function required to have fast gradient computations

theano/scan_module/scan_utils.py

@@ -930,3 +930,34 @@ class scan_args(object):
                          'mit_sot_in_slices')):
                 getattr(res, attr).extend(getattr(other, attr))
         return res
+
+
+def forced_replace(out, x, y):
+    """
+    :param out: Theano Variable
+    :param x: Theano Variable
+    :param y: Theano Variable
+
+    This function checks all internal values of the graph that computes the
+    variable ``out`` for occurances of values identical with ``x``. If such
+    occurances are encountered then they are replaced with variable ``y``.
+    For example:
+        out := sigmoid(wu)*(1-sigmoid(wu))
+        x := sigmoid(wu)
+        forced_replace(out, x, y) := y*(1-y)
+    """
+    if out is None:
+        return None
+
+    def traverse(graph, x):
+        if equal_computations([graph], [x]):
+            return [graph]
+        elif not graph.owner:
+            return []
+        else:
+            rval = []
+            for inp in graph.owner.inputs:
+                rval += traverse(inp, x)
+            return rval
+    to_replace = traverse(out, x)
+    return clone(out, replace=dict((v, y) for v in to_replace))