提交 4e5b2223 authored 作者: Kelvin Xu's avatar Kelvin Xu 提交者: Kelvin Xu

subgrad documentation moved from tensor to theano.gradient

上级 4829418f
...@@ -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:
......
...@@ -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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