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# Source code for torch.distributed.optim.zero_redundancy_optimizer

    # Copyright (c) Facebook, Inc. and its affiliates. All rights reserved.
    #
    # This source code is licensed under the BSD license found in the
    # LICENSE file in the root directory of this source tree.

    import collections
    import copy
    import enum
    import inspect
    import io
    import logging
    from itertools import chain
    from typing import Any, Callable, Dict, List, Optional, Set, Type, Union

    import torch
    import torch.distributed as dist
    from torch.distributed.algorithms.join import Join, Joinable, JoinHook
    from torch.distributed.optim.utils import functional_optim_map
    from torch.optim import Optimizer

    logger = logging.getLogger(__name__)

    __all__ = ["ZeroRedundancyOptimizer"]

    # Credits:  classy_vision/generic/distributed_util.py
    def _recursive_copy_to_device(
        value: Any,
        non_blocking: bool,
        device: torch.device,
    ) -> Any:
        r"""
        Recursively searches lists, tuples, dicts and copies tensors to device if
        possible. Non-tensor values are passed as-is in the result.

        .. note:  These are all copies, so if there are two objects that reference
        the same object, then after this call, there will be two different objects
        referenced on the device.
        """
        if isinstance(value, torch.Tensor):
            return value.to(device, non_blocking=non_blocking)

        if isinstance(value, (list, tuple)):
            values = [
                _recursive_copy_to_device(val, non_blocking=non_blocking, device=device)
                for val in value
            ]
            return values if isinstance(value, list) else tuple(values)

        if isinstance(value, collections.abc.Mapping):
            return {
                key: _recursive_copy_to_device(
                    val, non_blocking=non_blocking, device=device
                )
                for key, val in value.items()
            }

        return value

    def _is_trainable(param: torch.Tensor) -> bool:
        r"""
        Returns if a parameter is trainable, where trainability is equivalent to
        requiring a gradient.
        """
        return param.requires_grad

    def _broadcast_object(
        obj: Any,
        src_rank: int,
        group: object = dist.group.WORLD,
        device: torch.device = torch.device("cpu"),
    ) -> Any:
        r"""
        Broadcasts an object to the given group, sending the object if called from
        the source rank and receiving the object otherwise.

        Arguments:
            obj: object to broadcast; only used if called on the source rank.
            src_rank (int): source rank.
            group (``ProcessGroup``, optional): group used for the broadcast
                (default: ``dist.group.WORLD``).
            device (``torch.device``, optional): device to send from or receive
                to (default: ``torch.device("cpu")``).

        Returns:
            The broadcasted object.
        """
        if dist.get_rank() == src_rank:
            # Send the object
            buffer = io.BytesIO()
            torch.save(obj, buffer)
            data = bytearray(buffer.getbuffer())
            length_tensor = torch.LongTensor([len(data)]).to(device)
            data_send_tensor = torch.ByteTensor(data).to(device)
            dist.broadcast(length_tensor, src=src_rank, group=group, async_op=False)
            dist.broadcast(data_send_tensor, src=src_rank, group=group, async_op=False)
        else:
            # Receive the object
            length_tensor = torch.LongTensor([0]).to(device)
            dist.broadcast(length_tensor, src=src_rank, group=group, async_op=False)
            data_recv_tensor = torch.empty(
                [int(length_tensor.item())], dtype=torch.uint8, device=device
            )
            dist.broadcast(data_recv_tensor, src=src_rank, group=group, async_op=False)
            buffer = io.BytesIO(data_recv_tensor.cpu().numpy())
            obj = torch.load(buffer, map_location=device)
        return obj

    class _ZeROJoinHook(JoinHook):
        def __init__(self, zero):
            assert isinstance(zero, ZeroRedundancyOptimizer), (
                "ZeRO join hook requires passing in a ZeroRedundancyOptimizer "
                "instance as the state"
            )
            self.zero = zero
            super().__init__()

        def main_hook(self):
            """
            Performs an optimizer step, which updates the joined process's shard of
            the parameters and broadcasts those parameters.
            """
            self.zero.step()

    class _DDPBucketAssignment:
        r"""
        This represents a :class:`DistributedDataParallel` bucket assignment,
        meaning a (possibly non-strict) subset of the parameters corresponding to
        a DDP bucket assigned to a rank to update.

        Attributes:
            bucket_index (int): index of the bucket determined by the DDP gradient
                bucket all-reduce order.
            parameters (List[torch.Tensor]): model parameters in the bucket
                assigned to this rank.
            offset (int): offset into the :class:`GradBucket` 's :meth:`parameters`
                giving the index of the first element in the passed-in
                ``parameters``; this equivalently indexes into the
                :class:`GradBucket` 's :meth:`gradients`.
            device (torch.device): device on which the parameters are stored.
            tensor (torch.Tensor): flattened tensor giving the data of the
                parameter subset assigned to the rank.
        """

        def __init__(
            self,
            bucket_index: int,
            parameters: List[torch.Tensor],
            offset: int,
        ):
            self.bucket_index = bucket_index
            self.parameters = parameters
            self.offset = offset
            if len(self.parameters) == 0:
                raise ValueError("Empty bucket assignment")
            # DDP guarantees all parameters in the bucket have the same device
            self.device: torch.device = self.parameters[0].device
            self.tensor: Optional[torch.Tensor] = None

    class _OverlapStatus(enum.IntEnum):
        r"""
        This defines the three possible statuses that
        :class:`ZeroRedundancyOptimizer` can be in when overlapping with
        :class:`DistributedDataParallel`.

            ``UNINITIALIZED``: The ZeRO instance is effectively uninitialized and
                is waiting for DDP to finalize its bucketing.
            ``DDP_HAS_REBUILT_BUCKETS``: DDP has rebuilt its buckets, meaning that
                its bucketing is finalized. The ZeRO instance can now collect the
                necessary information about the DDP bucketing.
            ``INITIALIZED``: The ZeRO instance is fully initialized and can now
                optimize parameters.
        """
        UNINITIALIZED = 0
        DDP_HAS_REBUILT_BUCKETS = 1
        INITIALIZED = 2

    class _OverlapInfo:
        r"""
        This contains the information needed by :class:`ZeroRedundancyOptimizer`
        to overlap with :class:`DistributedDataParallel`.

        Arguments:
            world_size (int): world size of the process group being used.

        Attributes:
            shard_buckets (bool): if ``True``, then the assignment of each
                :class:`DistributedDataParallel` bucket is partitioned across
                possibly multiple :class:`ZeroRedundancyOptimizer` instances (i.e.
                across possibly multiple ranks) to approximate uniformity following
                a threshold given by the total parameter size divided by the world
                size; if ``False``, then each bucket is wholly assigned to a single
                :class:`ZeroRedundancyOptimizer` instance (i.e. to a single rank);
                this should be set to the value passed into the hook constructor.
            status (_OverlapStatus): current status; see :class:`_OverlapStatus`
                for more information.
            params_per_bucket (List[List[torch.Tensor]]): ``params_per_bucket[i]``
                gives the model parameters in the ``i``th bucket.
            params_per_rank (List[List[torch.Tensor]]): ``params_per_rank[i]``
                gives the model parameters assigned to the ``i``th rank, where the
                parameters are grouped by increasing bucket indices.
            offsets (Dict[int, int]): maps from bucket index to the offset in
                ``self.params_per_rank[rank]`` giving the index of the first
                parameter in that bucket, where ``rank`` is this process's own
                rank; the keys of this :class:`dict` are the bucket indices
                assigned to this rank.
            num_bucket_assignments (int): total number of bucket assignments across
                all ranks; this is equal to the number of
                :class:`DistributedDataParallel` gradient buckets if
                ``shard_buckets=False`` and possibly greater otherwise.
            total_size (int, optional): total size of all buckets (i.e. sum of
                ``param.numel()`` for all ``param`` across all buckets) if
                ``shard_buckets=True``; otherwise, ``None``.
            broadcast_handles (List[Work]): :class:`list` of async work handles for
                the parameter broadcasts.
            bucket_index_to_future (Dict[int, torch.futures.Future]):
                :class:`dict` mapping bucket index to the corresponding all-reduce
                future.
            bucket_index_to_bucket (Dict[int, dist.GradBucket]): :class:`dict`
                mapping bucket index to the corresponding bucket.
            bucket_indices_seen (List[int]): :class:`list` of the bucket indices
                seen on this iteration.
        """

        def __init__(self, world_size) -> None:
            self.status: _OverlapStatus = _OverlapStatus.UNINITIALIZED
            self.shard_buckets: bool = False

            # Modified per bucket reconstruction
            self.params_per_bucket: List[List[torch.Tensor]] = []
            self.params_per_rank: List[List[torch.Tensor]] = [[] for _ in range(world_size)]
            self.offsets: Dict[int, int] = {}
            # Group Ranks
            self.assigned_ranks_per_bucket: List[Set[int]] = []
            self.num_bucket_assignments: int = 0
            self.total_size: Optional[int] = None

            # Modified per iteration
            self.broadcast_handles: List[Any] = []
            self.bucket_indices_seen: List[int] = []
            # Used by `hook_with_zero_step()`
            self.bucket_index_to_future: Dict[int, torch.futures.Future] = {}
            self.bucket_index_to_bucket: Dict[int, dist.GradBucket] = {}

        def wait_for_broadcasts(self) -> None:
            r"""
            Waits for all parameter broadcasts. This should be called once all
            broadcasts have been scheduled, meaning ``self.broadcast_handles`` is
            filled. This clears ``self.broadcast_handles`` in preparation for the
            next iteration.
            """
            assert (
                len(self.broadcast_handles) == self.num_bucket_assignments
            ), f"Missing at least one broadcast handle on rank {dist.get_rank()}"
            _ = [x.wait() for x in self.broadcast_handles]
            self.broadcast_handles.clear()

        def clear_per_iter_info(self) -> None:
            r"""
            Clears the data structures that are modified per-iteration. This should
            be called at the end of an iteration.
            """
            self.bucket_indices_seen.clear()
            self.bucket_index_to_future.clear()
            self.bucket_index_to_bucket.clear()

    class ZeroRedundancyOptimizer(Optimizer, Joinable):
        r"""
        This class wraps an arbitrary :class:`optim.Optimizer
        <torch.optim.Optimizer>` and shards its states across ranks in the group as
        described by ZeRO_. The local optimizer instance in each rank is only
        responsible for updating approximately ``1 / world_size`` parameters and
        hence only needs to keep ``1 / world_size`` optimizer states. After
        parameters are updated locally, each rank will broadcast its parameters to
        all other peers to keep all model replicas in the same state.
        ``ZeroRedundancyOptimizer`` can be used in conjunction with
        :class:`torch.nn.parallel.DistributedDataParallel` to reduce per-rank peak
        memory consumption.

        ``ZeroRedundancyOptimizer`` uses a sorted-greedy algorithm to pack a number
        of parameters at each rank. Each parameter belongs to a single rank and is
        not divided among ranks. The partition is arbitrary and might not match the
        the parameter registration or usage order.

        Arguments:
            params (``Iterable``): an ``Iterable`` of :class:`torch.Tensor` s
                or :class:`dict` s giving all parameters, which will be sharded
                across ranks.

        Keyword Args:
            optimizer_class (:class:`torch.nn.Optimizer`): the class of the local
                optimizer.
            process_group (``ProcessGroup``, optional): ``torch.distributed``
                ``ProcessGroup`` (default: ``dist.group.WORLD`` initialized by
                :meth:`torch.distributed.init_process_group`).
            parameters_as_bucket_view (bool, optional): if ``True``, parameters are
                packed into buckets to speed up communication, and ``param.data``
                fields point to bucket views at different offsets; if ``False``,
                each individual parameter is communicated separately, and each
                ``params.data`` stays intact (default: ``False``).
            overlap_with_ddp (bool, optional): if ``True``, :meth:`step` is
                overlapped with :class:`DistributedDataParallel` 's gradient
                synchronization; this requires (1) either a functional optimizer
                for the ``optimizer_class`` argument or one with a functional
                equivalent and (2) registering a DDP communication hook
                constructed from one of the functions in ``ddp_zero_hook.py``;
                parameters are packed into buckets matching those in
                :class:`DistributedDataParallel`, meaning that the
                ``parameters_as_bucket_view`` argument is ignored.
                If ``False``, :meth:`step` runs disjointly after the backward pass
                (per normal).
                (default: ``False``)
            **defaults: any trailing arguments, which are forwarded to the local
                optimizer.

        Example::

            >>> # xdoctest: +SKIP
            >>> import torch.nn as nn
            >>> from torch.distributed.optim import ZeroRedundancyOptimizer
            >>> from torch.nn.parallel import DistributedDataParallel as DDP
            >>> model = nn.Sequential(*[nn.Linear(2000, 2000).to(rank) for _ in range(20)])
            >>> ddp = DDP(model, device_ids=[rank])
            >>> opt = ZeroRedundancyOptimizer(
            >>>     ddp.parameters(),
            >>>     optimizer_class=torch.optim.Adam,
            >>>     lr=0.01
            >>> )
            >>> ddp(inputs).sum().backward()
            >>> opt.step()

        .. warning::
            Currently, ``ZeroRedundancyOptimizer`` requires that all of the
            passed-in parameters are the same dense type.

        .. warning::
            If you pass ``overlap_with_ddp=True``, be wary of the following: Given
            the way that overlapping :class:`DistributedDataParallel` with
            :class:`ZeroRedundancyOptimizer` is currently implemented, the first
            two or three training iterations do not perform parameter updates in
            the optimizer step, depending on if ``static_graph=False`` or
            ``static_graph=True``, respectively. This is because it needs
            information about the gradient bucketing strategy used by
            :class:`DistributedDataParallel`, which is not finalized until the
            second forward pass if ``static_graph=False`` or until the third
            forward pass if ``static_graph=True``. To adjust for this, one option
            is to prepend dummy inputs.

        .. warning:: ZeroRedundancyOptimizer is experimental and subject to change.

        .. _ZeRO: https://arxiv.org/abs/1910.02054

        """

        def __init__(
            self,
            params,
            optimizer_class: Type[Optimizer],
            process_group: Optional[Any] = None,
            parameters_as_bucket_view: bool = False,
            overlap_with_ddp: bool = False,
            **defaults: Any,
        ):
            # Perform type and assumption checks on the input parameters
            params = self._verify_and_init_params(params)
            self._verify_same_dense_param_type()

            # NOTE: The parent constructor uses `add_param_group()` which is
            # partially overloaded in ZeroRedundancyOptimizer, so we use the
            # `initialized` flag to dissociate the behaviour of `add_param_group()`
            # between the parent and child.
            self.initialized = False

            Optimizer.__init__(self, params, defaults)
            Joinable.__init__(self)
            # Now, all parameters are held in both `self._all_params` and
            # `self.param_groups`

            # Internal data structures (`_cache` indicates lazily evaluated)
            self._param_to_rank_cache: Dict[torch.Tensor, int] = {}
            self._param_to_index_cache: Dict[torch.Tensor, int] = {}
            self._partition_parameters_cache: List[List[Dict]] = []
            self._index_to_param_cache: List[torch.Tensor] = []
            self._device_to_params_per_rank_cache: Dict[
                torch.device, List[List[torch.Tensor]]
            ] = {}
            self._bucket_assignments_per_rank_cache: List[
                Dict[int, _DDPBucketAssignment]
            ] = []
            self._is_trainable_mask = self._get_is_trainable_mask()

            # Default device for collective communication and buckets
            self._default_device = self._all_params[0].device

            self.process_group = (
                process_group if process_group is not None else dist.group.WORLD
            )
            self.world_size: int = dist.get_world_size(self.process_group)
            self.rank: int = dist.get_rank(self.process_group)
            self.global_rank: int = dist.distributed_c10d.get_global_rank(
                self.process_group, self.rank
            )

            self._overlap_with_ddp: bool = overlap_with_ddp
            self._optim_defaults = defaults
            self._optim_constructor = self._get_optimizer_constructor(optimizer_class)

            # If `overlap_with_ddp=True`, local optimizer initialization is delayed
            # to run time after the necessary information has been collected
            if not overlap_with_ddp:
                self._init_local_optimizer()
            else:
                self._overlap_info: _OverlapInfo = _OverlapInfo(self.world_size)
                if parameters_as_bucket_view:
                    logger.warning(
                        "`parameters_as_bucket_view=True` will be ignored since "
                        "`overlap_with_ddp=True`; instead, a different bucketing "
                        "strategy will be used"
                    )

            # `self._buckets` is used if `parameters_as_bucket_view=True`, in
            # which case parameter data is flattened into contiguous bucket tensors
            self.parameters_as_bucket_view = parameters_as_bucket_view
            self._buckets: List[List[torch.Tensor]] = []
            self._build_param_buckets()

            # Optional consolidated optimizer state, only populated if this rank
            # is the target in `consolidate_state_dict()`
            self._all_state_dicts: List[Dict[str, Any]] = []

            self.initialized = True

        def _clear_cache(self) -> None:
            r"""
            Clears the cached data structures giving partition information.
            """
            self._partition_parameters_cache.clear()
            self._param_to_rank_cache.clear()
            self._index_to_param_cache.clear()
            self._param_to_index_cache.clear()
            self._device_to_params_per_rank_cache.clear()
            self._bucket_assignments_per_rank_cache.clear()

        def add_param_group(self, param_group: dict) -> None:
            r"""
            Add a parameter group to the :class:`Optimizer` 's ``param_groups``.

            This can be useful when fine tuning a pre-trained network, as frozen
            layers can be made trainable and added to the :class:`Optimizer` as
            training progresses.

            Arguments:
                param_group (dict): specifies the parameters to be optimized and
                    group-specific optimization options.

            .. warning:: This method handles updating the shards on all partitions
                but needs to be called on all ranks. Calling this on a subset of
                the ranks will cause the training to hang because communication
                primitives are called depending on the managed parameters and
                expect all the ranks to participate on the same set of parameters.
            """
            if self.initialized and self._overlap_with_ddp:
                raise RuntimeError(
                    "ZeroRedundancyOptimizer with `overlap_with_ddp=True` only "
                    "supports a single parameter group"
                )

            super().add_param_group(param_group)
            # NOTE: The rest of the method assumes that the call to the parent's
            # `add_param_group()` appends the new parameter group and preserves
            # the previous parameter-group ordering

            if self.initialized:
                # Force a re-partitioning of the parameters
                self._clear_cache()
                param_groups = self._partition_parameters()[self.rank]
                # NOTE: All parameters in the old parameter groups should be
                # assigned to the same ranks so that the local optimizers do not
                # need to be reinitialized

                # Add the parameters assigned to this rank from the new parameter
                # group to the local optimizer, if any
                if len(param_groups) == len(self.optim.param_groups) + 1:
                    self.optim.add_param_group(param_groups[-1])

                # Update the bucketing strategy accordingly
                if self.parameters_as_bucket_view:
                    self._build_param_buckets()

        def consolidate_state_dict(self, to: int = 0) -> None:
            r"""
            Consolidate a list of ``state_dict`` s (one per rank) on the target
            rank.

            Arguments:
                to (int): the rank that receives the optimizer states (default: 0).

            Raises:
                RuntimeError: if ``overlap_with_ddp=True`` and this method is
                    called before this :class:`ZeroRedundancyOptimizer` instance
                    has been fully initialized, which happens once
                    :class:`DistributedDataParallel` gradient buckets have been
                    rebuilt.

            .. warning:: This needs to be called on all ranks.
            """
            self._check_overlap_initialized()

            # Sync the exposed `param_groups` attributes to the local optimizer in
            # case they have been updated
            self._sync_param_groups(self.param_groups, self.optim.param_groups)

            # Pull the sharded state from all ranks and store them in rank order
            empty_messenger = torch.tensor(
                [0], dtype=torch.uint8, device=self._default_device
            )

            # NOTE: We wastefully use `broadcast()` (e.g. instead of `gather()`)
            # due to compatibility issues with NCCL backend; a possible follow-up
            # is to move all sharded state management to RPC RRef
            self._all_state_dicts = []
            for rank in range(self.world_size):
                global_rank = dist.distributed_c10d.get_global_rank(
                    self.process_group, rank
                )
                if self.rank == to:
                    # Consolidate all local `state_dict`s on this rank, storing on
                    # CPU to save GPU memory
                    if rank == self.rank:
                        # Directly append own optimizer state
                        self._all_state_dicts.append(
                            _recursive_copy_to_device(
                                self.optim.state_dict(),
                                non_blocking=True,
                                device=torch.device("cpu"),
                            )
                        )
                    else:
                        # Receive the optimizer state from the source rank
                        local_state_dict = _broadcast_object(
                            empty_messenger,
                            src_rank=global_rank,
                            group=self.process_group,
                            device=self._default_device,
                        )
                        self._all_state_dicts.append(
                            _recursive_copy_to_device(
                                local_state_dict,
                                non_blocking=True,
                                device=torch.device("cpu"),
                            )
                        )
                else:
                    if rank == self.rank:
                        # Send the optimizer state to the target rank
                        _ = _broadcast_object(
                            self.optim.state_dict(),
                            src_rank=self.global_rank,
                            group=self.process_group,
                            device=self._default_device,
                        )
                    elif rank != to:
                        # Discard the received object; `broadcast()` is used for
                        # compatibility reasons
                        _ = _broadcast_object(
                            empty_messenger,
                            src_rank=global_rank,
                            group=self.process_group,
                            device=self._default_device,
                        )

        def _verify_params_per_rank(
            self,
            params_per_rank: List[List[torch.Tensor]],
        ) -> None:
            r"""
            Verifies ``params_per_rank`` for :meth:`_partition_parameters`,
            checking that ``params_per_rank`` has length equal to the world size
            and that it does not contain any parameters not passed into the
            :class:`ZeroRedundancyOptimizer` constructor.

            The parameters in ``params_per_rank`` being a strict subset of those
            passed into the constructor is valid since some parameters may be
            frozen.

            Raises:
                ValueError: if ``params_per_rank`` does not have length equal to
                    the world size or if it contains a parameter that was not
                    passed into the :class:`ZeroRedundancyOptimizer` constructor.
            """
            if len(params_per_rank) != self.world_size:
                raise ValueError(
                    "`params_per_rank` must have length equal to the world size"
                )
            all_params_set = set(self._all_params)
            for params in params_per_rank:
                for param in params:
                    if param not in all_params_set:
                        raise ValueError(
                            "Passing a new parameter in `params_per_rank` that "
                            "was not passed into the ZeroRedundancyOptimizer "
                            "constructor"
                        )

        def _partition_param_group(
            self, param_group: Dict[str, Any], params_per_rank: List[List[torch.Tensor]]
        ) -> None:
            r"""
            Partitions the parameter group ``param_group`` according to
            ``params_per_rank`` by modifying ``self._partition_parameters_cache``.

            This method should only be used as a subroutine for
            :meth:`_partition_parameters`.

            Arguments:
                param_group (dict[str, Any]): a parameter group as normally defined
                    in an optimizer state.
                params_per_rank (list[list[torch.Tensor]]): a :class:`list` of
                    length world size containing :class:`list` s of parameters to
                    assign to each rank.
            """
            for rank, params in enumerate(params_per_rank):
                rank_param_group = copy.copy(param_group)
                rank_param_group["params"] = params
                self._partition_parameters_cache[rank].append(rank_param_group)

        def _partition_parameters(
            self,
            params_per_rank: Optional[List[List[torch.Tensor]]] = None,
        ) -> List[List[Dict]]:
            r"""
            Partitions parameters across distributed data parallel ranks.

            Arguments:
                params_per_rank (list[list[torch.Tensor]], optional): a
                    :class:`list` of length world size containing :class:`list` s
                    of parameters to assign to each rank; this provides a way to
                    specify a partition manually.
                    If ``None``, the parameters are partitioned according to an
                    internal algorithm.
                    (default: ``None``)

            Returns:
                A :class:`list` where each element of the list contains the
                ``param_groups`` for a rank (which itself is a :class:`list` of
                :class:`dict`); element 0 corresponds to rank 0, etc.; each rank
                stores the ``param_groups`` for all ranks for the collective
                communication in :meth:`step`.

            Raises:
                ValueError: see :meth:`_validate_params_per_rank`.
                RuntimeError: if ``params_per_rank`` is not ``None`` and this
                    :class:`ZeroRedundancyOptimizer` instance is using more than
                    one parameter group.
            """
            if params_per_rank is None:
                # Partition the parameters optimizing for uniformity
                if len(self._partition_parameters_cache) == 0:
                    self._partition_parameters_cache = [[] for _ in range(self.world_size)]
                    sizes = [0] * self.world_size
                    for param_group in self.param_groups:
                        param_group_params_per_rank: List[List] = [
                            [] for _ in range(self.world_size)
                        ]
                        # Sort the parameters by size (largest first)
                        params_sorted = sorted(
                            param_group["params"], key=lambda t: t.numel(), reverse=True
                        )
                        for param in params_sorted:
                            # Greedily add the parameter to rank with smallest size so far
                            rank = self._get_min_index(sizes)
                            param_group_params_per_rank[rank].append(param)
                            sizes[rank] += param.numel()
                        # Apply the constructed partition of the parameter group
                        self._partition_param_group(
                            param_group, param_group_params_per_rank
                        )

                return self._partition_parameters_cache

            # Partition the parameters according to `params_per_rank`
            assert len(self._partition_parameters_cache) == 0, (
                "Specifying `params_per_rank` should only be done when the "
                "parameters have not been partitioned yet"
            )
            if len(self.param_groups) != 1:
                raise RuntimeError(
                    "Specifying `params_per_rank` only supports a single parameter group"
                )
            self._verify_params_per_rank(params_per_rank)
            self._partition_parameters_cache = [[] for _ in range(self.world_size)]

            # Apply the passed-in partition of the parameter group
            param_group = self.param_groups[0]
            self._partition_param_group(param_group, params_per_rank)

            return self._partition_parameters_cache

        @property
        def _param_to_rank(self) -> Dict[torch.Tensor, int]:
            r"""
            :class:`dict` mapping parameters to their assigned data parallel rank
            in the partition.
            """
            if len(self._param_to_rank_cache) == 0:
                for rank, param_groups in enumerate(self._partition_parameters()):
                    for param_group in param_groups:
                        for param in param_group["params"]:
                            self._param_to_rank_cache[param] = rank
            return self._param_to_rank_cache

        @property
        def _param_to_index(self) -> Dict[torch.Tensor, int]:
            r"""
            :class:`dict` mapping parameters to their indices in the global
            optimizer state.

            NOTE: This assumes that the global optimizer state's indexing (in
            ``state_dict``) follows a linear ordering over the parameter groups.
            """
            if len(self._param_to_index_cache) == 0:
                self._param_to_index_cache = {
                    p: i
                    for i, p in enumerate(chain(*(g["params"] for g in self.param_groups)))
                }
            return self._param_to_index_cache

        @property
        def _index_to_param(self) -> List[torch.Tensor]:
            r"""
            List mapping parameter indices in the global optimizer scheme to the
            actual params.
            """
            if len(self._index_to_param_cache) == 0:
                self._index_to_param_cache = list(
                    chain(*(g["params"] for g in self.param_groups))
                )
            return self._index_to_param_cache

        def _broadcast_params_from_rank(self, rank: int):
            r"""
            Broadcasts the shard of parameters from a given rank to all other
            ranks asynchronously.

            Arguments:
                rank (int): the source rank.

            Returns:
                A :class:`list` of async work handles for the ``broadcast()`` s
                performed to synchronize the parameters.
            """
            assert not self._overlap_with_ddp, (
                "`_broadcast_params_from_rank()` should not be used if "
                "`overlap_with_ddp=True`; instead, the broadcasting should "
                "happen in the DDP communication hook"
            )
            handles = []
            if self.parameters_as_bucket_view:
                for dev_i_buckets in self._buckets:
                    bucket = dev_i_buckets[rank]
                    global_rank = dist.distributed_c10d.get_global_rank(
                        self.process_group, rank
                    )
                    handles.append(
                        dist.broadcast(
                            tensor=bucket,
                            src=global_rank,
                            group=self.process_group,
                            async_op=True,
                        )
                    )
            else:
                param_groups = self._partition_parameters()[rank]
                global_rank = dist.distributed_c10d.get_global_rank(
                    self.process_group, rank
                )
                for param_group in param_groups:
                    for param in param_group["params"]:
                        handles.append(
                            dist.broadcast(
                                tensor=param.data,
                                src=global_rank,
                                group=self.process_group,
                                async_op=True,
                            )
                        )
            return handles

        def _sync_params(self):
            r"""
            Syncs all parameter shards across the ranks.

            This rank sends its shard of the parameters to all other ranks and
            receives a shard from each other rank. This is done using
            ``broadcast()``. Parameters are sent bucket-by-bucket if
            ``parameters_as_bucket_view=True``and sent parameter-by-parameter
            otherwise.
            """
            handles = []
            for rank in range(self.world_size):
                handles.extend(self._broadcast_params_from_rank(rank))
            _ = [x.wait() for x in handles]

        @property
        def _device_to_params_per_rank(
            self,
        ) -> Dict[torch.device, List[List[torch.Tensor]]]:
            r"""
            :class:`dict` mapping each device to a :class:`list` of the per-rank parameter
            lists filtered to only include the parameters stored on that device.
            Each per-rank parameter list gives the parameters assigned to that rank
            to update.

            This is used for constructing the parameter buckets if
            ``parameters_as_bucket_view=True``.

            Let ``dev_i`` denote the ``i``th device for this rank. Then:
            ``dev_0`` maps to a list containing:
                rank 0's assigned parameters stored on ``dev_0``,
                rank 1's assigned parameters stored on ``dev_0``,
                ...
            ``dev_1`` maps to a list containing:
                rank 0's assigned parameters stored on ``dev_1``,
                rank 1's assigned parameters stored on ``dev_1``,
                ...
            ...
            """
            assert self.parameters_as_bucket_view, (
                "`_device_to_params_per_rank` should only be used if "
                "`parameters_as_bucket_view=True`"
            )
            if len(self._device_to_params_per_rank_cache) == 0:
                for rank, param_groups in enumerate(self._partition_parameters()):
                    for param_group in param_groups:
                        for param in param_group["params"]:
                            device = param.device
                            if device not in self._device_to_params_per_rank_cache:
                                self._device_to_params_per_rank_cache[device] = [
                                    [] for _ in range(self.world_size)
                                ]
                            self._device_to_params_per_rank_cache[device][rank].append(
                                param
                            )
            return self._device_to_params_per_rank_cache

        def _get_min_index(
            self,
            values: List[int],
            disallowed_indices: Optional[Set[int]] = None,
        ) -> int:
            r"""
            Returns ``values.index(min(values))``, except only uses one pass. It
            also excludes any indices in ``disallowed_indices`` if provided.

            Arguments:
                values: (List[int]): :class:`list` of values.
                disallowed_indices (Optional[Set[int]]): indices that are
                    disallowed from being the returned min index.
            """
            min_index = -1
            min_value = float("inf")
            for i, value in enumerate(values):
                if disallowed_indices and i in disallowed_indices:
                    continue
                if value < min_value:
                    min_value = value
                    min_index = i
            assert min_index >= 0, "All indices are disallowed"
            return min_index

        def _assign_bucket_subset_to_rank(
            self,
            bucket_index: int,
            bucket_params: List[torch.Tensor],
            bucket_offset: int,
            assigned_rank: int,
            assigned_ranks_per_bucket: List[Set[int]],
        ) -> None:
            r"""
            Assigns the model parameters given by ``bucket_params``, representing a
            (possibly non-strict) subset of the parameters corresponding to a
            :class:`DistributedDataParallel` bucket, to the rank with the least
            size assigned so far and collects relevant information.

            Arguments:
                bucket_index (int): index of the :class:`DistributedDataParallel`
                    gradient bucket.
                bucket_params (List[torch.Tensor]): subset of the parameters
                    corresponding to the bucket to assign.
                bucket_offset (int): offset giving the index of the first element
                    in ``bucket_params`` in the bucket's full parameter list.
                assigned_rank (int): group rank to assign to.
                assigned_ranks_per_bucket (List[Set[int]]): :class:`set` of group ranks
                    assigned to each bucket.
            """
            overlap_info = self._overlap_info
            if len(bucket_params) == 0:
                raise ValueError("Empty bucket assignment")
            params_per_rank = overlap_info.params_per_rank
            offsets = overlap_info.offsets

            self._bucket_assignments_per_rank_cache[assigned_rank][
                bucket_index
            ] = _DDPBucketAssignment(bucket_index, bucket_params, bucket_offset)
            if self.global_rank == assigned_rank:
                offsets[bucket_index] = len(params_per_rank[assigned_rank])
            params_per_rank[assigned_rank].extend(bucket_params)
            assigned_ranks_per_bucket[bucket_index].add(assigned_rank)
            self._overlap_info.num_bucket_assignments += 1

        @property
        def _bucket_assignments_per_rank(self) -> List[Dict[int, _DDPBucketAssignment]]:
            r"""
            :class:`list` of length world size consisting of :class:`dict` s
            mapping bucket indices to :class:`_DDPBucketAssignment` s for each
            rank.
            """
            assert self._overlap_with_ddp, (
                "`_bucket_assignments_per_rank` only be used if `overlap_with_ddp=True`"
            )
            if len(self._bucket_assignments_per_rank_cache) > 0:
                return self._bucket_assignments_per_rank_cache

            overlap_info = self._overlap_info
            assert overlap_info.status == _OverlapStatus.INITIALIZED

            self._bucket_assignments_per_rank_cache = [{} for _ in range(self.world_size)]
            params_per_bucket = overlap_info.params_per_bucket

            if overlap_info.shard_buckets:
                # Define the assignment threshold to approximate uniformity
                assert overlap_info.total_size is not None, "`total_size` was not computed"
                threshold = overlap_info.total_size / self.world_size  # type: ignore[operator]
                size_per_rank = [0 for _ in range(self.world_size)]

            num_buckets = len(params_per_bucket)
            overlap_info.assigned_ranks_per_bucket = [set() for _ in range(num_buckets)]
            assigned_ranks_per_bucket = overlap_info.assigned_ranks_per_bucket
            if not overlap_info.shard_buckets:
                # Assign each DDP bucket entirely to a single rank
                for bucket_index, bucket_params in enumerate(params_per_bucket):
                    assert len(bucket_params) > 0, "Empty bucket"
                    assigned_rank = self._get_assigned_rank(bucket_index)
                    self._assign_bucket_subset_to_rank(
                        bucket_index,
                        bucket_params,
                        0,
                        assigned_rank,
                        assigned_ranks_per_bucket,
                    )
            else:
                # Assign each DDP bucket to possibly multiple ranks
                # Specifically, sort the DDP buckets by increasing size, and for
                # each bucket, iteratively assign the maximal unassigned subset
                # with size less than `threshold` to the rank with the least total
                # size so far -- each such assignment is represented by a
                # `_DDPBucketAssignment` instance and only contains parameters from
                # a single DDP bucket
                params_per_bucket_enum = sorted(
                    enumerate(params_per_bucket), key=lambda x: sum(p.numel() for p in x[1])
                )
                for bucket_index, bucket_params in params_per_bucket_enum:
                    assert len(bucket_params) > 0, "Empty bucket"
                    bucket_offset = 0
                    assignment_size = 0
                    for param_index, param in enumerate(bucket_params):
                        param_numel = param.numel()
                        if (
                            assignment_size + param_numel >= threshold
                            and param_index > bucket_offset
                        ):
                            assigned_rank = self._get_min_index(
                                size_per_rank, assigned_ranks_per_bucket[bucket_index]
                            )
                            # Include up to but not including the parameter that
                            # exceeded the threshold
                            self._assign_bucket_subset_to_rank(
                                bucket_index,
                                bucket_params[bucket_offset:param_index],
                                bucket_offset,
                                assigned_rank,
                                assigned_ranks_per_bucket,
                            )
                            size_per_rank[assigned_rank] += assignment_size
                            bucket_offset = param_index
                            assignment_size = 0
                        assignment_size += param_numel
                    # Assign the remainder of the bucket so that no assignment
                    # spans across two buckets
                    assigned_rank = self._get_min_index(
                        size_per_rank, assigned_ranks_per_bucket[bucket_index]
                    )
                    self._assign_bucket_subset_to_rank(
                        bucket_index,
                        bucket_params[bucket_offset:],
                        bucket_offset,
                        assigned_rank,
                        assigned_ranks_per_bucket,
                    )
                    size_per_rank[assigned_rank] += assignment_size

            return self._bucket_assignments_per_rank_cache

        def _local_step(
            self,
            gradients: Optional[List[Optional[torch.Tensor]]] = None,
            closure: Optional[Callable[[], float]] = None,
            **kwargs: Any,
        ) -> Optional[float]:
            r"""
            Performs a single optimizer step without syncing parameters across
            ranks.

            Arguments:
                gradients (list[Optional[torch.Tensor]], optional): a :class:`list`
                    of length equal to the number of parameters assigned to this
                    rank containing gradient tensors or ``None`` as its elements;
                    a ``None`` in the :class:`list` indicates that the
                    corresponding parameter should not be updated.
                    If the argument itself is ``None``, then all parameters are
                    updated, and the gradients are assumed to be already populated.
                    (default: ``None``)
                closure (Callable): a closure that re-evaluates the model and
                    returns the loss; optional for most optimizers and should be
                    ``None`` if ``gradients`` is not ``None``; (default: ``None``)
            Returns:
                Optional loss depending on the underlying local optimizer.

            .. warning::
                The argument ``gradients`` should only be specified (i.e. not
                ``None``) if ``overlap_with_ddp=True``, in which case
                :class:`ZeroRedundancyOptimizer` wraps a functional optimizer.
            """
            Join.notify_join_context(self)
            # Check if the model trainability has changed
            is_trainable_mask = self._get_is_trainable_mask()
            if is_trainable_mask != self._is_trainable_mask:
                if self._overlap_with_ddp:
                    raise RuntimeError(
                        "ZeroRedundancyOptimizer with `overlap_with_ddp=True` "
                        "does not support changing parameter trainability at run "
                        "time"
                    )
                logger.warning(
                    "ZeroRedundancyOptimizer detected that the trainable "
                    "parameters changed; rebuilding the parameter buckets if "
                    "enabled"
                )
                self._build_param_buckets()
                self._is_trainable_mask = is_trainable_mask

            # Sync the exposed `param_groups` attributes to the local optimizer in
            # case they have been updated
            self._sync_param_groups(self.param_groups, self.optim.param_groups)

            # Run the optimizer step on this shard only
            if gradients is None:
                loss = (
                    self.optim.step(**kwargs)
                    if closure is None
                    else self.optim.step(closure=closure, **kwargs)
                )
            else:
                assert self._overlap_with_ddp, (
                    "Specifying `gradients` should not "
                    "be used when `overlap_with_ddp=False`"
                )
                assert closure is None, (
                    "`closure` is not supported when using a local functional optimizer"
                )
                loss = self.optim.step(gradients=gradients)

            # Sync any updated attributes in the local optimizer to the exposed
            # `param_groups`
            self._sync_param_groups(self.optim.param_groups, self.param_groups)

            return loss

        def step(
            self,
            closure: Optional[Callable[[], float]] = None,
            **kwargs: Any,
        ) -> Optional[float]:
            r"""
            Performs a single optimizer step and syncs parameters across all ranks.

            Arguments:
                closure (Callable): a closure that re-evaluates the model and
                    returns the loss; optional for most optimizers.
            Returns:
                Optional loss depending on the underlying local optimizer.

            .. note: Any extra parameters are passed to the base optimizer as-is.
            """
            if self._overlap_with_ddp:
                logger.warning(
                    "`step()` should not be included in the training loop when "
                    "`overlap_with_ddp=True`"
                )
                return None

            # Perform the local optimizer step
            loss = self._local_step(closure=closure, **kwargs)

            # Sync all of the updated parameter shards across the ranks
            self._sync_params()

            return loss

        def join_hook(self, **kwargs):
            r"""
            Returns the ZeRO join hook, which enables training on uneven inputs by
            shadowing the collective communications in the optimizer step.

            Gradients must be properly set before this hook is called.

            Arguments:
                kwargs (dict): a :class:`dict` containing any keyword arguments
                    to modify the behavior of the join hook at run time; all
                    :class:`Joinable` instances sharing the same join context
                    manager are forwarded the same value for ``kwargs``.

            This hook does not support any keyword arguments; i.e. ``kwargs`` is
            unused.
            """
            return _ZeROJoinHook(self)

        @property
        def join_device(self) -> torch.device:
            return self._default_device

        @property
        def join_process_group(self) -> Any:
            return self.process_group

        def load_state_dict(self, state_dict: Dict[str, Any]) -> None:
            r"""
            Load the state pertaining to the given rank from the input
            ``state_dict``, updating the local optimizer as needed.

            Arguments:
                state_dict (dict): optimizer state; should be an object returned
                    from a call to :meth:`state_dict`.

            Raises:
                RuntimeError: if ``overlap_with_ddp=True`` and this method is
                    called before this :class:`ZeroRedundancyOptimizer` instance
                    has been fully initialized, which happens once
                    :class:`DistributedDataParallel` gradient buckets have been
                    rebuilt.
            """
            self._check_overlap_initialized()

            for index, value in state_dict["state"].items():
                param = self._index_to_param[index]
                if self._param_to_rank[param] != self.rank:
                    # Clear any state irrelevant to this rank
                    state_dict["state"][index] = None
                else:
                    # Load the parameter state to the local optimizer
                    self.optim.state[param] = _recursive_copy_to_device(
                        value, non_blocking=True, device=param.device
                    )
                    # Force zero-dimensional tensors (like Adam "step") on CPU
                    for state_name, state_value in self.optim.state[param].items():
                        if torch.is_tensor(state_value) and state_value.dim() == 0:
                            self.optim.state[param][state_name] = state_value.cpu()

            super().load_state_dict(state_dict)

            # Sync the input state with the exposed and local optimizer states
            self._sync_param_groups(state_dict["param_groups"], self.param_groups)
            self._sync_param_groups(self.param_groups, self.optim.param_groups)

        def state_dict(self) -> Dict[str, Any]:
            r"""
            Returns the last global optimizer state known to this rank.

            .. warning:
                If the state has not been consolidated to this rank, this raises a
                runtime error, and even if it has, the state may not be up-to-date,
                depending on when :meth:`consolidate_state_dict` was last called.

            Raises:
                RuntimeError: if ``overlap_with_ddp=True`` and this method is
                    called before this :class:`ZeroRedundancyOptimizer` instance
                    has been fully initialized, which happens once
                    :class:`DistributedDataParallel` gradient buckets have been
                    rebuilt; or if this method is called without a preceding call
                    to :meth:`consolidate_state_dict`.
            """
            self._check_overlap_initialized()

            if len(self._all_state_dicts) == 0:
                raise RuntimeError(
                    "Optimizer state has not been consolidated on this rank. "
                    f"Please call `consolidate_state_dict(to={self.rank})` on "
                    "all ranks beforehand if you meant to save the global state."
                )

            # Get the possibly-stale global optimizer state that uses global
            # parameter indexing
            state_dict = super().state_dict()

            # Update the global optimizer state with local state information,
            # factoring in the translation from local to global indexing
            for rank, local_state_dict in enumerate(self._all_state_dicts):
                local_param_groups = local_state_dict["param_groups"]
                global_param_groups = self._partition_parameters()[rank]
                assert len(local_param_groups) == len(
                    global_param_groups
                ), "Mismatch between number of local and global parameter groups"

                for local_param_group, global_param_group in zip(
                    local_param_groups, global_param_groups
                ):
                    # `local_param_group` stores local indices, while
                    # `global_param_group` stores the tensors directly
                    local_param_indices = local_param_group["params"]
                    global_params = global_param_group["params"]

                    assert len(local_param_indices) == len(
                        global_params
                    ), "Mismatch between number of local and global parameters in parameter group"
                    for local_param_index, global_param in zip(
                        local_param_indices, global_params
                    ):
                        # Update the global parameter state, if any
                        if local_param_index in local_state_dict["state"]:
                            global_param_index = self._param_to_index[global_param]
                            state_dict["state"][global_param_index] = local_state_dict[
                                "state"
                            ][local_param_index]

            # Sort the parameters in the state
            state_dict["state"] = dict(sorted(state_dict["state"].items()))
            return state_dict

        @staticmethod
        def _sync_param_groups(
            src_param_groups: List[Dict[Any, Any]],
            dst_param_groups: List[Dict[Any, Any]],
        ) -> None:
            r"""
            Syncs the attributes from the source parameter groups to the
            destination parameter groups.

            Example attributes include learning rate or scheduler attributes. The
            two parameter groups should have the same length (i.e. same number of
            parameter groups).

            Arguments:
                src_param_groups (list[dict]): parameter groups giving the
                    attribute settings to copy.
                dst_param_groups (list[dict]): parameter groups giving the
                    attribute settings to set.
            """
            assert len(src_param_groups) == len(
                dst_param_groups
            ), "Mismatch between number of source and destination parameter groups"
            for src_param_group, dst_param_group in zip(src_param_groups, dst_param_groups):
                # Sync all attributes except the parameters
                for attr in filter(lambda x: x != "params", src_param_group.keys()):
                    dst_param_group[attr] = src_param_group[attr]

        def _build_param_buckets(self) -> None:
            r"""
            Builds parameter buckets if ``parameters_as_bucket_view=True`` so
            that for each device that stores this rank's parameters, there is a
            bucket (represented as a tensor) containing all of the parameters on
            that device that are assigned to a given rank in the parameter update
            partition.

            This method is called in the constructor and any time parameter
            trainability is changed.

            .. warning::
                The current implementation assumes that all of the parameters in a
                bucket are of the same dense type when allocating the bucket's
                tensor.

            .. warning::
                If the model parameters are stored across more than one device,
                then the storage partitioning must be the same across all
                processes in order for parameter synchronization to work.
            """
            if not self.parameters_as_bucket_view or self._overlap_with_ddp:
                return

            # `self._buckets[i][j]` are the parameters stored on device i and
            # assigned to rank j
            num_devices = len(self._device_to_params_per_rank)
            self._buckets = [[] for _ in range(num_devices)]  # type: ignore[assignment]

            for dev_i, (device, params_per_rank) in enumerate(
                self._device_to_params_per_rank.items()
            ):
                for params in params_per_rank:
                    bucket_size = 0
                    dtype = None
                    trainable_params = []
                    for param in params:
                        if not _is_trainable(param):
                            # Clone in case the parameter was previously part of
                            # a bucket to avoid the data from being destroyed
                            param.data = param.data.detach().clone()
                        else:
                            bucket_size += param.numel()
                            trainable_params.append(param)
                        dtype = param.dtype  # assumes all same dtype

                    if bucket_size == 0:
                        # Create a dummy bucket if there are no parameters
                        bucket = torch.zeros(1, device=device)
                    else:
                        # Construct the bucket (assuming all dense and same dtype)
                        bucket = torch.empty(bucket_size, dtype=dtype, device=device)
                        offset = 0
                        for param in trainable_params:
                            offset_next = offset + param.numel()
                            bucket[offset:offset_next].copy_(param.data.flatten())
                            param.data = bucket[offset:offset_next].view_as(param.data)
                            offset = offset_next
                    self._buckets[dev_i].append(bucket)  # type: ignore[arg-type]

        def _build_ddp_param_buckets(self) -> None:
            r"""
            For each DDP bucket with parameters assigned to this rank, flattens the
            data of those parameters into a single tensor and saves the tensor to
            the ``tensor`` attribute in the corresponding
            :class:`_DDPBucketAssignment` instance stored in
            ``self._bucket_assignments_per_rank``.

            :class:`DistributedDataParallel` guarantees that the parameters
            corresponding to a gradient bucket have the same device and the same
            dtype.
            """
            for bucket_assignments in self._bucket_assignments_per_rank:
                for bucket_assignment in bucket_assignments.values():
                    params = bucket_assignment.parameters
                    bucket_size = 0
                    dtype = None
                    for param in params:
                        assert _is_trainable(param), (
                            "Model parameter "
                            "corresponding to a gradient in a DDP bucket should "
                            "require a gradient"
                        )
                        bucket_size += param.numel()
                        dtype = param.dtype  # assumes all same dtype
                    assert bucket_size > 0, "Empty bucket"

                    # Construct the bucket tensor (assuming all dense and same dtype)
                    tensor = torch.empty(
                        bucket_size, dtype=dtype, device=bucket_assignment.device
                    )
                    offset = 0
                    for param in params:
                        offset_next = offset + param.numel()
                        tensor[offset:offset_next].copy_(param.data.flatten())
                        param.data = tensor[offset:offset_next].view_as(param.data)
                        offset = offset_next
                    bucket_assignment.tensor = tensor

        def _verify_and_init_params(
            self,
            params: Any,
        ) -> Union[List[torch.Tensor], List[dict]]:
            r"""
            Verifies the type of ``params`` and initializes ``self._all_params``
            as a :class:`list` of all parameters if ``params`` is valid.

            Arguments:
                params (Any): Candidate parameter list or parameter groups to
                    verify.

            Raises:
                TypeError: ``params`` has an invalid type.
                ValueError: ``params`` is empty.

            Returns:
                The persistent form of ``params`` to be passed into the parent
                :class:`Optimizer` constructor -- i.e. returns ``params`` as a
                :class:`list` to ensure that it can be iterated over again.
            """
            if isinstance(params, torch.Tensor):
                raise TypeError(
                    "`params` argument should be an iterable of "
                    f"Tensors, but got {torch.typename(params)}"
                )
            try:
                all_params = list(params)
            except TypeError as e:
                raise TypeError(
                    "`params` argument should be an iterable of Tensors"
                    f" or dicts, but got {torch.typename(params)}"
                ) from e
            if len(all_params) == 0:
                raise ValueError("ZeroRedundancyOptimizer got an empty parameter list")
            all_tensors = True
            all_dicts = True
            for param in all_params:
                all_tensors &= isinstance(param, torch.Tensor)
                all_dicts &= isinstance(param, dict)
            if not all_tensors and not all_dicts:
                raise TypeError(
                    "`params` argument should be an iterable of Tensors or dicts"
                )
            # Ensure that `self._all_params` contains a list of all parameters
            if all_tensors:
                self._all_params = all_params
            elif all_dicts:
                self._all_params = []
                # `all_params` contains parameter groups (not parameters)
                for param_group in all_params:
                    if "params" not in param_group:
                        raise ValueError(
                            "Each parameter group passed-in via `params` must "
                            "have a 'params' key mapping to the parameters in "
                            "the group"
                        )
                    self._all_params.extend(param_group["params"])
            return all_params

        def _verify_same_dense_param_type(self) -> None:
            r"""
            Verifies that all parameters are of the same dense type.

            The method assumes that ``self._all_params`` has been initialized
            and is non-empty.

            Raises:
                ValueError: ``params`` contains sparse parameters or parameters
                of varying dense types.

            NOTE: This method can be removed once support for sparse parameters
            and varying parameter types is added.
            """
            typename = torch.typename(self._all_params[0])
            if self._all_params[0].is_sparse:
                raise ValueError(
                    "ZeroRedundancyOptimizer only supports using "
                    "the same dense type for all parameters but got "
                    f"{typename}"
                )
            for param in self._all_params[1:]:
                other_typename = torch.typename(param)
                if other_typename != typename:
                    raise ValueError(
                        "ZeroRedundancyOptimizer only supports "
                        "using the same dense type for all "
                        f"parameters but got both {typename} and "
                        f"{other_typename}"
                    )

        def _get_is_trainable_mask(self) -> List[bool]:
            r"""
            Returns a boolean mask indicating if each parameter is trainable
            (``requires_grad``) or not.
            """
            return list(map(_is_trainable, self._all_params))

        def _init_local_optimizer(self) -> None:
            r"""
            Initializes this rank's local optimizer, responsible for its subset of
            the parameters.

            The local optimizer is saved in ``self.optim``.
            """
            assert (
                self._optim_constructor is not None
            ), "The local optimizer class has not been set"

            param_groups = self._partition_parameters()[self.rank]
            # `overlap_with_ddp=True` requires a local functional optimizer
            if self._overlap_with_ddp:
                # Functional optimizers only support a single parameter group and
                # require passing in the parameters as a list
                assert len(param_groups) == 1, (
                    "Initializing the local "
                    "functional optimizer with more than one parameter group"
                )
                params = param_groups[0]["params"]
                # Try to pass `_allow_empty_param_list=True` to avoid erroring
                if (
                    "_allow_empty_param_list"
                    in inspect.signature(self._optim_constructor).parameters
                ):
                    self.optim: Any = self._optim_constructor(
                        params, **self._optim_defaults, _allow_empty_param_list=True
                    )
                else:
                    logger.warning(
                        "%s does not support the argument "
                        "`_allow_empty_param_list`; ZeroRedundancyOptimizer may "
                        "error due to an empty parameter list",
                        self._optim_constructor
                    )
                    self.optim: Any = self._optim_constructor(params, **self._optim_defaults)  # type: ignore[no-redef]

                # Log information about the DDP and ZeRO bucketing
                if dist.get_debug_level() != dist.DebugLevel.OFF:
                    local_numel = sum(p.numel() for p in params)
                    num_assigned_buckets = len(
                        self._bucket_assignments_per_rank[self.global_rank]
                    )
                    logger.info(
                        "rank %s with %s parameters "
                        "across %s buckets",
                        self.global_rank, local_numel, num_assigned_buckets
                    )
                    if self.global_rank == 0:
                        logger.info(
                            "%s DDP "
                            "buckets and "
                            "%s bucket "
                            "assignments",
                            len(self._overlap_info.params_per_bucket), self._overlap_info.num_bucket_assignments
                        )
            else:
                # NOTE: Passing `param_groups` into the local optimizer constructor
                # bypasses the empty parameter list check
                self.optim: Optimizer = self._optim_constructor(param_groups, **self._optim_defaults)  # type: ignore[no-redef]

            # TODO: Manually add `self.param_groups` if using a functional
            # optimizer; remove this if/when the functional optimizers support
            # multiple parameter groups
            if self._overlap_with_ddp and not hasattr(self.optim, "param_groups"):
                assert hasattr(self.optim, "param_group"), (
                    "The functional optimizer should set at least one of the "
                    "attributes `param_group` or `param_groups`"
                )
                self.optim.param_groups = [self.optim.param_group]  # type: ignore[attr-defined]

            self._sync_param_groups(self.optim.param_groups, self.param_groups)

        def _init_zero_for_overlap(self) -> None:
            r"""
            Performs a delayed initialization of the local optimizer and the
            supporting data structures.
            """
            assert self._overlap_with_ddp, (
                "`_init_zero_for_overlap()` should only be called when "
                "`overlap_with_ddp=True`"
            )
            self._overlap_info.status = _OverlapStatus.INITIALIZED
            self._clear_cache()
            self._partition_parameters(self._overlap_info.params_per_rank)
            self._build_ddp_param_buckets()
            self._init_local_optimizer()

        def _get_assigned_rank(self, bucket_index: int) -> int:
            r"""
            Returns the single rank assigned to a :class:`DistributedDataParallel`
            gradient bucket.

            Arguments:
                bucket_index (int): index of the :class:`DistributedDataParallel`
                    bucket for which to get the assigned rank.
            """
            assert not self._overlap_info.shard_buckets, (
                "The bucket assignment requires global bucket information and "
                "will be computed later; there should be no need to use this "
                "method"
            )
            return bucket_index % self.world_size

        def _check_overlap_initialized(self):
            r"""
            Checks that the delayed initialization has occurred (see
            :meth:`_init_zero_for_overlap`) if ``overlap_with_ddp=True``, and
            raises a ``RuntimeError`` if not. This should preface methods that
            should not be run before that delayed initialization.

            Raises:
                RuntimeError: if ``overlap_with_ddp=True`` and
                    :meth:`_init_zero_for_overlap` has not been called.
            """
            if (
                self._overlap_with_ddp
                and self._overlap_info.status != _OverlapStatus.INITIALIZED
            ):
                raise RuntimeError(
                    "This method should not be called until this "
                    "ZeroRedundancyOptimizer instance has been fully "
                    "initialized"
                )

        def _get_optimizer_constructor(self, optimizer_class: Any) -> Any:
            r"""
            Returns the proper optimizer constructor, performing the necessary
            validation and transformation depending on ``overlap_with_ddp``.

            Returns:

                - ``optimizer_class`` if ``overlap_with_ddp=False`` and
                    ``optimizer_class`` is not a functional optimizer.
                - ``optimizer_class`` if ``overlap_with_ddp=True`` and
                    ``optimizer_class`` is already a functional optimizer.
                - The functional equivalent of ``optimizer_class`` if
                    ``overlap_with_ddp=True`` and ``optimizer_class`` is not
                    already a functional optimizer (assuming the equivalent
                    exists).

            Raises:
                ValueError:

                    - if ``overlap_with_ddp=True`` but ``optimizer_class`` is
                        neither a functional optimizer nor translatable to a
                        functional optimizer.
                    - if ``overlap_with_ddp=False`` and ``optimizer_class`` is a
                        functional optimizer.
            """
            functional_optims = functional_optim_map.values()
            if not self._overlap_with_ddp:
                if optimizer_class in functional_optims:
                    # Using a functional optimizer is only supported when
                    # `overlap_with_ddp=True`
                    raise ValueError(
                        f"Passing in a functional optimizer {optimizer_class} "
                        "when `overlap_with_ddp=False`"
                    )
                else:
                    return optimizer_class
            else:
                if optimizer_class in functional_optims:
                    # Already a functional optimizer
                    return optimizer_class
                elif optimizer_class in functional_optim_map:
                    # Translate the passed-in optimizer class to its functional
                    # equivalent if `overlap_with_ddp=True`
                    optim_constructor = functional_optim_map[optimizer_class]
                    logger.info(
                        "Using the functional optimizer %s "
                        "instead of %s since "
                        "`overlap_with_ddp=True`",
                        optim_constructor, optimizer_class
                    )
                    return optim_constructor
                else:
                    raise ValueError(
                        "Using `ddp_with_overlap=True` requires using a "
                        "functional optimizer, but there is no supported functional "
                        f"optimizer equivalent for {optimizer_class}"
                    )

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