void SGDUpdater::Save(bool save_aux, dmlc::Stream *fo) const {
  int saved = 0;
  for (const auto& it : model_) {
    if (it.second.Empty()) continue;
    int n = param_.V_dim;
        fo->Write(&it.first, sizeof(feaid_t));
    fo->Write(it.second.w, sizeof(real_t));
    if (it.second.V) {
      for (int i = 0; i < n;   i) {
        fo->Write(it.second.V[i], sizeof(real_t));
      }
    }
    if (save_aux) {
      fo->Write(&(it.second.z), sizeof(real_t));
      fo->Write(&(it.second.sqrt_g), sizeof(real_t));
    }
    saved    ;
  }
  LOG(INFO) << "saved " << saved << " kv pairs";
}