Cache Scan.connection_pattern(). Hopefully, it will speed up theano.grad.

theano/scan_module/scan_op.py

@@ -1285,6 +1285,11 @@ class Scan(PureOp):
         return ipos + opos
 
     def connection_pattern(self, node):
+        # We cache this, as grad call connection_pattern, and it call
+        # grad in its turn. I was a case where theano.grad() took 4h
+        # that had many scan one inside each others.
+        if hasattr(node.tag, 'connection_pattern'):
+            return node.tag.connection_pattern
         # The gradient wrt to n_steps is disconnected
         connection_pattern = [[False for output in node.outputs]]
         connection_pattern += [[False for output in node.outputs]
@@ -1391,6 +1396,8 @@ class Scan(PureOp):
                         for k in xrange(len(connection_pattern)):
                             if connection_pattern[k][jidx]:
                                 connection_pattern[k][iidx] = True
+
+        node.tag.connection_pattern = connection_pattern
         return connection_pattern
 
     ### GRAD FUNCTION