Add ability to merge apply nodes without inputs

theano/gof/opt.py

@@ -484,9 +484,11 @@ class MergeFeature(object):
         # signature -> variable (for constants)
         self.const_sig_inv = _metadict()
 
-        # For all variables
+        # For all Apply nodes
         # Set of distinct (not mergeable) nodes
         self.nodes_seen = set()
+        # Ordered set of distinct (not mergeable) nodes without any input
+        self.noinput_nodes = OrderedSet()
 
         # Each element of scheduled is a list of list of (out, new_out) pairs.
         # Each list of pairs represent the substitution needed to replace all
@@ -514,6 +516,10 @@ class MergeFeature(object):
             self.nodes_seen.discard(node)
             self.process_node(fgraph, node)
 
+        # Since we are in on_change_input, node should have inputs.
+        if not isinstance(node, string_types):
+            assert node.inputs
+
         if isinstance(new_r, graph.Constant):
             self.process_constant(fgraph, new_r)
 
@@ -526,6 +532,8 @@ class MergeFeature(object):
 
     def on_prune(self, fgraph, node, reason):
         self.nodes_seen.discard(node)
+        if not node.inputs:
+            self.noinput_nodes.discard(node)
         for c in node.inputs:
             if isinstance(c, graph.Constant) and (len(c.clients) <= 1):
                 # This was the last node using this constant
@@ -592,7 +600,10 @@ class MergeFeature(object):
 
                     merge_candidates.extend(assert_clients)
         else:
-            merge_candidates = []
+            # If two nodes have no input, but perform the same operation,
+            # they are not always constant-folded, so we want to merge them.
+            # In that case, the candidates are all the nodes without inputs.
+            merge_candidates = self.noinput_nodes
 
         replacement_candidates = []
         for candidate in merge_candidates:
@@ -672,6 +683,8 @@ class MergeFeature(object):
             self.scheduled.append(replacement_candidates)
         else:
             self.nodes_seen.add(node)
+            if not node.inputs:
+                self.noinput_nodes.add(node)
 
     def get_merged_assert_input(self, node, candidate):
         new_inputs = []