}
    }
  });
  if (!s.ok()) {
    return s;
  }

  std::unordered_map<int64_t, int64_t> gradients_size;
  // TODO(apassos) multiple threads could be dequeuing from op_stack at the same
  // time, for better CPU backprop performance.
  VLOG(1) << "Initial stack:";
  if (VLOG_IS_ON(1)) {
    for (auto t : op_stack) {
      VLOG(1) << "  " << t;
    }
  }
  while (!op_stack.empty()) {