Fix gradient of split when there are disconnected outputs

theano/tensor/basic.py

@@ -3225,8 +3225,23 @@ class Split(Op):
 
     def grad(self, inputs, g_outputs):
         """Join the gradients along the axis that was used to split x."""
-        _, axis, n = inputs
-        return [join(axis, *g_outputs),
+        x, axis, n = inputs
+        outputs = self(*inputs, **dict(return_list=True))
+        # If all the output gradients are disconnected, then so are the inputs
+        if python_all([isinstance(g.type, DisconnectedType)
+                       for g in g_outputs]):
+            return [DisconnectedType()(),
+                    grad_undefined(self, 1, axis),
+                    grad_undefined(self, 2, n)]
+        # Else, we have to make them zeros before joining them
+        new_g_outputs = []
+        for o, g in zip(outputs, g_outputs):
+            if isinstance(g.type, DisconnectedType):
+                new_g_outputs.append(o.zeros_like())
+            else:
+                new_g_outputs.append(g)
+
+        return [join(axis, *new_g_outputs),
                 grad_undefined(self, 1, axis),
                 grad_undefined(self, 2, n)]
 

theano/tensor/tests/test_basic.py

@@ -44,7 +44,7 @@ from theano.tensor import (_shared, wvector, bvector, autocast_float_as,
         dtensor3, SpecifyShape, Mean,
         itensor3, Tile, switch, Diagonal, Diag,
         nonzero, flatnonzero, nonzero_values,
-        stacklists, DimShuffle)
+        stacklists, DimShuffle, hessian)
 
 from theano.tests import unittest_tools as utt
 
@@ -3067,6 +3067,14 @@ class T_Join_and_Split(unittest.TestCase):
         assert len([n for n in topo if isinstance(n, self.join_op)]) == 0
         assert f.maker.fgraph.outputs[0].dtype == 'int64'
 
+    def test_stack_hessian(self):
+        # Test the gradient of stack when used in hessian, see gh-1589
+        a = tensor.dvector('a')
+        b = tensor.dvector('b')
+        A = stack([a, b])
+        B = A.T.dot(A)
+        hessian(B.sum(), [a, b])
+
     def test_join_concatenate_one_element(self):
         ''' Fast test of concatenate as this is an alias for join.
         also test that we remove the Join op if there is only 1 input'''