Neural Networks

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We have so far focused on one example neural network, but one can also build neural
We have so far focused on one example neural network, but one can also build neural
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networks with other {\bf
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networks with other """architectures""" (meaning patterns of connectivity between neurons), including ones with multiple hidden layers.
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architectures} (meaning patterns of connectivity between neurons), including ones with multiple hidden layers.
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The most common choice is a <math>n_l</math>-layered network
The most common choice is a <math>n_l</math>-layered network
where layer <math>1</math> is the input layer, layer <math>n_l</math> is the output layer, and each
where layer <math>1</math> is the input layer, layer <math>n_l</math> is the output layer, and each
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output of the network, we can successively compute all the activations in layer
output of the network, we can successively compute all the activations in layer
<math>L_2</math>, then layer <math>L_3</math>, and so on, up to layer <math>L_{n_l}</math>, using Equations~(\ref{eqn-forwardprop1}-\ref{eqn-forwardprop2}).  This is one
<math>L_2</math>, then layer <math>L_3</math>, and so on, up to layer <math>L_{n_l}</math>, using Equations~(\ref{eqn-forwardprop1}-\ref{eqn-forwardprop2}).  This is one
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example of a {\bf feedforward} neural network, since the connectivity graph
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example of a """feedforward""" neural network, since the connectivity graph
does not have any directed loops or cycles.
does not have any directed loops or cycles.
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%We will write <math>s_l</math> to denote the
 
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%number of units in layer <math>l</math> of the network (not counting the bias unit).
 
Neural networks can also have multiple output units.  For example, here is a network
Neural networks can also have multiple output units.  For example, here is a network

Revision as of 23:05, 26 February 2011

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