// the shape inference is complete.
  BackEdgeHelper back_edge;
  TF_RETURN_IF_ERROR(back_edge.Remove(graph));
  TF_RETURN_IF_ERROR(PropagateShapes(graph, arg_shapes,
                                     back_edge.RemovedEdges(), &shape_refiner));
  TF_RETURN_IF_ERROR(back_edge.Replace());

  // Currently information does not flow "backward" from consumers to producers