TY - JOUR
T1 - Design of continuous attractor networks with monotonic tuning using a symmetry principle
AU - Machens, Christian K.
AU - Brody, Carlos D.
N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2008/2
Y1 - 2008/2
N2 - Neurons that sustain elevated firing in the absence of stimuli have been found in many neural systems. In graded persistent activity, neurons can sustain firing at many levels, suggesting a widely found type of network dynamics in which networks can relax to any one of a continuum of stationary states. The reproduction of these findings in model networks of nonlinear neurons has turned out to be nontrivial. A particularly insightful model has been the "bump attractor," in which a continuous attractor emerges through an underlying symmetry in the network connectivity matrix. This model, however, cannot account for data in which the persistent firing of neurons is a monotonie-rather than a bell-shaped - function of a stored variable. Here, we show that the symmetry used in the bump attractor network can be employed to create a whole family of continuous attractor networks, including those with monotonie tuning. Our design is based on tuning the external inputs to networks that have a connectivity matrix with Toeplitz symmetry. In particular, we provide a complete analytical solution of a line attractor network with monotonic tuning and show that for many other networks, the numerical tuning of synaptic weights reduces to the computation of a single parameter.
AB - Neurons that sustain elevated firing in the absence of stimuli have been found in many neural systems. In graded persistent activity, neurons can sustain firing at many levels, suggesting a widely found type of network dynamics in which networks can relax to any one of a continuum of stationary states. The reproduction of these findings in model networks of nonlinear neurons has turned out to be nontrivial. A particularly insightful model has been the "bump attractor," in which a continuous attractor emerges through an underlying symmetry in the network connectivity matrix. This model, however, cannot account for data in which the persistent firing of neurons is a monotonie-rather than a bell-shaped - function of a stored variable. Here, we show that the symmetry used in the bump attractor network can be employed to create a whole family of continuous attractor networks, including those with monotonie tuning. Our design is based on tuning the external inputs to networks that have a connectivity matrix with Toeplitz symmetry. In particular, we provide a complete analytical solution of a line attractor network with monotonic tuning and show that for many other networks, the numerical tuning of synaptic weights reduces to the computation of a single parameter.
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U2 - 10.1162/neco.2007.07-06-297
DO - 10.1162/neco.2007.07-06-297
M3 - Article
C2 - 18047414
AN - SCOPUS:38649118901
VL - 20
SP - 452
EP - 485
JO - Neural Computation
JF - Neural Computation
SN - 0899-7667
IS - 2
ER -