add generic add operator

paddle/framework/backward.cc

@@ -141,9 +141,35 @@ static std::unique_ptr<OperatorBase> BackwardRecursive(
         net->ops_[op_offset]->Rename(name, dup_outputs.back());
       }
       // collect all the offset to append `add` op for each alias
-      insert_position.push_back(
-          {dup_op.back(), OpRegistry::CreateOp("add", {{"X", {dup_outputs}}},
-                                               {{"Out", {name}}}, {})});
+      //
+      // one variable is shared between multiple operators.
+      // insert add operator one by one, then add it to output
+      if (dup_outputs.size() == 2) {
+        insert_position.push_back(
+            {dup_op.back(),
+             OpRegistry::CreateOp(
+                 "add", {{"X", {dup_outputs[0]}}, {"Y", {dup_outputs[1]}}},
+                 {{"Out", {name}}}, {})});
+      } else {
+        for (size_t output_idx = 0; output_idx < dup_outputs.size() - 1;
+             ++output_idx) {
+          auto insert_add_x = dup_outputs[output_idx];
+          auto insert_add_y = dup_outputs[output_idx];
+          auto insert_add_out = name + "@SHARED@" + std::to_string(output_idx);
+          // first add op inserted
+          if (output_idx == dup_outputs.size() - 1) {
+            insert_add_out = name;
+          }
+          if (output_idx != 0) {
+            insert_add_y = name + "@SHARED@" + std::to_string(output_idx);
+          }
+          insert_position.push_back(
+              {dup_op.back(),
+               OpRegistry::CreateOp(
+                   "add", {{"X", {insert_add_x}}, {"Y", {insert_add_y}}},
+                   {{"Out", {insert_add_out}}}, {})});
+        }
+      }
     }
 
     // make sure the inserted `add` ops follow the BFS order.