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pytensor
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d94634fa
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d94634fa
authored
4月 02, 2011
作者:
Razvan Pascanu
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fixing the documentation as Jonathan Taylor suggested in a email send to
theano-users.
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8fa982b4
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examples.txt
doc/tutorial/examples.txt
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doc/tutorial/examples.txt
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d94634fa
...
@@ -99,7 +99,8 @@ Computing gradients
...
@@ -99,7 +99,8 @@ Computing gradients
Now let's use Theano for a slightly more sophisticated task: create a
Now let's use Theano for a slightly more sophisticated task: create a
function which computes the derivative of some expression ``y`` with
function which computes the derivative of some expression ``y`` with
respect to its parameter ``x``. For instance, we can compute the
respect to its parameter ``x``. To do this we will use the macro ``T.grad``.
For instance, we can compute the
gradient of :math:`x^2` with respect to :math:`x`. Note that:
gradient of :math:`x^2` with respect to :math:`x`. Note that:
:math:`d(x^2)/dx = 2 \cdot x`.
:math:`d(x^2)/dx = 2 \cdot x`.
...
@@ -158,12 +159,13 @@ logistic is: :math:`ds(x)/dx = s(x) \cdot (1 - s(x))`.
...
@@ -158,12 +159,13 @@ logistic is: :math:`ds(x)/dx = s(x) \cdot (1 - s(x))`.
array([[ 0.25 , 0.19661193],
array([[ 0.25 , 0.19661193],
[ 0.19661193, 0.10499359]])
[ 0.19661193, 0.10499359]])
In general, for any **scalar** expression ``s``, ``T.grad(s, w)`` provides
The resulting function computes the gradient of its first argument
the theano expression for computing :math:`\frac{\partial s}{\partial w}`. In
with respect to the second. In this way, Theano can be used for
this way Theano can be used for doing **efficient** symbolic differentiation
`automatic differentiation <http://en.wikipedia.org/wiki/Automatic_differentiation>`_.
(as
As opposed to what this page tell, Theano do efficient symbolic differentiation
the expression return by ``TT.grad`` will be optimized during compilation) even for
even for function with many inputs.
function with many inputs. ( see `automatic differentiation <http://en.wikipedia.org/wiki/Automatic_differentiation>`_ for a description
of symbolic differentiation).
.. note::
.. note::
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