  void Update(const int64 batch_index, const int64 cross_count,
              const OutType& cross) const {
    const int64 output_index = output_start_indices_[batch_index] + cross_count;

    auto indices_matrix = indices_out_->matrix<int64>();
    indices_matrix(output_index, 0) = batch_index;
    indices_matrix(output_index, 1) = cross_count;

    auto value_vec = values_out_->vec<OutType>();
    value_vec(output_index) = cross;
  }
  void Update(const int64 batch_index, const int64 cross_count,
              const OutType& cross) const {
    const int64 output_index = output_start_indices_[batch_index] + cross_count;

    auto indices_matrix = indices_out_->matrix<int64>();
    indices_matrix(output_index, 0) = batch_index;
    indices_matrix(output_index, 1) = cross_count;

    auto value_vec = values_out_->vec<OutType>();
    value_vec(output_index) = cross;
  }