def serialized(self):
        to_ret = {}
        for group, requirements in self.items():
            to_ret[group] = [str(requirement) for requirement in requirements]
        return to_ret
def _acc_grads(g_sum, g_w, g):
  """Accumulate gradients in g, weighted by g_w."""
  return [g_sum_i + g_w * g_i for g_sum_i, g_i in zip(g_sum, g)]