Linear Decoders

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where <math>a^{(3)}</math> is the output.  In the autoencoder, <math>a^{(3)}</math> is our approximate reconstruction of the input <math>x = a^{(1)}</math>.  
where <math>a^{(3)}</math> is the output.  In the autoencoder, <math>a^{(3)}</math> is our approximate reconstruction of the input <math>x = a^{(1)}</math>.  
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<math>
 
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\begin{align}
 
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z^{(3)} &= W^{(2)} a^{(2)} + b^{(2)} \\
 
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a^{(3)} &= f(z^{(3)})
 
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\end{align}
 
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</math>
 
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<math>
 
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\begin{align}
 
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z^{(3)} &= W^{(2)} a^{(2)} + b^{(2)} \\
 
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a^{(3)} &= f(z^{(3)})
 
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\end{align}
 
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</math>
 
Because we used a sigmoid activation function for <math>f(z^{(3)})</math>, we needed to constrain or scale the inputs to be in the range <math>[0,1]</math>,  
Because we used a sigmoid activation function for <math>f(z^{(3)})</math>, we needed to constrain or scale the inputs to be in the range <math>[0,1]</math>,  

Revision as of 05:33, 8 March 2013

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