subgrad doc

doc/library/tensor/basic.txt

@@ -1543,6 +1543,86 @@ Gradient / Differentiation
     :rtype: variable or list of variables (matching `wrt`)
     :returns: gradients of the cost with respect to each of the `wrt` terms
     
+.. function:: subgrad(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 subgrad 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 subgrad as `start` with any other `cost` (e.g. weight decay).
+    
+    In an MLP, we could use subgrad to iteratively backpropagate:
+    >>> 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.subgrad(
+    >>>         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.
+        Gradients are computed with respect to `wrt`.
+    
+    :type end : List of Variables.
+        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.
+
 
 .. _R_op_list:
 

theano/gradient.py

@@ -545,8 +545,8 @@ def grad(cost, wrt, consider_constant=None,
 
 def subgrad(wrt, end, start=None, cost=None, details=False):
     '''
-    With respect to wrt, computes gradients of known_grads, cost, 
-    or both, up to grad_end theano variables in theano digraph. 
+    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.
     
@@ -555,38 +555,49 @@ def subgrad(wrt, end, start=None, cost=None, details=False):
     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 at the 
-    output of the process. These are obtained by performing a subgrad 
-    from the cost or previously known_grads up to the outputs of the 
-    process (grad_end). The gradients obtained from the user defined 
-    gradient of the process can then be fed into another subgrad as 
-    known_grads with any other cost functions (e.g. weight decay), and 
-    so on.
-    
-    parameters
-    ----------
-    wrt : list
-        gradients are computed with respect to (wrt) these variables.
-    end : list
-        theano variables where to stop the backpropagation of gradients
-        (they will be considered constant in theano.grad).
-    start : dict
-        Theano variables, gradients (key, value) in the forward part 
-        (near a cost) of the graph for which gradients are known. 
-        These will be used to compute the gradients backwards 
-        up to the variables in grad_end (they will be used as known_grads
-        in theano.grad).
-    cost : theano scalar
-        additional costs for which to compute the gradients. For 
-        example, these could be weight decay, or l1 constraint on output
-    details: bool
-        when True, return OrderedDict of wrt, gradients, and lists of
-        gradients derived from known_grads, cost_grads, respectively
-        (in same order as wrt)
+    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 subgrad 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 subgrad as `start` with any other `cost` (e.g. weight decay).
+    
+    :type wrt : List of Variables.
+        Gradients are computed with respect to `wrt`.
+    
+    :type end : List of Variables.
+        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).
     
-    return
-    ------
-    Returns an OrderedDict of params (keys), gradients (values)
+    :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.
     '''
     assert ((cost is not None) or (start is not None))
     assert isinstance(end, list)
@@ -633,6 +644,7 @@ def subgrad(wrt, end, start=None, cost=None, details=False):
     
     if details:
         return wrt_grads, end_grads, start_grads, cost_grads
+    
     return wrt_grads, end_grads
 
 def _node_to_pattern(node):