pytorch/torch/nn/modules/batchnorm.py

from typing import Optional, Any

import torch
from torch import Tensor
from torch.nn.parameter import Parameter, UninitializedParameter, UninitializedBuffer

from .. import functional as F
from .. import init
from ._functions import SyncBatchNorm as sync_batch_norm
from .lazy import LazyModuleMixin
from .module import Module


class _NormBase(Module):
    """Common base of _InstanceNorm and _BatchNorm"""

    _version = 2
    __constants__ = ["track_running_stats", "momentum", "eps", "num_features", "affine"]
    num_features: int
    eps: float
    momentum: float
    affine: bool
    track_running_stats: bool
    # WARNING: weight and bias purposely not defined here.
    # See https://github.com/pytorch/pytorch/issues/39670

    def __init__(
        self,
        num_features: int,
        eps: float = 1e-5,
        momentum: float = 0.1,
        affine: bool = True,
        track_running_stats: bool = True,
        device=None,
        dtype=None
    ) -> None:
        factory_kwargs = {'device': device, 'dtype': dtype}
        super(_NormBase, self).__init__()
        self.num_features = num_features
        self.eps = eps
        self.momentum = momentum
        self.affine = affine
        self.track_running_stats = track_running_stats
        if self.affine:
            self.weight = Parameter(torch.empty(num_features, **factory_kwargs))
            self.bias = Parameter(torch.empty(num_features, **factory_kwargs))
        else:
            self.register_parameter("weight", None)
            self.register_parameter("bias", None)
        if self.track_running_stats:
            self.register_buffer('running_mean', torch.zeros(num_features, **factory_kwargs))
            self.register_buffer('running_var', torch.ones(num_features, **factory_kwargs))
            self.running_mean: Optional[Tensor]
            self.running_var: Optional[Tensor]
            self.register_buffer('num_batches_tracked',
                                 torch.tensor(0, dtype=torch.long,
                                              **{k: v for k, v in factory_kwargs.items() if k != 'dtype'}))
            self.num_batches_tracked: Optional[Tensor]
        else:
            self.register_buffer("running_mean", None)
            self.register_buffer("running_var", None)
            self.register_buffer("num_batches_tracked", None)
        self.reset_parameters()

    def reset_running_stats(self) -> None:
        if self.track_running_stats:
            # running_mean/running_var/num_batches... are registered at runtime depending
            # if self.track_running_stats is on
            self.running_mean.zero_()  # type: ignore[union-attr]
            self.running_var.fill_(1)  # type: ignore[union-attr]
            self.num_batches_tracked.zero_()  # type: ignore[union-attr,operator]

    def reset_parameters(self) -> None:
        self.reset_running_stats()
        if self.affine:
            init.ones_(self.weight)
            init.zeros_(self.bias)

    def _check_input_dim(self, input):
        raise NotImplementedError

    def extra_repr(self):
        return (
            "{num_features}, eps={eps}, momentum={momentum}, affine={affine}, "
            "track_running_stats={track_running_stats}".format(**self.__dict__)
        )

    def _load_from_state_dict(
        self,
        state_dict,
        prefix,
        local_metadata,
        strict,
        missing_keys,
        unexpected_keys,
        error_msgs,
    ):
        version = local_metadata.get("version", None)

        if (version is None or version < 2) and self.track_running_stats:
            # at version 2: added num_batches_tracked buffer
            #               this should have a default value of 0
            num_batches_tracked_key = prefix + "num_batches_tracked"
            if num_batches_tracked_key not in state_dict:
                state_dict[num_batches_tracked_key] = torch.tensor(0, dtype=torch.long)

        super(_NormBase, self)._load_from_state_dict(
            state_dict,
            prefix,
            local_metadata,
            strict,
            missing_keys,
            unexpected_keys,
            error_msgs,
        )


class _BatchNorm(_NormBase):
    def __init__(
        self,
        num_features,
        eps=1e-5,
        momentum=0.1,
        affine=True,
        track_running_stats=True,
        device=None,
        dtype=None
    ):
        factory_kwargs = {'device': device, 'dtype': dtype}
        super(_BatchNorm, self).__init__(
            num_features, eps, momentum, affine, track_running_stats, **factory_kwargs
        )

    def forward(self, input: Tensor) -> Tensor:
        self._check_input_dim(input)

        # exponential_average_factor is set to self.momentum
        # (when it is available) only so that it gets updated
        # in ONNX graph when this node is exported to ONNX.
        if self.momentum is None:
            exponential_average_factor = 0.0
        else:
            exponential_average_factor = self.momentum

        if self.training and self.track_running_stats:
            # TODO: if statement only here to tell the jit to skip emitting this when it is None
            if self.num_batches_tracked is not None:  # type: ignore[has-type]
                self.num_batches_tracked.add_(1)  # type: ignore[has-type]
                if self.momentum is None:  # use cumulative moving average
                    exponential_average_factor = 1.0 / float(self.num_batches_tracked)
                else:  # use exponential moving average
                    exponential_average_factor = self.momentum

        r"""
        Decide whether the mini-batch stats should be used for normalization rather than the buffers.
        Mini-batch stats are used in training mode, and in eval mode when buffers are None.
        """
        if self.training:
            bn_training = True
        else:
            bn_training = (self.running_mean is None) and (self.running_var is None)

        r"""
        Buffers are only updated if they are to be tracked and we are in training mode. Thus they only need to be
        passed when the update should occur (i.e. in training mode when they are tracked), or when buffer stats are
        used for normalization (i.e. in eval mode when buffers are not None).
        """
        return F.batch_norm(
            input,
            # If buffers are not to be tracked, ensure that they won't be updated
            self.running_mean
            if not self.training or self.track_running_stats
            else None,
            self.running_var if not self.training or self.track_running_stats else None,
            self.weight,
            self.bias,
            bn_training,
            exponential_average_factor,
            self.eps,
        )


class _LazyNormBase(LazyModuleMixin, _NormBase):

    weight: UninitializedParameter  # type: ignore[assignment]
    bias: UninitializedParameter  # type: ignore[assignment]

    def __init__(self, eps=1e-5, momentum=0.1, affine=True, track_running_stats=True,
                 device=None, dtype=None) -> None:
        factory_kwargs = {'device': device, 'dtype': dtype}
        super(_LazyNormBase, self).__init__(
            # affine and track_running_stats are hardcoded to False to
            # avoid creating tensors that will soon be overwritten.
            0,
            eps,
            momentum,
            False,
            False,
            **factory_kwargs,
        )
        self.affine = affine
        self.track_running_stats = track_running_stats
        if self.affine:
            self.weight = UninitializedParameter(**factory_kwargs)
            self.bias = UninitializedParameter(**factory_kwargs)
        if self.track_running_stats:
            self.running_mean = UninitializedBuffer(**factory_kwargs)
            self.running_var = UninitializedBuffer(**factory_kwargs)
            self.num_batches_tracked = torch.tensor(
                0, dtype=torch.long, **{k: v for k, v in factory_kwargs.items() if k != 'dtype'})

    def reset_parameters(self) -> None:
        if not self.has_uninitialized_params() and self.num_features != 0:
            super().reset_parameters()

    def initialize_parameters(self, input) -> None:  # type: ignore[override]
        if self.has_uninitialized_params():
            self.num_features = input.shape[1]
            if self.affine:
                assert isinstance(self.weight, UninitializedParameter)
                assert isinstance(self.bias, UninitializedParameter)
                self.weight.materialize((self.num_features,))
                self.bias.materialize((self.num_features,))
            if self.track_running_stats:
                self.running_mean.materialize((self.num_features,))  # type:ignore[union-attr]
                self.running_var.materialize((self.num_features,))  # type:ignore[union-attr]
            self.reset_parameters()


class BatchNorm1d(_BatchNorm):
    r"""Applies Batch Normalization over a 2D or 3D input (a mini-batch of 1D
    inputs with optional additional channel dimension) as described in the paper
    `Batch Normalization: Accelerating Deep Network Training by Reducing
    Internal Covariate Shift <https://arxiv.org/abs/1502.03167>`__ .

    .. math::

        y = \frac{x - \mathrm{E}[x]}{\sqrt{\mathrm{Var}[x] + \epsilon}} * \gamma + \beta

    The mean and standard-deviation are calculated per-dimension over
    the mini-batches and :math:`\gamma` and :math:`\beta` are learnable parameter vectors
    of size `C` (where `C` is the input size). By default, the elements of :math:`\gamma` are set
    to 1 and the elements of :math:`\beta` are set to 0. The standard-deviation is calculated
    via the biased estimator, equivalent to `torch.var(input, unbiased=False)`.

    Also by default, during training this layer keeps running estimates of its
    computed mean and variance, which are then used for normalization during
    evaluation. The running estimates are kept with a default :attr:`momentum`
    of 0.1.

    If :attr:`track_running_stats` is set to ``False``, this layer then does not
    keep running estimates, and batch statistics are instead used during
    evaluation time as well.

    .. note::
        This :attr:`momentum` argument is different from one used in optimizer
        classes and the conventional notion of momentum. Mathematically, the
        update rule for running statistics here is
        :math:`\hat{x}_\text{new} = (1 - \text{momentum}) \times \hat{x} + \text{momentum} \times x_t`,
        where :math:`\hat{x}` is the estimated statistic and :math:`x_t` is the
        new observed value.

    Because the Batch Normalization is done over the `C` dimension, computing statistics
    on `(N, L)` slices, it's common terminology to call this Temporal Batch Normalization.

    Args:
        num_features: :math:`C` from an expected input of size
            :math:`(N, C, L)` or :math:`L` from input of size :math:`(N, L)`
        eps: a value added to the denominator for numerical stability.
            Default: 1e-5
        momentum: the value used for the running_mean and running_var
            computation. Can be set to ``None`` for cumulative moving average
            (i.e. simple average). Default: 0.1
        affine: a boolean value that when set to ``True``, this module has
            learnable affine parameters. Default: ``True``
        track_running_stats: a boolean value that when set to ``True``, this
            module tracks the running mean and variance, and when set to ``False``,
            this module does not track such statistics, and initializes statistics
            buffers :attr:`running_mean` and :attr:`running_var` as ``None``.
            When these buffers are ``None``, this module always uses batch statistics.
            in both training and eval modes. Default: ``True``

    Shape:
        - Input: :math:`(N, C)` or :math:`(N, C, L)`
        - Output: :math:`(N, C)` or :math:`(N, C, L)` (same shape as input)

    Examples::

        >>> # With Learnable Parameters
        >>> m = nn.BatchNorm1d(100)
        >>> # Without Learnable Parameters
        >>> m = nn.BatchNorm1d(100, affine=False)
        >>> input = torch.randn(20, 100)
        >>> output = m(input)
    """

    def _check_input_dim(self, input):
        if input.dim() != 2 and input.dim() != 3:
            raise ValueError(
                "expected 2D or 3D input (got {}D input)".format(input.dim())
            )


class LazyBatchNorm1d(_LazyNormBase, _BatchNorm):
    r"""A :class:`torch.nn.BatchNorm1d` module with lazy initialization of
    the ``num_features`` argument of the :class:`BatchNorm1d` that is inferred
    from the ``input.size(1)``.
    The attributes that will be lazily initialized are `weight`, `bias`,
    `running_mean` and `running_var`.

    Check the :class:`torch.nn.modules.lazy.LazyModuleMixin` for further documentation
    on lazy modules and their limitations.

    Args:
        eps: a value added to the denominator for numerical stability.
            Default: 1e-5
        momentum: the value used for the running_mean and running_var
            computation. Can be set to ``None`` for cumulative moving average
            (i.e. simple average). Default: 0.1
        affine: a boolean value that when set to ``True``, this module has
            learnable affine parameters. Default: ``True``
        track_running_stats: a boolean value that when set to ``True``, this
            module tracks the running mean and variance, and when set to ``False``,
            this module does not track such statistics, and initializes statistics
            buffers :attr:`running_mean` and :attr:`running_var` as ``None``.
            When these buffers are ``None``, this module always uses batch statistics.
            in both training and eval modes. Default: ``True``
    """

    cls_to_become = BatchNorm1d  # type: ignore[assignment]

    def _check_input_dim(self, input):
        if input.dim() != 2 and input.dim() != 3:
            raise ValueError(
                "expected 2D or 3D input (got {}D input)".format(input.dim())
            )


class BatchNorm2d(_BatchNorm):
    r"""Applies Batch Normalization over a 4D input (a mini-batch of 2D inputs
    with additional channel dimension) as described in the paper
    `Batch Normalization: Accelerating Deep Network Training by Reducing
    Internal Covariate Shift <https://arxiv.org/abs/1502.03167>`__ .

    .. math::

        y = \frac{x - \mathrm{E}[x]}{ \sqrt{\mathrm{Var}[x] + \epsilon}} * \gamma + \beta

    The mean and standard-deviation are calculated per-dimension over
    the mini-batches and :math:`\gamma` and :math:`\beta` are learnable parameter vectors
    of size `C` (where `C` is the input size). By default, the elements of :math:`\gamma` are set
    to 1 and the elements of :math:`\beta` are set to 0. The standard-deviation is calculated
    via the biased estimator, equivalent to `torch.var(input, unbiased=False)`.

    Also by default, during training this layer keeps running estimates of its
    computed mean and variance, which are then used for normalization during
    evaluation. The running estimates are kept with a default :attr:`momentum`
    of 0.1.

    If :attr:`track_running_stats` is set to ``False``, this layer then does not
    keep running estimates, and batch statistics are instead used during
    evaluation time as well.

    .. note::
        This :attr:`momentum` argument is different from one used in optimizer
        classes and the conventional notion of momentum. Mathematically, the
        update rule for running statistics here is
        :math:`\hat{x}_\text{new} = (1 - \text{momentum}) \times \hat{x} + \text{momentum} \times x_t`,
        where :math:`\hat{x}` is the estimated statistic and :math:`x_t` is the
        new observed value.

    Because the Batch Normalization is done over the `C` dimension, computing statistics
    on `(N, H, W)` slices, it's common terminology to call this Spatial Batch Normalization.

    Args:
        num_features: :math:`C` from an expected input of size
            :math:`(N, C, H, W)`
        eps: a value added to the denominator for numerical stability.
            Default: 1e-5
        momentum: the value used for the running_mean and running_var
            computation. Can be set to ``None`` for cumulative moving average
            (i.e. simple average). Default: 0.1
        affine: a boolean value that when set to ``True``, this module has
            learnable affine parameters. Default: ``True``
        track_running_stats: a boolean value that when set to ``True``, this
            module tracks the running mean and variance, and when set to ``False``,
            this module does not track such statistics, and initializes statistics
            buffers :attr:`running_mean` and :attr:`running_var` as ``None``.
            When these buffers are ``None``, this module always uses batch statistics.
            in both training and eval modes. Default: ``True``

    Shape:
        - Input: :math:`(N, C, H, W)`
        - Output: :math:`(N, C, H, W)` (same shape as input)

    Examples::

        >>> # With Learnable Parameters
        >>> m = nn.BatchNorm2d(100)
        >>> # Without Learnable Parameters
        >>> m = nn.BatchNorm2d(100, affine=False)
        >>> input = torch.randn(20, 100, 35, 45)
        >>> output = m(input)
    """

    def _check_input_dim(self, input):
        if input.dim() != 4:
            raise ValueError("expected 4D input (got {}D input)".format(input.dim()))


class LazyBatchNorm2d(_LazyNormBase, _BatchNorm):
    r"""A :class:`torch.nn.BatchNorm2d` module with lazy initialization of
    the ``num_features`` argument of the :class:`BatchNorm2d` that is inferred
    from the ``input.size(1)``.
    The attributes that will be lazily initialized are `weight`, `bias`,
    `running_mean` and `running_var`.

    Check the :class:`torch.nn.modules.lazy.LazyModuleMixin` for further documentation
    on lazy modules and their limitations.

    Args:
        eps: a value added to the denominator for numerical stability.
            Default: 1e-5
        momentum: the value used for the running_mean and running_var
            computation. Can be set to ``None`` for cumulative moving average
            (i.e. simple average). Default: 0.1
        affine: a boolean value that when set to ``True``, this module has
            learnable affine parameters. Default: ``True``
        track_running_stats: a boolean value that when set to ``True``, this
            module tracks the running mean and variance, and when set to ``False``,
            this module does not track such statistics, and initializes statistics
            buffers :attr:`running_mean` and :attr:`running_var` as ``None``.
            When these buffers are ``None``, this module always uses batch statistics.
            in both training and eval modes. Default: ``True``
    """

    cls_to_become = BatchNorm2d  # type: ignore[assignment]

    def _check_input_dim(self, input):
        if input.dim() != 4:
            raise ValueError("expected 4D input (got {}D input)".format(input.dim()))


class BatchNorm3d(_BatchNorm):
    r"""Applies Batch Normalization over a 5D input (a mini-batch of 3D inputs
    with additional channel dimension) as described in the paper
    `Batch Normalization: Accelerating Deep Network Training by Reducing
    Internal Covariate Shift <https://arxiv.org/abs/1502.03167>`__ .

    .. math::

        y = \frac{x - \mathrm{E}[x]}{ \sqrt{\mathrm{Var}[x] + \epsilon}} * \gamma + \beta

    The mean and standard-deviation are calculated per-dimension over
    the mini-batches and :math:`\gamma` and :math:`\beta` are learnable parameter vectors
    of size `C` (where `C` is the input size). By default, the elements of :math:`\gamma` are set
    to 1 and the elements of :math:`\beta` are set to 0. The standard-deviation is calculated
    via the biased estimator, equivalent to `torch.var(input, unbiased=False)`.

    Also by default, during training this layer keeps running estimates of its
    computed mean and variance, which are then used for normalization during
    evaluation. The running estimates are kept with a default :attr:`momentum`
    of 0.1.

    If :attr:`track_running_stats` is set to ``False``, this layer then does not
    keep running estimates, and batch statistics are instead used during
    evaluation time as well.

    .. note::
        This :attr:`momentum` argument is different from one used in optimizer
        classes and the conventional notion of momentum. Mathematically, the
        update rule for running statistics here is
        :math:`\hat{x}_\text{new} = (1 - \text{momentum}) \times \hat{x} + \text{momentum} \times x_t`,
        where :math:`\hat{x}` is the estimated statistic and :math:`x_t` is the
        new observed value.

    Because the Batch Normalization is done over the `C` dimension, computing statistics
    on `(N, D, H, W)` slices, it's common terminology to call this Volumetric Batch Normalization
    or Spatio-temporal Batch Normalization.

    Args:
        num_features: :math:`C` from an expected input of size
            :math:`(N, C, D, H, W)`
        eps: a value added to the denominator for numerical stability.
            Default: 1e-5
        momentum: the value used for the running_mean and running_var
            computation. Can be set to ``None`` for cumulative moving average
            (i.e. simple average). Default: 0.1
        affine: a boolean value that when set to ``True``, this module has
            learnable affine parameters. Default: ``True``
        track_running_stats: a boolean value that when set to ``True``, this
            module tracks the running mean and variance, and when set to ``False``,
            this module does not track such statistics, and initializes statistics
            buffers :attr:`running_mean` and :attr:`running_var` as ``None``.
            When these buffers are ``None``, this module always uses batch statistics.
            in both training and eval modes. Default: ``True``

    Shape:
        - Input: :math:`(N, C, D, H, W)`
        - Output: :math:`(N, C, D, H, W)` (same shape as input)

    Examples::

        >>> # With Learnable Parameters
        >>> m = nn.BatchNorm3d(100)
        >>> # Without Learnable Parameters
        >>> m = nn.BatchNorm3d(100, affine=False)
        >>> input = torch.randn(20, 100, 35, 45, 10)
        >>> output = m(input)
    """

    def _check_input_dim(self, input):
        if input.dim() != 5:
            raise ValueError("expected 5D input (got {}D input)".format(input.dim()))


class LazyBatchNorm3d(_LazyNormBase, _BatchNorm):
    r"""A :class:`torch.nn.BatchNorm3d` module with lazy initialization of
    the ``num_features`` argument of the :class:`BatchNorm3d` that is inferred
    from the ``input.size(1)``.
    The attributes that will be lazily initialized are `weight`, `bias`,
    `running_mean` and `running_var`.

    Check the :class:`torch.nn.modules.lazy.LazyModuleMixin` for further documentation
    on lazy modules and their limitations.

    Args:
        eps: a value added to the denominator for numerical stability.
            Default: 1e-5
        momentum: the value used for the running_mean and running_var
            computation. Can be set to ``None`` for cumulative moving average
            (i.e. simple average). Default: 0.1
        affine: a boolean value that when set to ``True``, this module has
            learnable affine parameters. Default: ``True``
        track_running_stats: a boolean value that when set to ``True``, this
            module tracks the running mean and variance, and when set to ``False``,
            this module does not track such statistics, and initializes statistics
            buffers :attr:`running_mean` and :attr:`running_var` as ``None``.
            When these buffers are ``None``, this module always uses batch statistics.
            in both training and eval modes. Default: ``True``
    """

    cls_to_become = BatchNorm3d  # type: ignore[assignment]

    def _check_input_dim(self, input):
        if input.dim() != 5:
            raise ValueError("expected 5D input (got {}D input)".format(input.dim()))


class SyncBatchNorm(_BatchNorm):
    r"""Applies Batch Normalization over a N-Dimensional input (a mini-batch of [N-2]D inputs
    with additional channel dimension) as described in the paper
    `Batch Normalization: Accelerating Deep Network Training by Reducing
    Internal Covariate Shift <https://arxiv.org/abs/1502.03167>`__ .

    .. math::

        y = \frac{x - \mathrm{E}[x]}{ \sqrt{\mathrm{Var}[x] + \epsilon}} * \gamma + \beta

    The mean and standard-deviation are calculated per-dimension over all
    mini-batches of the same process groups. :math:`\gamma` and :math:`\beta`
    are learnable parameter vectors of size `C` (where `C` is the input size).
    By default, the elements of :math:`\gamma` are sampled from
    :math:`\mathcal{U}(0, 1)` and the elements of :math:`\beta` are set to 0.
    The standard-deviation is calculated via the biased estimator, equivalent to
    `torch.var(input, unbiased=False)`.

    Also by default, during training this layer keeps running estimates of its
    computed mean and variance, which are then used for normalization during
    evaluation. The running estimates are kept with a default :attr:`momentum`
    of 0.1.

    If :attr:`track_running_stats` is set to ``False``, this layer then does not
    keep running estimates, and batch statistics are instead used during
    evaluation time as well.

    .. note::
        This :attr:`momentum` argument is different from one used in optimizer
        classes and the conventional notion of momentum. Mathematically, the
        update rule for running statistics here is
        :math:`\hat{x}_\text{new} = (1 - \text{momentum}) \times \hat{x} + \text{momentum} \times x_t`,
        where :math:`\hat{x}` is the estimated statistic and :math:`x_t` is the
        new observed value.

    Because the Batch Normalization is done for each channel in the ``C`` dimension, computing
    statistics on ``(N, +)`` slices, it's common terminology to call this Volumetric Batch
    Normalization or Spatio-temporal Batch Normalization.

    Currently :class:`SyncBatchNorm` only supports
    :class:`~torch.nn.DistributedDataParallel` (DDP) with single GPU per process. Use
    :meth:`torch.nn.SyncBatchNorm.convert_sync_batchnorm()` to convert
    :attr:`BatchNorm*D` layer to :class:`SyncBatchNorm` before wrapping
    Network with DDP.

    Args:
        num_features: :math:`C` from an expected input of size
            :math:`(N, C, +)`
        eps: a value added to the denominator for numerical stability.
            Default: ``1e-5``
        momentum: the value used for the running_mean and running_var
            computation. Can be set to ``None`` for cumulative moving average
            (i.e. simple average). Default: 0.1
        affine: a boolean value that when set to ``True``, this module has
            learnable affine parameters. Default: ``True``
        track_running_stats: a boolean value that when set to ``True``, this
            module tracks the running mean and variance, and when set to ``False``,
            this module does not track such statistics, and initializes statistics
            buffers :attr:`running_mean` and :attr:`running_var` as ``None``.
            When these buffers are ``None``, this module always uses batch statistics.
            in both training and eval modes. Default: ``True``
        process_group: synchronization of stats happen within each process group
            individually. Default behavior is synchronization across the whole
            world

    Shape:
        - Input: :math:`(N, C, +)`
        - Output: :math:`(N, C, +)` (same shape as input)

    .. note::
        Synchronization of batchnorm statistics occurs only while training, i.e.
        synchronization is disabled when ``model.eval()`` is set or if
        ``self.training`` is otherwise ``False``.

    Examples::

        >>> # With Learnable Parameters
        >>> m = nn.SyncBatchNorm(100)
        >>> # creating process group (optional)
        >>> # ranks is a list of int identifying rank ids.
        >>> ranks = list(range(8))
        >>> r1, r2 = ranks[:4], ranks[4:]
        >>> # Note: every rank calls into new_group for every
        >>> # process group created, even if that rank is not
        >>> # part of the group.
        >>> process_groups = [torch.distributed.new_group(pids) for pids in [r1, r2]]
        >>> process_group = process_groups[0 if dist.get_rank() <= 3 else 1]
        >>> # Without Learnable Parameters
        >>> m = nn.BatchNorm3d(100, affine=False, process_group=process_group)
        >>> input = torch.randn(20, 100, 35, 45, 10)
        >>> output = m(input)

        >>> # network is nn.BatchNorm layer
        >>> sync_bn_network = nn.SyncBatchNorm.convert_sync_batchnorm(network, process_group)
        >>> # only single gpu per process is currently supported
        >>> ddp_sync_bn_network = torch.nn.parallel.DistributedDataParallel(
        >>>                         sync_bn_network,
        >>>                         device_ids=[args.local_rank],
        >>>                         output_device=args.local_rank)
    """

    def __init__(
        self,
        num_features: int,
        eps: float = 1e-5,
        momentum: float = 0.1,
        affine: bool = True,
        track_running_stats: bool = True,
        process_group: Optional[Any] = None,
        device=None,
        dtype=None
    ) -> None:
        factory_kwargs = {'device': device, 'dtype': dtype}
        super(SyncBatchNorm, self).__init__(
            num_features, eps, momentum, affine, track_running_stats, **factory_kwargs
        )
        self.process_group = process_group

    def _check_input_dim(self, input):
        if input.dim() < 2:
            raise ValueError(
                "expected at least 2D input (got {}D input)".format(input.dim())
            )

    def _check_non_zero_input_channels(self, input):
        if input.size(1) == 0:
            raise ValueError(
                "SyncBatchNorm number of input channels should be non-zero"
            )

    def forward(self, input: Tensor) -> Tensor:
        # currently only GPU input is supported
        if not input.is_cuda:
            raise ValueError("SyncBatchNorm expected input tensor to be on GPU")

        self._check_input_dim(input)
        self._check_non_zero_input_channels(input)

        # exponential_average_factor is set to self.momentum
        # (when it is available) only so that it gets updated
        # in ONNX graph when this node is exported to ONNX.
        if self.momentum is None:
            exponential_average_factor = 0.0
        else:
            exponential_average_factor = self.momentum

        if self.training and self.track_running_stats:
            assert self.num_batches_tracked is not None
            self.num_batches_tracked.add_(1)
            if self.momentum is None:  # use cumulative moving average
                exponential_average_factor = 1.0 / self.num_batches_tracked.item()
            else:  # use exponential moving average
                exponential_average_factor = self.momentum

        r"""
        Decide whether the mini-batch stats should be used for normalization rather than the buffers.
        Mini-batch stats are used in training mode, and in eval mode when buffers are None.
        """
        if self.training:
            bn_training = True
        else:
            bn_training = (self.running_mean is None) and (self.running_var is None)

        r"""
        Buffers are only updated if they are to be tracked and we are in training mode. Thus they only need to be
        passed when the update should occur (i.e. in training mode when they are tracked), or when buffer stats are
        used for normalization (i.e. in eval mode when buffers are not None).
        """
        # If buffers are not to be tracked, ensure that they won't be updated
        running_mean = (
            self.running_mean if not self.training or self.track_running_stats else None
        )
        running_var = (
            self.running_var if not self.training or self.track_running_stats else None
        )

        # Don't sync batchnorm stats in inference mode (model.eval()).
        need_sync = (bn_training and self.training)
        if need_sync:
            process_group = torch.distributed.group.WORLD
            if self.process_group:
                process_group = self.process_group
            world_size = torch.distributed.get_world_size(process_group)
            need_sync = world_size > 1

        # fallback to framework BN when synchronization is not necessary
        if not need_sync:
            return F.batch_norm(
                input,
                running_mean,
                running_var,
                self.weight,
                self.bias,
                bn_training,
                exponential_average_factor,
                self.eps,
            )
        else:
            assert bn_training
            return sync_batch_norm.apply(
                input,
                self.weight,
                self.bias,
                running_mean,
                running_var,
                self.eps,
                exponential_average_factor,
                process_group,
                world_size,
            )

    @classmethod
    def convert_sync_batchnorm(cls, module, process_group=None):
        r"""Helper function to convert all :attr:`BatchNorm*D` layers in the model to
        :class:`torch.nn.SyncBatchNorm` layers.

        Args:
            module (nn.Module): module containing one or more :attr:`BatchNorm*D` layers
            process_group (optional): process group to scope synchronization,
                default is the whole world

        Returns:
            The original :attr:`module` with the converted :class:`torch.nn.SyncBatchNorm`
            layers. If the original :attr:`module` is a :attr:`BatchNorm*D` layer,
            a new :class:`torch.nn.SyncBatchNorm` layer object will be returned
            instead.

        Example::

            >>> # Network with nn.BatchNorm layer
            >>> module = torch.nn.Sequential(
            >>>            torch.nn.Linear(20, 100),
            >>>            torch.nn.BatchNorm1d(100),
            >>>          ).cuda()
            >>> # creating process group (optional)
            >>> # ranks is a list of int identifying rank ids.
            >>> ranks = list(range(8))
            >>> r1, r2 = ranks[:4], ranks[4:]
            >>> # Note: every rank calls into new_group for every
            >>> # process group created, even if that rank is not
            >>> # part of the group.
            >>> process_groups = [torch.distributed.new_group(pids) for pids in [r1, r2]]
            >>> process_group = process_groups[0 if dist.get_rank() <= 3 else 1]
            >>> sync_bn_module = torch.nn.SyncBatchNorm.convert_sync_batchnorm(module, process_group)

        """
        module_output = module
        if isinstance(module, torch.nn.modules.batchnorm._BatchNorm):
            module_output = torch.nn.SyncBatchNorm(
                module.num_features,
                module.eps,
                module.momentum,
                module.affine,
                module.track_running_stats,
                process_group,
            )
            if module.affine:
                with torch.no_grad():
                    module_output.weight = module.weight
                    module_output.bias = module.bias
            module_output.running_mean = module.running_mean
            module_output.running_var = module.running_var
            module_output.num_batches_tracked = module.num_batches_tracked
            if hasattr(module, "qconfig"):
                module_output.qconfig = module.qconfig
        for name, child in module.named_children():
            module_output.add_module(
                name, cls.convert_sync_batchnorm(child, process_group)
            )
        del module
        return module_output