AddCtrlEdge(scope, increment_op, group_deps);
  AddCtrlEdge(scope, weights_0_update_op, increment_op);
  AddCtrlEdge(scope, weights_1_update_op, increment_op);

  AddCtrlEdge(scope, some_ctrl_input, weights_0_update_op);
  AddCtrlEdge(scope, some_ctrl_input, weights_1_update_op);

  AddCtrlEdge(scope, matmul_0, group_deps);
  AddCtrlEdge(scope, matmul_1, group_deps);

          return false;
        }

        return TryToContractEdge(from, to);
      }).status());

  // Phase 1: apply a heuristic to ensure that we don't mess up clustering due
  // to "group_deps".  After this phase most edges should have been contracted.

  VLOG(4) << "Running phase 1";
  TF_RETURN_IF_ERROR(
      ForEachEdgeInPostOrder([&](Cluster* from,