}

    // Update g->name_map with the name_map from the scope, which will contain
    // the new gradient ops.
    for (int i = first_new_node_id; i < g->graph.num_node_ids(); ++i) {
      Node* n = g->graph.FindNodeId(i);
      if (n == nullptr) continue;

      // Adding the gradients to the graph can alter the prefix to prevent
      // name collisions only if this prefix has not been provided explicitly

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