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Following a stimulus, the neural response typically strongly varies in time and across neurons before settling to a steady-state. While classical population coding theory disregards the temporal dimension, recent works have argued that trajectories of transient activity can be particularly informative about stimulus identity and may form the basis of computations through dynamics. Yet the dynamical mechanisms needed to generate a population code based on transient trajectories have not been fully elucidated. Here we examine transient coding in a broad class of high-dimensional linear networks of recurrently connected units. We start by reviewing a well-known result that leads to a distinction between two classes of networks: networks in which all inputs lead to weak, decaying transients, and networks in which specific inputs elicit amplified transient responses and are mapped onto output states during the dynamics. Theses two classes are simply distinguished based on the spectrum of the symmetric part of the connectivity matrix. For the second class of networks, which is a sub-class of non-normal networks, we provide a procedure to identify transiently amplified inputs and the corresponding readouts. We first apply these results to standard randomly-connected and two-population networks. We then build minimal, low-rank networks that robustly implement trajectories mapping a specific input onto a specific orthogonal output state. Finally, we demonstrate that the capacity of the obtained networks increases proportionally with their size.
This article was published in the following journal.
Name: PLoS computational biology
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A computer architecture, implementable in either hardware or software, modeled after biological neural networks. Like the biological system in which the processing capability is a result of the interconnection strengths between arrays of nonlinear processing nodes, computerized neural networks, often called perceptrons or multilayer connectionist models, consist of neuron-like units. A homogeneous group of units makes up a layer. These networks are good at pattern recognition. They are adaptive, performing tasks by example, and thus are better for decision-making than are linear learning machines or cluster analysis. They do not require explicit programming.
An early embryonic developmental process of CHORDATES that is characterized by morphogenic movements of ECTODERM resulting in the formation of the NEURAL PLATE; the NEURAL CREST; and the NEURAL TUBE. Improper closure of the NEURAL GROOVE results in congenital NEURAL TUBE DEFECTS.
The two longitudinal ridges along the PRIMITIVE STREAK appearing near the end of GASTRULATION during development of nervous system (NEURULATION). The ridges are formed by folding of NEURAL PLATE. Between the ridges is a neural groove which deepens as the fold become elevated. When the folds meet at midline, the groove becomes a closed tube, the NEURAL TUBE.
A tube of ectodermal tissue in an embryo that will give rise to the CENTRAL NERVOUS SYSTEM, including the SPINAL CORD and the BRAIN. Lumen within the neural tube is called neural canal which gives rise to the central canal of the spinal cord and the ventricles of the brain. For malformation of the neural tube, see NEURAL TUBE DEFECTS.
The region in the dorsal ECTODERM of a chordate embryo that gives rise to the future CENTRAL NERVOUS SYSTEM. Tissue in the neural plate is called the neuroectoderm, often used as a synonym of neural plate.