targets.reserve(grad.size());
  used_in_grads.reserve(grad.size());
  std::unordered_map<int64_t, TapeTensor> sources_that_are_targets;
  for (int grad_index = 0, end = grad.size(); grad_index < end; ++grad_index) {
    Gradient* grad_tensor = grad[grad_index];
    if (grad_tensor != nullptr) {
      int64_t tensor_id = vspace_.TensorId(grad_tensor);
      targets.push_back(tensor_id);