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2_19_09_LinearRecurrentNetworks_1

2_19_09_LinearRecurrentNetworks_1 - Outline of the Lecture...

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Outline of the Lecture Outline of the Lecture Linear Recurrent Network Models  Linear Recurrent Network Models  Recurrent Matrices      Eigenvalues, Eigenvectors        Recurrent Matrices      Eigenvalues, Eigenvectors        Properties Properties
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Synaptic-Matrix Eigenvector  Synaptic-Matrix Eigenvector  Properties Determine  Properties Determine  Responses of Linear  Responses of Linear  Recurrent Networks Recurrent Networks    
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A full feedforward network has vector inputs and outputs connected by a weight matrix.
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A recurrent network is a feedforward network with a recurrent synaptic weight matrix.
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For a feedforward network: For a recurrent network: τ r dv a dt = - v a + F W ab b =1 N a å u b æ è ç ö ø ÷ æ è ç ö ø ÷ τ r d r v dt = - r v + F W × r u ( ) τ r d r v dt = - r v + F W × r u + M × r v ( )
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Assuming that the activation function F is linear, that is, F(x)=x, and denoting the input as h = W .
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