def METHOD_NAME(
    self,
    state_dict: Dict[str, Dict[str, Union[Dict[str, Tensor], str]]],
    *,
    warmup_with_run: bool = False,
) -> None:
    graph_dict = dict()
    for _, sub_state_dict in state_dict.items():
        cache_order = sub_state_dict["cache_order"]
        graph_dict[cache_order] = sub_state_dict
    if self._cache is None:
        self._cache = LRUCache(self._cache_size)
    for _, sub_state_dict in sorted(graph_dict.items()):
        cache_key = sub_state_dict["cache_key"]
        graph = self._cache.get(cache_key)
        assert graph is None
        graph = self._init_and_get_a_graph_in_cache(cache_key)
        with AvoidRecursiveCacheCall(graph):
            graph.METHOD_NAME(
                sub_state_dict, warmup_with_run=warmup_with_run
            )