refine backward

paddle/framework/backward.cc

@@ -124,6 +124,9 @@ static std::unique_ptr<OperatorBase> BackwardRecursive(
     std::list<Pos> insert_position;
     for (auto& dup_output_op : dup_output_ops) {
       const std::string& name = dup_output_op.first;
+      // duplicate @Empty@ don't need to be added
+      if (name == kEmptyVarName) continue;
+
       auto& dup_op = dup_output_op.second;
       // no duplicate output
       if (dup_op.size() == 1) continue;
@@ -209,7 +212,7 @@ std::unique_ptr<OperatorBase> Backward(
     const OperatorBase& forwardOp,
     const std::unordered_set<std::string>& no_grad_vars) {
   std::unordered_set<std::string> no_grad_names;
-  no_grad_names.reserve(no_grad_vars.size());
+  no_grad_names.reserve(no_grad_vars.size() + 1);
 
   no_grad_names.insert(std::string(kEmptyVarName) + kGradVarSuffix);
 

paddle/operators/net_op.cc

@@ -31,10 +31,13 @@ void NetOp::CompleteAddOp(bool calc) {
   for (auto& op : ops_) {
     for (auto& ipt : op->Inputs()) {
       for (auto& var_name : ipt.second) {
-        if (!Contains(output_set, var_name)) {  // Not other op's output
-          input_set.insert(var_name);
-        } else {
+        // If input variable has been in output set, then it will be
+        // added into intermediate_outputs_. Otherwise, it will be
+        // added into input set.
+        if (Contains(output_set, var_name)) {
           intermediate_outputs_.insert(var_name);
+        } else {
+          input_set.insert(var_name);
         }
       }
     }