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pytensor
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aba531c0
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aba531c0
authored
5月 27, 2013
作者:
Frederic
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Fix doc indentation. They are part of their section, not at the global scope.
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cb6e3a07
隐藏空白字符变更
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38 行增加
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36 行删除
+38
-36
nnet.txt
doc/library/tensor/nnet/nnet.txt
+38
-36
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doc/library/tensor/nnet/nnet.txt
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aba531c0
...
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@@ -77,30 +77,30 @@
Returns the softplus nonlinearity applied to x
:Parameter: *x* - symbolic Tensor (or compatible)
:Return type: same as x
:Returns: elementwise softplus: :math:`softplus(x) = \log_e{\left(1 + \exp(x)\right)}`.
:Returns: elementwise softplus: :math:`softplus(x) = \log_e{\left(1 + \exp(x)\right)}`.
.. note:: The underlying code will return an exact 0 if an element of x is too small.
.. note:: The underlying code will return an exact 0 if an element of x is too small.
.. code-block:: python
.. code-block:: python
x,y,b = T.dvectors('x','y','b')
W = T.dmatrix('W')
y = T.nnet.softplus(T.dot(W,x) + b)
x,y,b = T.dvectors('x','y','b')
W = T.dmatrix('W')
y = T.nnet.softplus(T.dot(W,x) + b)
.. function:: softmax(x)
Returns the softmax function of x:
:Parameter: *x* symbolic **2D** Tensor (or compatible).
:Parameter: *x* symbolic **2D** Tensor (or compatible).
:Return type: same as x
:Returns: a symbolic 2D tensor whose ijth element is :math:`softmax_{ij}(x) = \frac{\exp{x_{ij}}}{\sum_k\exp(x_{ik})}`.
:Returns: a symbolic 2D tensor whose ijth element is :math:`softmax_{ij}(x) = \frac{\exp{x_{ij}}}{\sum_k\exp(x_{ik})}`.
The softmax function will, when applied to a matrix, compute the softmax values row-wise.
The softmax function will, when applied to a matrix, compute the softmax values row-wise.
.. code-block:: python
.. code-block:: python
x,y,b = T.dvectors('x','y','b')
W = T.dmatrix('W')
y = T.nnet.softmax(T.dot(W,x) + b)
x,y,b = T.dvectors('x','y','b')
W = T.dmatrix('W')
y = T.nnet.softmax(T.dot(W,x) + b)
.. function:: binary_crossentropy(output,target)
...
...
@@ -111,27 +111,27 @@ The softmax function will, when applied to a matrix, compute the softmax values
* *output* - symbolic Tensor (or compatible)
:Return type: same as target
:Returns: a symbolic tensor, where the following is applied elementwise :math:`crossentropy(t,o) = -(t\cdot log(o) + (1 - t) \cdot log(1 - o))`.
:Returns: a symbolic tensor, where the following is applied elementwise :math:`crossentropy(t,o) = -(t\cdot log(o) + (1 - t) \cdot log(1 - o))`.
The following block implements a simple auto-associator with a sigmoid
nonlinearity and a reconstruction error which corresponds to the binary
cross-entropy (note that this assumes that x will contain values between 0 and
1):
The following block implements a simple auto-associator with a
sigmoid nonlinearity and a reconstruction error which corresponds
to the binary cross-entropy (note that this assumes that x will
contain values between 0 and
1):
.. code-block:: python
.. code-block:: python
x, y, b = T.dvectors('x', 'y', 'b')
W = T.dmatrix('W')
h = T.nnet.sigmoid(T.dot(W, x) + b)
x_recons = T.nnet.sigmoid(T.dot(V, h) + c)
recon_cost = T.nnet.binary_crossentropy(x_recons, x).mean()
x, y, b = T.dvectors('x', 'y', 'b')
W = T.dmatrix('W')
h = T.nnet.sigmoid(T.dot(W, x) + b)
x_recons = T.nnet.sigmoid(T.dot(V, h) + c)
recon_cost = T.nnet.binary_crossentropy(x_recons, x).mean()
.. function:: categorical_crossentropy(coding_dist,true_dist)
Return the cross-entropy between an approximating distribution and a true distribution.
Return the cross-entropy between an approximating distribution and a true distribution.
The cross entropy between two probability distributions measures the average number of bits
needed to identify an event from a set of possibilities, if a coding scheme is used based
on a given probability distribution q, rather than the "true" distribution p. Mathematically, this
on a given probability distribution q, rather than the "true" distribution p. Mathematically, this
function computes :math:`H(p,q) = - \sum_x p(x) \log(q(x))`, where
p=true_dist and q=coding_dist.
...
...
@@ -145,15 +145,17 @@ cross-entropy (note that this assumes that x will contain values between 0 and
:Return type: tensor of rank one-less-than `coding_dist`
.. note:: An application of the scenario where *true_dist* has a 1-of-N representation
is in classification with softmax outputs. If `coding_dist` is the output of
the softmax and `true_dist` is a vector of correct labels, then the function
will compute ``y_i = - \log(coding_dist[i, one_of_n[i]])``, which corresponds
to computing the neg-log-probability of the correct class (which is typically
the training criterion in classification settings).
.. note:: An application of the scenario where *true_dist* has a
1-of-N representation is in classification with softmax
outputs. If `coding_dist` is the output of the softmax and
`true_dist` is a vector of correct labels, then the function
will compute ``y_i = - \log(coding_dist[i, one_of_n[i]])``,
which corresponds to computing the neg-log-probability of the
correct class (which is typically the training criterion in
classification settings).
.. code-block:: python
.. code-block:: python
y = T.nnet.softmax(T.dot(W, x) + b)
cost = T.nnet.categorical_crossentropy(y, o)
# o is either the above-mentioned 1-of-N vector or 2D tensor
y = T.nnet.softmax(T.dot(W, x) + b)
cost = T.nnet.categorical_crossentropy(y, o)
# o is either the above-mentioned 1-of-N vector or 2D tensor
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