Neural Networks

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<div align=center>
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[[Image:Sigmoid_Function.png|400px|center|Sigmoid activation function.]]
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[[Image:Sigmoid_Function.png|400px|top|Sigmoid activation function.]]
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[[Image:Tanh_Function.png|400px|center|Tanh activation function.]]
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[[Image:Tanh_Function.png|400px|top|Tanh activation function.]]
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</div>
The <math>\tanh(z)</math> function is a rescaled version of the sigmoid, and its output range is
The <math>\tanh(z)</math> function is a rescaled version of the sigmoid, and its output range is
<math>[-1,1]</math> instead of <math>[0,1]</math>.
<math>[-1,1]</math> instead of <math>[0,1]</math>.
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Note that unlike CS221 and (parts of) CS229, we are not using the convention
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Note that unlike some other venues (including the OpenClassroom videos, and parts of CS229), we are not using the convention
here of <math>x_0=1</math>.  Instead, the intercept term is handled separately by the parameter <math>b</math>.
here of <math>x_0=1</math>.  Instead, the intercept term is handled separately by the parameter <math>b</math>.
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A neural network is put together by hooking together many of our simple
A neural network is put together by hooking together many of our simple
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``neurons,'' so that the output of a neuron can be the input of another.  For
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"neurons," so that the output of a neuron can be the input of another.  For
example, here is a small neural network:
example, here is a small neural network:
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In this figure, we have used circles to also denote the inputs to the network.  The circles
In this figure, we have used circles to also denote the inputs to the network.  The circles
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labeled ``+1'' are called '''bias units''', and correspond to the intercept term.
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labeled "+1" are called '''bias units''', and correspond to the intercept term.
The leftmost layer of the network is called the '''input layer''', and the
The leftmost layer of the network is called the '''input layer''', and the
rightmost layer the '''output layer''' (which, in this example, has only one
rightmost layer the '''output layer''' (which, in this example, has only one
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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>\textstyle n_l</math>-layered network
The most common choice is a <math>\textstyle n_l</math>-layered network
where layer <math>\textstyle 1</math> is the input layer, layer <math>\textstyle n_l</math> is the output layer, and each
where layer <math>\textstyle 1</math> is the input layer, layer <math>\textstyle n_l</math> is the output layer, and each
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example of a '''feedforward''' neural network, since the connectivity graph
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>\textstyle s_l</math> to denote the
 
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%number of units in layer <math>\textstyle l</math> of the network (not counting the bias unit).
 
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patient, and the different outputs <math>y_i</math>'s might indicate presence or absence
patient, and the different outputs <math>y_i</math>'s might indicate presence or absence
of different diseases.)
of different diseases.)
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{{Sparse_Autoencoder}}
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{{Languages|神经网络|中文}}

Latest revision as of 19:38, 6 April 2013

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