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:

Xiao, Zhuocheng ^[1]; Zhang, Jiwei ^[2]; Sornborger, Andrew T.  ^[3];

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Tao, Louis ^[4]

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+ Show Author Affiliations

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:

2017-11-07

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