Test for the bug regarding grad of states with multiple taps.

theano/scan_module/tests/test_scan.py

@@ -2677,6 +2677,39 @@ class T_Scan(unittest.TestCase):
         assert numpy.allclose(f(vx, vA), vR)
 
 
+    def test_grad_multiple_taps_state(self):
+        # The test is based on the code provided by Timothy Lillicrap
+
+        def onestep(xdl,xprev, w):
+            xnew = tensor.tanh(tensor.dot(w,xprev))
+            return xnew
+        xinit = tensor.tensor3('xinit')
+        w = tensor.matrix('w')
+        (xseq, updates) = theano.scan(n_steps = 10,
+                                     fn = onestep,
+                                     outputs_info = [dict(initial = xinit, taps=[-4,-1])],
+                                        non_sequences = w)
+        loss = (xseq[-1]**2).sum()
+        cost_fn = theano.function([xinit, w],
+                                  loss,
+                                  no_default_updates = True,
+                                  allow_input_downcast = True)
+        gw, gx = tensor.grad(loss, [w, xinit])
+        grad_fn = theano.function([xinit, w], [gx,gw],
+                                 allow_input_downcast = True)
+        rng  = numpy.random.RandomState(utt.fetch_seed())
+        v_x  = numpy.array(rng.uniform(size=(5,2,3), low=-.5, high=.5),
+                           dtype=theano.config.floatX)
+        v_w = numpy.array(rng.uniform(size=(2,2)), dtype= theano.config.floatX)
+        analytic_grad = grad_fn(v_x, v_w)
+        num_grad = multiple_outputs_numeric_grad(cost_fn,
+                                                 [v_x, v_w])
+        max_err, max_err_pos = num_grad.max_err(analytic_grad)
+        if max_err > 1e-2:
+            raise Exception(theano.tensor.verify_grad.E_grad,
+                    (max_err, 1e-2, max_err_pos))
+
+
 def test_speed():
     #
     # This function prints out the speed of very simple recurrent