factored out the _is_zero logic

theano/gradient.py

@@ -929,14 +929,9 @@ def _populate_grad_dict(var_to_node_to_idx,
                         # it's not undefined or disconnected
                         # The only other valid thing it can be is 0
 
-                        no_constant_value = True
-                        try:
-                            constant_value = theano.get_constant_value(term)
-                            no_constant_value = False
-                        except TypeError:
-                            pass
-
-                        if no_constant_value:
+                        is_zero = _is_zero(term)
+                        assert is_zero in ['yes', 'no', 'maybe']:
+                        if is_zero == 'maybe':
                             msg = "%s.grad returned %s of type %s for input"
                             msg += " %d. This input's only connections to "
                             msg += "the cost through this op are via "
@@ -950,8 +945,7 @@ def _populate_grad_dict(var_to_node_to_idx,
                             msg = msg % (str(node.op), str(term),
                                     str(type(term)), i)
 
-                            raise ValueError(msg)
-                        if constant_value != 0:
+                        if is_zero == 'no':
                             msg = "%s.grad returned %s of type %s for input"
                             msg += " %d. Since this input is only connected "
                             msg += "to integer-valued outputs, it should "
@@ -959,7 +953,7 @@ def _populate_grad_dict(var_to_node_to_idx,
                             msg += "%s."
 
                             msg % (str(node.op), str(term), str(type(term)),
-                                    i, str(constant_value))
+                                    i, str(theano.get_constant_value(term)))
 
                             raise ValueError(msg)
 
@@ -1688,3 +1682,30 @@ def hessian(cost, wrt, consider_constant=None,
                  "script that generated the error)")
         hessians.append(hess)
     return format_as(using_list, using_tuple, hessians)
+
+def _is_zero(x):
+    """
+    Returns 'yes', 'no', or 'maybe' indicating whether x
+    is always 0.
+    'maybe' means that x is an expression that is complicated enough
+    that we can't tell that it simplifies to 0.
+    """
+    if not hasattr(x, 'type'):
+        return np.all(x == 0.)
+    if isinstance(term.type, NullType):
+        return 'no'
+    if isinstance(term.type, DisconnectedType):
+        return 'yes'
+
+    no_constant_value = True
+    try:
+        constant_value = theano.get_constant_value(term)
+        no_constant_value = False
+    except TypeError:
+        pass
+
+    if no_constant_value:
+        return 'maybe'
+
+    if constant_value != 0.:
+        return no