SCIENCES; Biological Science; Computer Science

Citation Formats

Xiao, Zhuocheng, Zhang, Jiwei, Sornborger, Andrew T., and Tao, Louis. Cusps enable line attractors for neural computation. United States: N. p., 2017. Web. doi:10.1103/PhysRevE.96.052308.
Xiao, Zhuocheng, Zhang, Jiwei, Sornborger, Andrew T., & Tao, Louis. Cusps enable line attractors for neural computation. United States. doi:10.1103/PhysRevE.96.052308.
Xiao, Zhuocheng, Zhang, Jiwei, Sornborger, Andrew T., and Tao, Louis. Tue . "Cusps enable line attractors for neural computation". United States. doi:10.1103/PhysRevE.96.052308. https://www.osti.gov/servlets/purl/1411361.
@article{osti_1411361,
title = {Cusps enable line attractors for neural computation},
author = {Xiao, Zhuocheng and Zhang, Jiwei and Sornborger, Andrew T. and Tao, Louis},
abstractNote = {Here, line attractors in neuronal networks have been suggested to be the basis of many brain functions, such as working memory, oculomotor control, head movement, locomotion, and sensory processing. In this paper, we make the connection between line attractors and pulse gating in feed-forward neuronal networks. In this context, because of their neutral stability along a one-dimensional manifold, line attractors are associated with a time-translational invariance that allows graded information to be propagated from one neuronal population to the next. To understand how pulse-gating manifests itself in a high-dimensional, nonlinear, feedforward integrate-and-fire network, we use a Fokker-Planck approach to analyze system dynamics. We make a connection between pulse-gated propagation in the Fokker-Planck and population-averaged mean-field (firing rate) models, and then identify an approximate line attractor in state space as the essential structure underlying graded information propagation. An analysis of the line attractor shows that it consists of three fixed points: a central saddle with an unstable manifold along the line and stable manifolds orthogonal to the line, which is surrounded on either side by stable fixed points. Along the manifold defined by the fixed points, slow dynamics give rise to a ghost. We show that this line attractor arises at a cusp catastrophe, where a fold bifurcation develops as a function of synaptic noise; and that the ghost dynamics near the fold of the cusp underly the robustness of the line attractor. Understanding the dynamical aspects of this cusp catastrophe allows us to show how line attractors can persist in biologically realistic neuronal networks and how the interplay of pulse gating, synaptic coupling, and neuronal stochasticity can be used to enable attracting one-dimensional manifolds and, thus, dynamically control the processing of graded information.},
doi = {10.1103/PhysRevE.96.052308},
journal = {Physical Review E},
number = 5,
volume = 96,
place = {United States},
year = {2017},
month = {11}
}

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