std::vector<int64_t> targets;
  std::vector<Gradient*> used_in_grads;
  // We may end up with slightly fewer elements than we reserve, but grad.size()
  // should be a reasonably tight upper bound.
  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) {