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testgroup
pytensor
Commits
4e5b2223
提交
4e5b2223
authored
10月 20, 2014
作者:
Kelvin Xu
提交者:
Kelvin Xu
10月 23, 2014
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电子邮件补丁
差异文件
subgrad documentation moved from tensor to theano.gradient
上级
4829418f
隐藏空白字符变更
内嵌
并排
正在显示
2 个修改的文件
包含
36 行增加
和
95 行删除
+36
-95
basic.txt
doc/library/tensor/basic.txt
+0
-94
gradient.py
theano/gradient.py
+36
-1
没有找到文件。
doc/library/tensor/basic.txt
浏览文件 @
4e5b2223
...
@@ -1658,100 +1658,6 @@ Gradient / Differentiation
...
@@ -1658,100 +1658,6 @@ Gradient / Differentiation
:rtype: variable or list of variables (matching `wrt`)
:rtype: variable or list of variables (matching `wrt`)
:returns: gradients of the cost with respect to each of the `wrt` terms
:returns: gradients of the cost with respect to each of the `wrt` terms
.. function:: subgraph_grad(wrt, end, start=None, cost=None, details=False)
With respect to `wrt`, computes gradients of cost and/or from existing
`start` gradients, up to the `end` variables of a symbolic digraph.
In other words, computes gradients for a subgraph of the
symbolic theano function. Ignores all disconnected inputs.
This can be useful when one needs to perform the gradient descent
iteratively (e.g. one layer at a time in an MLP), or when a particular
operation is not differentiable in theano (e.g. stochastic sampling
from a multinomial). In the latter case, the gradient of the
non-differentiable process could be approximated by user-defined
formula, which could be calculated using the gradients of a cost
with respect to samples (0s and 1s). These gradients are obtained
by performing a subgraph_grad from the `cost` or previously known gradients
(`start`) up to the outputs of the stochastic process (`end`).
A dictionary mapping gradients obtained from the user-defined
differentiation of the process, to variables, could then be fed into
another subgraph_grad as `start` with any other `cost` (e.g. weight decay).
In an MLP, we could use subgraph_grad to iteratively backpropagate:
.. testcode:: subgraph_grad
import theano
import numpy as np
x, t = theano.tensor.fvector('x'), theano.tensor.fvector('t')
w1 = theano.shared(np.random.randn(3,4))
w2 = theano.shared(np.random.randn(4,2))
a1 = theano.tensor.tanh(theano.tensor.dot(x,w1))
a2 = theano.tensor.tanh(theano.tensor.dot(a1,w2))
cost2 = theano.tensor.sqr(a2 - t).sum()
cost2 += theano.tensor.sqr(w2.sum())
cost1 = theano.tensor.sqr(w1.sum())
params = [[w2],[w1]]
costs = [cost2,cost1]
grad_ends = [[a1], [x]]
next_grad = None
param_grads = []
for i in xrange(2):
param_grad, next_grad = theano.subgraph_grad(
wrt=params[i], end=grad_ends[i],
start=next_grad, cost=costs[i]
)
next_grad = dict(zip(grad_ends[i], next_grad))
param_grads.extend(param_grad)
:type wrt: list of variables
:param wrt:
Gradients are computed with respect to `wrt`.
:type end: list of variables
:param end:
Theano variables at which to end gradient descent (they are
considered constant in theano.grad). For convenience, the
gradients with respect to these variables are also returned.
:type start: dictionary of variables
:param start:
If not None, a dictionary mapping variables to their
gradients. This is useful when the gradient on some variables
are known. These are used to compute the gradients backwards up
to the variables in `end` (they are used as known_grad in
theano.grad).
:type cost: scalar (0-dimensional) variable
:param cost:
Additional costs for which to compute the gradients. For
example, these could be weight decay, an l1 constraint, MSE,
NLL, etc. May optionally be None if start is provided.
.. warning::
If the gradients of `cost` with respect to any of the `start`
variables is already part of the `start` dictionary, then it
may be counted twice with respect to `wrt` and `end`.
:type details: bool
:param details:
When True, additionally returns the list of gradients from
`start` and of `cost`, respectively, with respect to `wrt` (not
`end`).
:rtype: Tuple of 2 or 4 Lists of Variables
:return: Returns lists of gradients with respect to `wrt` and `end`,
respectively.
.. versionadded:: 0.6.1
.. _R_op_list:
.. _R_op_list:
...
...
theano/gradient.py
浏览文件 @
4e5b2223
...
@@ -567,6 +567,33 @@ def subgraph_grad(wrt, end, start=None, cost=None, details=False):
...
@@ -567,6 +567,33 @@ def subgraph_grad(wrt, end, start=None, cost=None, details=False):
subgraph_grad as `start` with any other `cost` (e.g. weight
subgraph_grad as `start` with any other `cost` (e.g. weight
decay).
decay).
In an MLP, we could use subgraph_grad to iteratively backpropagate:
.. code-block:: python
x, t = theano.tensor.fvector('x'), theano.tensor.fvector('t')
w1 = theano.shared(np.random.randn(3,4))
w2 = theano.shared(np.random.randn(4,2))
a1 = theano.tensor.tanh(theano.tensor.dot(x,w1))
a2 = theano.tensor.tanh(theano.tensor.dot(a1,w2))
cost2 = theano.tensor.sqr(a2 - t).sum()
cost2 += theano.tensor.sqr(w2.sum())
cost1 = theano.tensor.sqr(w1.sum())
params = [[w2],[w1]]
costs = [cost2,cost1]
grad_ends = [[a1], [x]]
next_grad = None
param_grads = []
for i in xrange(2):
param_grad, next_grad = theano.subgraph_grad(
wrt=params[i], end=grad_ends[i],
start=next_grad, cost=costs[i]
)
next_grad = dict(zip(grad_ends[i], next_grad))
param_grads.extend(param_grad)
:type wrt: list of variables
:type wrt: list of variables
:param wrt:
:param wrt:
Gradients are computed with respect to `wrt`.
Gradients are computed with respect to `wrt`.
...
@@ -593,7 +620,14 @@ def subgraph_grad(wrt, end, start=None, cost=None, details=False):
...
@@ -593,7 +620,14 @@ def subgraph_grad(wrt, end, start=None, cost=None, details=False):
: If the gradients of `cost` with respect to any of the `start`
: If the gradients of `cost` with respect to any of the `start`
variables is already part of the `start` dictionary, then it may
variables is already part of the `start` dictionary, then it may
be counted twice with respect to `wrt` and `end`.
be counted twice with respect to `wrt` and `end`.
.. warning::
If the gradients of `cost` with respect to any of the `start`
variables is already part of the `start` dictionary, then it
may be counted twice with respect to `wrt` and `end`.
:type details: bool
:type details: bool
:param details:
:param details:
When True, additionally returns the list of gradients from
When True, additionally returns the list of gradients from
...
@@ -605,6 +639,7 @@ def subgraph_grad(wrt, end, start=None, cost=None, details=False):
...
@@ -605,6 +639,7 @@ def subgraph_grad(wrt, end, start=None, cost=None, details=False):
:return: Returns lists of gradients with respect to `wrt` and `end`,
:return: Returns lists of gradients with respect to `wrt` and `end`,
respectively.
respectively.
.. versionadded:: 0.6.1
'''
'''
assert
((
cost
is
not
None
)
or
(
start
is
not
None
))
assert
((
cost
is
not
None
)
or
(
start
is
not
None
))
assert
isinstance
(
end
,
list
)
assert
isinstance
(
end
,
list
)
...
...
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