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# Source code for torch.nn.modules.conv

    import math
    import warnings

    import torch
    from torch import Tensor
    from torch.nn.parameter import Parameter, UninitializedParameter
    from .. import functional as F
    from .. import init
    from .lazy import LazyModuleMixin
    from .module import Module
    from .utils import _single, _pair, _triple, _reverse_repeat_tuple
    from torch._torch_docs import reproducibility_notes

    from ..common_types import _size_1_t, _size_2_t, _size_3_t
    from typing import Optional, List, Tuple, Union

    __all__ = ['Conv1d', 'Conv2d', 'Conv3d', 'ConvTranspose1d', 'ConvTranspose2d', 'ConvTranspose3d',
               'LazyConv1d', 'LazyConv2d', 'LazyConv3d', 'LazyConvTranspose1d', 'LazyConvTranspose2d',
               'LazyConvTranspose3d']

    convolution_notes = \
        {"groups_note": r"""* :attr:`groups` controls the connections between inputs and outputs.
          :attr:`in_channels` and :attr:`out_channels` must both be divisible by
          :attr:`groups`. For example,

            * At groups=1, all inputs are convolved to all outputs.
            * At groups=2, the operation becomes equivalent to having two conv
              layers side by side, each seeing half the input channels
              and producing half the output channels, and both subsequently
              concatenated.
            * At groups= :attr:`in_channels`, each input channel is convolved with
              its own set of filters (of size
              :math:`\frac{\text{out\_channels}}{\text{in\_channels}}`).""",

            "depthwise_separable_note": r"""When `groups == in_channels` and `out_channels == K * in_channels`,
            where `K` is a positive integer, this operation is also known as a "depthwise convolution".

            In other words, for an input of size :math:`(N, C_{in}, L_{in})`,
            a depthwise convolution with a depthwise multiplier `K` can be performed with the arguments
            :math:`(C_\text{in}=C_\text{in}, C_\text{out}=C_\text{in} \times \text{K}, ..., \text{groups}=C_\text{in})`."""}  # noqa: B950

    class _ConvNd(Module):

        __constants__ = ['stride', 'padding', 'dilation', 'groups',
                         'padding_mode', 'output_padding', 'in_channels',
                         'out_channels', 'kernel_size']
        __annotations__ = {'bias': Optional[torch.Tensor]}

        def _conv_forward(self, input: Tensor, weight: Tensor, bias: Optional[Tensor]) -> Tensor:  # type: ignore[empty-body]
            ...

        in_channels: int
        _reversed_padding_repeated_twice: List[int]
        out_channels: int
        kernel_size: Tuple[int, ...]
        stride: Tuple[int, ...]
        padding: Union[str, Tuple[int, ...]]
        dilation: Tuple[int, ...]
        transposed: bool
        output_padding: Tuple[int, ...]
        groups: int
        padding_mode: str
        weight: Tensor
        bias: Optional[Tensor]

        def __init__(self,
                     in_channels: int,
                     out_channels: int,
                     kernel_size: Tuple[int, ...],
                     stride: Tuple[int, ...],
                     padding: Tuple[int, ...],
                     dilation: Tuple[int, ...],
                     transposed: bool,
                     output_padding: Tuple[int, ...],
                     groups: int,
                     bias: bool,
                     padding_mode: str,
                     device=None,
                     dtype=None) -> None:
            factory_kwargs = {'device': device, 'dtype': dtype}
            super().__init__()
            if groups <= 0:
                raise ValueError('groups must be a positive integer')
            if in_channels % groups != 0:
                raise ValueError('in_channels must be divisible by groups')
            if out_channels % groups != 0:
                raise ValueError('out_channels must be divisible by groups')
            valid_padding_strings = {'same', 'valid'}
            if isinstance(padding, str):
                if padding not in valid_padding_strings:
                    raise ValueError(
                        f"Invalid padding string {padding!r}, should be one of {valid_padding_strings}")
                if padding == 'same' and any(s != 1 for s in stride):
                    raise ValueError("padding='same' is not supported for strided convolutions")

            valid_padding_modes = {'zeros', 'reflect', 'replicate', 'circular'}
            if padding_mode not in valid_padding_modes:
                raise ValueError(f"padding_mode must be one of {valid_padding_modes}, but got padding_mode='{padding_mode}'")
            self.in_channels = in_channels
            self.out_channels = out_channels
            self.kernel_size = kernel_size
            self.stride = stride
            self.padding = padding
            self.dilation = dilation
            self.transposed = transposed
            self.output_padding = output_padding
            self.groups = groups
            self.padding_mode = padding_mode
            # `_reversed_padding_repeated_twice` is the padding to be passed to
            # `F.pad` if needed (e.g., for non-zero padding types that are
            # implemented as two ops: padding + conv). `F.pad` accepts paddings in
            # reverse order than the dimension.
            if isinstance(self.padding, str):
                self._reversed_padding_repeated_twice = [0, 0] * len(kernel_size)
                if padding == 'same':
                    for d, k, i in zip(dilation, kernel_size,
                                       range(len(kernel_size) - 1, -1, -1)):
                        total_padding = d * (k - 1)
                        left_pad = total_padding // 2
                        self._reversed_padding_repeated_twice[2 * i] = left_pad
                        self._reversed_padding_repeated_twice[2 * i + 1] = (
                            total_padding - left_pad)
            else:
                self._reversed_padding_repeated_twice = _reverse_repeat_tuple(self.padding, 2)

            if transposed:
                self.weight = Parameter(torch.empty(
                    (in_channels, out_channels // groups, *kernel_size), **factory_kwargs))
            else:
                self.weight = Parameter(torch.empty(
                    (out_channels, in_channels // groups, *kernel_size), **factory_kwargs))
            if bias:
                self.bias = Parameter(torch.empty(out_channels, **factory_kwargs))
            else:
                self.register_parameter('bias', None)

            self.reset_parameters()

        def reset_parameters(self) -> None:
            # Setting a=sqrt(5) in kaiming_uniform is the same as initializing with
            # uniform(-1/sqrt(k), 1/sqrt(k)), where k = weight.size(1) * prod(*kernel_size)
            # For more details see: https://github.com/pytorch/pytorch/issues/15314#issuecomment-477448573
            init.kaiming_uniform_(self.weight, a=math.sqrt(5))
            if self.bias is not None:
                fan_in, _ = init._calculate_fan_in_and_fan_out(self.weight)
                if fan_in != 0:
                    bound = 1 / math.sqrt(fan_in)
                    init.uniform_(self.bias, -bound, bound)

        def extra_repr(self):
            s = ('{in_channels}, {out_channels}, kernel_size={kernel_size}'
                 ', stride={stride}')
            if self.padding != (0,) * len(self.padding):
                s += ', padding={padding}'
            if self.dilation != (1,) * len(self.dilation):
                s += ', dilation={dilation}'
            if self.output_padding != (0,) * len(self.output_padding):
                s += ', output_padding={output_padding}'
            if self.groups != 1:
                s += ', groups={groups}'
            if self.bias is None:
                s += ', bias=False'
            if self.padding_mode != 'zeros':
                s += ', padding_mode={padding_mode}'
            return s.format(**self.__dict__)

        def __setstate__(self, state):
            super().__setstate__(state)
            if not hasattr(self, 'padding_mode'):
                self.padding_mode = 'zeros'

    class Conv1d(_ConvNd):
        __doc__ = r"""Applies a 1D convolution over an input signal composed of several input
        planes.

        In the simplest case, the output value of the layer with input size
        :math:`(N, C_{\text{in}}, L)` and output :math:`(N, C_{\text{out}}, L_{\text{out}})` can be
        precisely described as:

        .. math::
            \text{out}(N_i, C_{\text{out}_j}) = \text{bias}(C_{\text{out}_j}) +
            \sum_{k = 0}^{C_{in} - 1} \text{weight}(C_{\text{out}_j}, k)
            \star \text{input}(N_i, k)

        where :math:`\star` is the valid `cross-correlation`_ operator,
        :math:`N` is a batch size, :math:`C` denotes a number of channels,
        :math:`L` is a length of signal sequence.
        """ + r"""

        This module supports :ref:`TensorFloat32<tf32_on_ampere>`.

        On certain ROCm devices, when using float16 inputs this module will use :ref:`different precision<fp16_on_mi200>` for backward.

        * :attr:`stride` controls the stride for the cross-correlation, a single
          number or a one-element tuple.

        * :attr:`padding` controls the amount of padding applied to the input. It
          can be either a string {{'valid', 'same'}} or a tuple of ints giving the
          amount of implicit padding applied on both sides.

        * :attr:`dilation` controls the spacing between the kernel points; also
          known as the à trous algorithm. It is harder to describe, but this `link`_
          has a nice visualization of what :attr:`dilation` does.

        {groups_note}

        Note:
            {depthwise_separable_note}
        Note:
            {cudnn_reproducibility_note}

        Note:
            ``padding='valid'`` is the same as no padding. ``padding='same'`` pads
            the input so the output has the shape as the input. However, this mode
            doesn't support any stride values other than 1.

        Note:
            This module supports complex data types i.e. ``complex32, complex64, complex128``.

        Args:
            in_channels (int): Number of channels in the input image
            out_channels (int): Number of channels produced by the convolution
            kernel_size (int or tuple): Size of the convolving kernel
            stride (int or tuple, optional): Stride of the convolution. Default: 1
            padding (int, tuple or str, optional): Padding added to both sides of
                the input. Default: 0
            padding_mode (str, optional): ``'zeros'``, ``'reflect'``,
                ``'replicate'`` or ``'circular'``. Default: ``'zeros'``
            dilation (int or tuple, optional): Spacing between kernel
                elements. Default: 1
            groups (int, optional): Number of blocked connections from input
                channels to output channels. Default: 1
            bias (bool, optional): If ``True``, adds a learnable bias to the
                output. Default: ``True``

        """.format(**reproducibility_notes, **convolution_notes) + r"""

        Shape:
            - Input: :math:`(N, C_{in}, L_{in})` or :math:`(C_{in}, L_{in})`
            - Output: :math:`(N, C_{out}, L_{out})` or :math:`(C_{out}, L_{out})`, where

              .. math::
                  L_{out} = \left\lfloor\frac{L_{in} + 2 \times \text{padding} - \text{dilation}
                            \times (\text{kernel\_size} - 1) - 1}{\text{stride}} + 1\right\rfloor

        Attributes:
            weight (Tensor): the learnable weights of the module of shape
                :math:`(\text{out\_channels},
                \frac{\text{in\_channels}}{\text{groups}}, \text{kernel\_size})`.
                The values of these weights are sampled from
                :math:`\mathcal{U}(-\sqrt{k}, \sqrt{k})` where
                :math:`k = \frac{groups}{C_\text{in} * \text{kernel\_size}}`
            bias (Tensor):   the learnable bias of the module of shape
                (out_channels). If :attr:`bias` is ``True``, then the values of these weights are
                sampled from :math:`\mathcal{U}(-\sqrt{k}, \sqrt{k})` where
                :math:`k = \frac{groups}{C_\text{in} * \text{kernel\_size}}`

        Examples::

            >>> m = nn.Conv1d(16, 33, 3, stride=2)
            >>> input = torch.randn(20, 16, 50)
            >>> output = m(input)

        .. _cross-correlation:
            https://en.wikipedia.org/wiki/Cross-correlation

        .. _link:
            https://github.com/vdumoulin/conv_arithmetic/blob/master/README.md
        """

        def __init__(
            self,
            in_channels: int,
            out_channels: int,
            kernel_size: _size_1_t,
            stride: _size_1_t = 1,
            padding: Union[str, _size_1_t] = 0,
            dilation: _size_1_t = 1,
            groups: int = 1,
            bias: bool = True,
            padding_mode: str = 'zeros',  # TODO: refine this type
            device=None,
            dtype=None
        ) -> None:
            factory_kwargs = {'device': device, 'dtype': dtype}
            # we create new variables below to make mypy happy since kernel_size has
            # type Union[int, Tuple[int]] and kernel_size_ has type Tuple[int]
            kernel_size_ = _single(kernel_size)
            stride_ = _single(stride)
            padding_ = padding if isinstance(padding, str) else _single(padding)
            dilation_ = _single(dilation)
            super().__init__(
                in_channels, out_channels, kernel_size_, stride_, padding_, dilation_,
                False, _single(0), groups, bias, padding_mode, **factory_kwargs)

        def _conv_forward(self, input: Tensor, weight: Tensor, bias: Optional[Tensor]):
            if self.padding_mode != 'zeros':
                return F.conv1d(F.pad(input, self._reversed_padding_repeated_twice, mode=self.padding_mode),
                                weight, bias, self.stride,
                                _single(0), self.dilation, self.groups)
            return F.conv1d(input, weight, bias, self.stride,
                            self.padding, self.dilation, self.groups)

        def forward(self, input: Tensor) -> Tensor:
            return self._conv_forward(input, self.weight, self.bias)

    class Conv2d(_ConvNd):
        __doc__ = r"""Applies a 2D convolution over an input signal composed of several input
        planes.

        In the simplest case, the output value of the layer with input size
        :math:`(N, C_{\text{in}}, H, W)` and output :math:`(N, C_{\text{out}}, H_{\text{out}}, W_{\text{out}})`
        can be precisely described as:

        .. math::
            \text{out}(N_i, C_{\text{out}_j}) = \text{bias}(C_{\text{out}_j}) +
            \sum_{k = 0}^{C_{\text{in}} - 1} \text{weight}(C_{\text{out}_j}, k) \star \text{input}(N_i, k)

        where :math:`\star` is the valid 2D `cross-correlation`_ operator,
        :math:`N` is a batch size, :math:`C` denotes a number of channels,
        :math:`H` is a height of input planes in pixels, and :math:`W` is
        width in pixels.
        """ + r"""

        This module supports :ref:`TensorFloat32<tf32_on_ampere>`.

        On certain ROCm devices, when using float16 inputs this module will use :ref:`different precision<fp16_on_mi200>` for backward.

        * :attr:`stride` controls the stride for the cross-correlation, a single
          number or a tuple.

        * :attr:`padding` controls the amount of padding applied to the input. It
          can be either a string {{'valid', 'same'}} or an int / a tuple of ints giving the
          amount of implicit padding applied on both sides.

        * :attr:`dilation` controls the spacing between the kernel points; also
          known as the à trous algorithm. It is harder to describe, but this `link`_
          has a nice visualization of what :attr:`dilation` does.

        {groups_note}

        The parameters :attr:`kernel_size`, :attr:`stride`, :attr:`padding`, :attr:`dilation` can either be:

            - a single ``int`` -- in which case the same value is used for the height and width dimension
            - a ``tuple`` of two ints -- in which case, the first `int` is used for the height dimension,
              and the second `int` for the width dimension

        Note:
            {depthwise_separable_note}

        Note:
            {cudnn_reproducibility_note}

        Note:
            ``padding='valid'`` is the same as no padding. ``padding='same'`` pads
            the input so the output has the shape as the input. However, this mode
            doesn't support any stride values other than 1.

        Note:
            This module supports complex data types i.e. ``complex32, complex64, complex128``.

        Args:
            in_channels (int): Number of channels in the input image
            out_channels (int): Number of channels produced by the convolution
            kernel_size (int or tuple): Size of the convolving kernel
            stride (int or tuple, optional): Stride of the convolution. Default: 1
            padding (int, tuple or str, optional): Padding added to all four sides of
                the input. Default: 0
            padding_mode (str, optional): ``'zeros'``, ``'reflect'``,
                ``'replicate'`` or ``'circular'``. Default: ``'zeros'``
            dilation (int or tuple, optional): Spacing between kernel elements. Default: 1
            groups (int, optional): Number of blocked connections from input
                channels to output channels. Default: 1
            bias (bool, optional): If ``True``, adds a learnable bias to the
                output. Default: ``True``
        """.format(**reproducibility_notes, **convolution_notes) + r"""

        Shape:
            - Input: :math:`(N, C_{in}, H_{in}, W_{in})` or :math:`(C_{in}, H_{in}, W_{in})`
            - Output: :math:`(N, C_{out}, H_{out}, W_{out})` or :math:`(C_{out}, H_{out}, W_{out})`, where

              .. math::
                  H_{out} = \left\lfloor\frac{H_{in}  + 2 \times \text{padding}[0] - \text{dilation}[0]
                            \times (\text{kernel\_size}[0] - 1) - 1}{\text{stride}[0]} + 1\right\rfloor

              .. math::
                  W_{out} = \left\lfloor\frac{W_{in}  + 2 \times \text{padding}[1] - \text{dilation}[1]
                            \times (\text{kernel\_size}[1] - 1) - 1}{\text{stride}[1]} + 1\right\rfloor

        Attributes:
            weight (Tensor): the learnable weights of the module of shape
                :math:`(\text{out\_channels}, \frac{\text{in\_channels}}{\text{groups}},`
                :math:`\text{kernel\_size[0]}, \text{kernel\_size[1]})`.
                The values of these weights are sampled from
                :math:`\mathcal{U}(-\sqrt{k}, \sqrt{k})` where
                :math:`k = \frac{groups}{C_\text{in} * \prod_{i=0}^{1}\text{kernel\_size}[i]}`
            bias (Tensor):   the learnable bias of the module of shape
                (out_channels). If :attr:`bias` is ``True``,
                then the values of these weights are
                sampled from :math:`\mathcal{U}(-\sqrt{k}, \sqrt{k})` where
                :math:`k = \frac{groups}{C_\text{in} * \prod_{i=0}^{1}\text{kernel\_size}[i]}`

        Examples:

            >>> # With square kernels and equal stride
            >>> m = nn.Conv2d(16, 33, 3, stride=2)
            >>> # non-square kernels and unequal stride and with padding
            >>> m = nn.Conv2d(16, 33, (3, 5), stride=(2, 1), padding=(4, 2))
            >>> # non-square kernels and unequal stride and with padding and dilation
            >>> m = nn.Conv2d(16, 33, (3, 5), stride=(2, 1), padding=(4, 2), dilation=(3, 1))
            >>> input = torch.randn(20, 16, 50, 100)
            >>> output = m(input)

        .. _cross-correlation:
            https://en.wikipedia.org/wiki/Cross-correlation

        .. _link:
            https://github.com/vdumoulin/conv_arithmetic/blob/master/README.md
        """

        def __init__(
            self,
            in_channels: int,
            out_channels: int,
            kernel_size: _size_2_t,
            stride: _size_2_t = 1,
            padding: Union[str, _size_2_t] = 0,
            dilation: _size_2_t = 1,
            groups: int = 1,
            bias: bool = True,
            padding_mode: str = 'zeros',  # TODO: refine this type
            device=None,
            dtype=None
        ) -> None:
            factory_kwargs = {'device': device, 'dtype': dtype}
            kernel_size_ = _pair(kernel_size)
            stride_ = _pair(stride)
            padding_ = padding if isinstance(padding, str) else _pair(padding)
            dilation_ = _pair(dilation)
            super().__init__(
                in_channels, out_channels, kernel_size_, stride_, padding_, dilation_,
                False, _pair(0), groups, bias, padding_mode, **factory_kwargs)

        def _conv_forward(self, input: Tensor, weight: Tensor, bias: Optional[Tensor]):
            if self.padding_mode != 'zeros':
                return F.conv2d(F.pad(input, self._reversed_padding_repeated_twice, mode=self.padding_mode),
                                weight, bias, self.stride,
                                _pair(0), self.dilation, self.groups)
            return F.conv2d(input, weight, bias, self.stride,
                            self.padding, self.dilation, self.groups)

        def forward(self, input: Tensor) -> Tensor:
            return self._conv_forward(input, self.weight, self.bias)

    class Conv3d(_ConvNd):
        __doc__ = r"""Applies a 3D convolution over an input signal composed of several input
        planes.

        In the simplest case, the output value of the layer with input size :math:`(N, C_{in}, D, H, W)`
        and output :math:`(N, C_{out}, D_{out}, H_{out}, W_{out})` can be precisely described as:

        .. math::
            out(N_i, C_{out_j}) = bias(C_{out_j}) +
                                    \sum_{k = 0}^{C_{in} - 1} weight(C_{out_j}, k) \star input(N_i, k)

        where :math:`\star` is the valid 3D `cross-correlation`_ operator
        """ + r"""

        This module supports :ref:`TensorFloat32<tf32_on_ampere>`.

        On certain ROCm devices, when using float16 inputs this module will use :ref:`different precision<fp16_on_mi200>` for backward.

        * :attr:`stride` controls the stride for the cross-correlation.

        * :attr:`padding` controls the amount of padding applied to the input. It
          can be either a string {{'valid', 'same'}} or a tuple of ints giving the
          amount of implicit padding applied on both sides.

        * :attr:`dilation` controls the spacing between the kernel points; also known as the à trous algorithm.
          It is harder to describe, but this `link`_ has a nice visualization of what :attr:`dilation` does.

        {groups_note}

        The parameters :attr:`kernel_size`, :attr:`stride`, :attr:`padding`, :attr:`dilation` can either be:

            - a single ``int`` -- in which case the same value is used for the depth, height and width dimension
            - a ``tuple`` of three ints -- in which case, the first `int` is used for the depth dimension,
              the second `int` for the height dimension and the third `int` for the width dimension

        Note:
            {depthwise_separable_note}

        Note:
            {cudnn_reproducibility_note}

        Note:
            ``padding='valid'`` is the same as no padding. ``padding='same'`` pads
            the input so the output has the shape as the input. However, this mode
            doesn't support any stride values other than 1.

        Note:
            This module supports complex data types i.e. ``complex32, complex64, complex128``.

        Args:
            in_channels (int): Number of channels in the input image
            out_channels (int): Number of channels produced by the convolution
            kernel_size (int or tuple): Size of the convolving kernel
            stride (int or tuple, optional): Stride of the convolution. Default: 1
            padding (int, tuple or str, optional): Padding added to all six sides of
                the input. Default: 0
            padding_mode (str, optional): ``'zeros'``, ``'reflect'``, ``'replicate'`` or ``'circular'``. Default: ``'zeros'``
            dilation (int or tuple, optional): Spacing between kernel elements. Default: 1
            groups (int, optional): Number of blocked connections from input channels to output channels. Default: 1
            bias (bool, optional): If ``True``, adds a learnable bias to the output. Default: ``True``
        """.format(**reproducibility_notes, **convolution_notes) + r"""

        Shape:
            - Input: :math:`(N, C_{in}, D_{in}, H_{in}, W_{in})` or :math:`(C_{in}, D_{in}, H_{in}, W_{in})`
            - Output: :math:`(N, C_{out}, D_{out}, H_{out}, W_{out})` or :math:`(C_{out}, D_{out}, H_{out}, W_{out})`,
              where

              .. math::
                  D_{out} = \left\lfloor\frac{D_{in} + 2 \times \text{padding}[0] - \text{dilation}[0]
                        \times (\text{kernel\_size}[0] - 1) - 1}{\text{stride}[0]} + 1\right\rfloor

              .. math::
                  H_{out} = \left\lfloor\frac{H_{in} + 2 \times \text{padding}[1] - \text{dilation}[1]
                        \times (\text{kernel\_size}[1] - 1) - 1}{\text{stride}[1]} + 1\right\rfloor

              .. math::
                  W_{out} = \left\lfloor\frac{W_{in} + 2 \times \text{padding}[2] - \text{dilation}[2]
                        \times (\text{kernel\_size}[2] - 1) - 1}{\text{stride}[2]} + 1\right\rfloor

        Attributes:
            weight (Tensor): the learnable weights of the module of shape
                             :math:`(\text{out\_channels}, \frac{\text{in\_channels}}{\text{groups}},`
                             :math:`\text{kernel\_size[0]}, \text{kernel\_size[1]}, \text{kernel\_size[2]})`.
                             The values of these weights are sampled from
                             :math:`\mathcal{U}(-\sqrt{k}, \sqrt{k})` where
                             :math:`k = \frac{groups}{C_\text{in} * \prod_{i=0}^{2}\text{kernel\_size}[i]}`
            bias (Tensor):   the learnable bias of the module of shape (out_channels). If :attr:`bias` is ``True``,
                             then the values of these weights are
                             sampled from :math:`\mathcal{U}(-\sqrt{k}, \sqrt{k})` where
                             :math:`k = \frac{groups}{C_\text{in} * \prod_{i=0}^{2}\text{kernel\_size}[i]}`

        Examples::

            >>> # With square kernels and equal stride
            >>> m = nn.Conv3d(16, 33, 3, stride=2)
            >>> # non-square kernels and unequal stride and with padding
            >>> m = nn.Conv3d(16, 33, (3, 5, 2), stride=(2, 1, 1), padding=(4, 2, 0))
            >>> input = torch.randn(20, 16, 10, 50, 100)
            >>> output = m(input)

        .. _cross-correlation:
            https://en.wikipedia.org/wiki/Cross-correlation

        .. _link:
            https://github.com/vdumoulin/conv_arithmetic/blob/master/README.md
        """

        def __init__(
            self,
            in_channels: int,
            out_channels: int,
            kernel_size: _size_3_t,
            stride: _size_3_t = 1,
            padding: Union[str, _size_3_t] = 0,
            dilation: _size_3_t = 1,
            groups: int = 1,
            bias: bool = True,
            padding_mode: str = 'zeros',
            device=None,
            dtype=None
        ) -> None:
            factory_kwargs = {'device': device, 'dtype': dtype}
            kernel_size_ = _triple(kernel_size)
            stride_ = _triple(stride)
            padding_ = padding if isinstance(padding, str) else _triple(padding)
            dilation_ = _triple(dilation)
            super().__init__(
                in_channels, out_channels, kernel_size_, stride_, padding_, dilation_,
                False, _triple(0), groups, bias, padding_mode, **factory_kwargs)

        def _conv_forward(self, input: Tensor, weight: Tensor, bias: Optional[Tensor]):
            if self.padding_mode != "zeros":
                return F.conv3d(
                    F.pad(
                        input, self._reversed_padding_repeated_twice, mode=self.padding_mode
                    ),
                    weight,
                    bias,
                    self.stride,
                    _triple(0),
                    self.dilation,
                    self.groups,
                )
            return F.conv3d(
                input, weight, bias, self.stride, self.padding, self.dilation, self.groups
            )

        def forward(self, input: Tensor) -> Tensor:
            return self._conv_forward(input, self.weight, self.bias)

    class _ConvTransposeNd(_ConvNd):
        def __init__(self, in_channels, out_channels, kernel_size, stride,
                     padding, dilation, transposed, output_padding,
                     groups, bias, padding_mode, device=None, dtype=None) -> None:
            if padding_mode != 'zeros':
                raise ValueError(f'Only "zeros" padding mode is supported for {self.__class__.__name__}')

            factory_kwargs = {'device': device, 'dtype': dtype}
            super().__init__(
                in_channels, out_channels, kernel_size, stride,
                padding, dilation, transposed, output_padding,
                groups, bias, padding_mode, **factory_kwargs)

        # dilation being an optional parameter is for backwards
        # compatibility
        def _output_padding(self, input: Tensor, output_size: Optional[List[int]],
                            stride: List[int], padding: List[int], kernel_size: List[int],
                            num_spatial_dims: int, dilation: Optional[List[int]] = None) -> List[int]:
            if output_size is None:
                ret = _single(self.output_padding)  # converting to list if was not already
            else:
                has_batch_dim = input.dim() == num_spatial_dims + 2
                num_non_spatial_dims = 2 if has_batch_dim else 1
                if len(output_size) == num_non_spatial_dims + num_spatial_dims:
                    output_size = output_size[num_non_spatial_dims:]
                if len(output_size) != num_spatial_dims:
                    raise ValueError(
                        "ConvTranspose{}D: for {}D input, output_size must have {} or {} elements (got {})"
                        .format(num_spatial_dims, input.dim(), num_spatial_dims,
                                num_non_spatial_dims + num_spatial_dims, len(output_size)))

                min_sizes = torch.jit.annotate(List[int], [])
                max_sizes = torch.jit.annotate(List[int], [])
                for d in range(num_spatial_dims):
                    dim_size = ((input.size(d + num_non_spatial_dims) - 1) * stride[d] -
                                2 * padding[d] +
                                (dilation[d] if dilation is not None else 1) * (kernel_size[d] - 1) + 1)
                    min_sizes.append(dim_size)
                    max_sizes.append(min_sizes[d] + stride[d] - 1)

                for i in range(len(output_size)):
                    size = output_size[i]
                    min_size = min_sizes[i]
                    max_size = max_sizes[i]
                    if size < min_size or size > max_size:
                        raise ValueError(
                            f"requested an output size of {output_size}, but valid sizes range "
                            f"from {min_sizes} to {max_sizes} (for an input of {input.size()[2:]})")

                res = torch.jit.annotate(List[int], [])
                for d in range(num_spatial_dims):
                    res.append(output_size[d] - min_sizes[d])

                ret = res
            return ret

    class ConvTranspose1d(_ConvTransposeNd):
        __doc__ = r"""Applies a 1D transposed convolution operator over an input image
        composed of several input planes.

        This module can be seen as the gradient of Conv1d with respect to its input.
        It is also known as a fractionally-strided convolution or
        a deconvolution (although it is not an actual deconvolution operation as it does
        not compute a true inverse of convolution). For more information, see the visualizations
        `here`_ and the `Deconvolutional Networks`_ paper.

        This module supports :ref:`TensorFloat32<tf32_on_ampere>`.

        On certain ROCm devices, when using float16 inputs this module will use :ref:`different precision<fp16_on_mi200>` for backward.

        * :attr:`stride` controls the stride for the cross-correlation.

        * :attr:`padding` controls the amount of implicit zero padding on both
          sides for ``dilation * (kernel_size - 1) - padding`` number of points. See note
          below for details.

        * :attr:`output_padding` controls the additional size added to one side
          of the output shape. See note below for details.

        * :attr:`dilation` controls the spacing between the kernel points; also known as the à trous algorithm.
          It is harder to describe, but the link `here`_ has a nice visualization of what :attr:`dilation` does.

        {groups_note}

        Note:
            The :attr:`padding` argument effectively adds ``dilation * (kernel_size - 1) - padding``
            amount of zero padding to both sizes of the input. This is set so that
            when a :class:`~torch.nn.Conv1d` and a :class:`~torch.nn.ConvTranspose1d`
            are initialized with same parameters, they are inverses of each other in
            regard to the input and output shapes. However, when ``stride > 1``,
            :class:`~torch.nn.Conv1d` maps multiple input shapes to the same output
            shape. :attr:`output_padding` is provided to resolve this ambiguity by
            effectively increasing the calculated output shape on one side. Note
            that :attr:`output_padding` is only used to find output shape, but does
            not actually add zero-padding to output.

        Note:
            In some circumstances when using the CUDA backend with CuDNN, this operator
            may select a nondeterministic algorithm to increase performance. If this is
            undesirable, you can try to make the operation deterministic (potentially at
            a performance cost) by setting ``torch.backends.cudnn.deterministic =
            True``.
            Please see the notes on :doc:`/notes/randomness` for background.

        Args:
            in_channels (int): Number of channels in the input image
            out_channels (int): Number of channels produced by the convolution
            kernel_size (int or tuple): Size of the convolving kernel
            stride (int or tuple, optional): Stride of the convolution. Default: 1
            padding (int or tuple, optional): ``dilation * (kernel_size - 1) - padding`` zero-padding
                will be added to both sides of the input. Default: 0
            output_padding (int or tuple, optional): Additional size added to one side
                of the output shape. Default: 0
            groups (int, optional): Number of blocked connections from input channels to output channels. Default: 1
            bias (bool, optional): If ``True``, adds a learnable bias to the output. Default: ``True``
            dilation (int or tuple, optional): Spacing between kernel elements. Default: 1
        """.format(**reproducibility_notes, **convolution_notes) + r"""

        Shape:
            - Input: :math:`(N, C_{in}, L_{in})` or :math:`(C_{in}, L_{in})`
            - Output: :math:`(N, C_{out}, L_{out})` or :math:`(C_{out}, L_{out})`, where

              .. math::
                  L_{out} = (L_{in} - 1) \times \text{stride} - 2 \times \text{padding} + \text{dilation}
                            \times (\text{kernel\_size} - 1) + \text{output\_padding} + 1

        Attributes:
            weight (Tensor): the learnable weights of the module of shape
                             :math:`(\text{in\_channels}, \frac{\text{out\_channels}}{\text{groups}},`
                             :math:`\text{kernel\_size})`.
                             The values of these weights are sampled from
                             :math:`\mathcal{U}(-\sqrt{k}, \sqrt{k})` where
                             :math:`k = \frac{groups}{C_\text{out} * \text{kernel\_size}}`
            bias (Tensor):   the learnable bias of the module of shape (out_channels).
                             If :attr:`bias` is ``True``, then the values of these weights are
                             sampled from :math:`\mathcal{U}(-\sqrt{k}, \sqrt{k})` where
                             :math:`k = \frac{groups}{C_\text{out} * \text{kernel\_size}}`

        .. _`here`:
            https://github.com/vdumoulin/conv_arithmetic/blob/master/README.md

        .. _`Deconvolutional Networks`:
            https://www.matthewzeiler.com/mattzeiler/deconvolutionalnetworks.pdf
        """

        def __init__(
            self,
            in_channels: int,
            out_channels: int,
            kernel_size: _size_1_t,
            stride: _size_1_t = 1,
            padding: _size_1_t = 0,
            output_padding: _size_1_t = 0,
            groups: int = 1,
            bias: bool = True,
            dilation: _size_1_t = 1,
            padding_mode: str = 'zeros',
            device=None,
            dtype=None
        ) -> None:
            factory_kwargs = {'device': device, 'dtype': dtype}
            kernel_size = _single(kernel_size)
            stride = _single(stride)
            padding = _single(padding)
            dilation = _single(dilation)
            output_padding = _single(output_padding)
            super().__init__(
                in_channels, out_channels, kernel_size, stride, padding, dilation,
                True, output_padding, groups, bias, padding_mode, **factory_kwargs)

        def forward(self, input: Tensor, output_size: Optional[List[int]] = None) -> Tensor:
            if self.padding_mode != 'zeros':
                raise ValueError('Only `zeros` padding mode is supported for ConvTranspose1d')

            assert isinstance(self.padding, tuple)
            # One cannot replace List by Tuple or Sequence in "_output_padding" because
            # TorchScript does not support `Sequence[T]` or `Tuple[T, ...]`.
            num_spatial_dims = 1
            output_padding = self._output_padding(
                input, output_size, self.stride, self.padding, self.kernel_size,  # type: ignore[arg-type]
                num_spatial_dims, self.dilation)  # type: ignore[arg-type]
            return F.conv_transpose1d(
                input, self.weight, self.bias, self.stride, self.padding,
                output_padding, self.groups, self.dilation)

    class ConvTranspose2d(_ConvTransposeNd):
        __doc__ = r"""Applies a 2D transposed convolution operator over an input image
        composed of several input planes.

        This module can be seen as the gradient of Conv2d with respect to its input.
        It is also known as a fractionally-strided convolution or
        a deconvolution (although it is not an actual deconvolution operation as it does
        not compute a true inverse of convolution). For more information, see the visualizations
        `here`_ and the `Deconvolutional Networks`_ paper.

        This module supports :ref:`TensorFloat32<tf32_on_ampere>`.

        On certain ROCm devices, when using float16 inputs this module will use :ref:`different precision<fp16_on_mi200>` for backward.

        * :attr:`stride` controls the stride for the cross-correlation.

        * :attr:`padding` controls the amount of implicit zero padding on both
          sides for ``dilation * (kernel_size - 1) - padding`` number of points. See note
          below for details.

        * :attr:`output_padding` controls the additional size added to one side
          of the output shape. See note below for details.

        * :attr:`dilation` controls the spacing between the kernel points; also known as the à trous algorithm.
          It is harder to describe, but the link `here`_ has a nice visualization of what :attr:`dilation` does.

        {groups_note}

        The parameters :attr:`kernel_size`, :attr:`stride`, :attr:`padding`, :attr:`output_padding`
        can either be:

            - a single ``int`` -- in which case the same value is used for the height and width dimensions
            - a ``tuple`` of two ints -- in which case, the first `int` is used for the height dimension,
              and the second `int` for the width dimension

        Note:
            The :attr:`padding` argument effectively adds ``dilation * (kernel_size - 1) - padding``
            amount of zero padding to both sizes of the input. This is set so that
            when a :class:`~torch.nn.Conv2d` and a :class:`~torch.nn.ConvTranspose2d`
            are initialized with same parameters, they are inverses of each other in
            regard to the input and output shapes. However, when ``stride > 1``,
            :class:`~torch.nn.Conv2d` maps multiple input shapes to the same output
            shape. :attr:`output_padding` is provided to resolve this ambiguity by
            effectively increasing the calculated output shape on one side. Note
            that :attr:`output_padding` is only used to find output shape, but does
            not actually add zero-padding to output.

        Note:
            {cudnn_reproducibility_note}

        Args:
            in_channels (int): Number of channels in the input image
            out_channels (int): Number of channels produced by the convolution
            kernel_size (int or tuple): Size of the convolving kernel
            stride (int or tuple, optional): Stride of the convolution. Default: 1
            padding (int or tuple, optional): ``dilation * (kernel_size - 1) - padding`` zero-padding
                will be added to both sides of each dimension in the input. Default: 0
            output_padding (int or tuple, optional): Additional size added to one side
                of each dimension in the output shape. Default: 0
            groups (int, optional): Number of blocked connections from input channels to output channels. Default: 1
            bias (bool, optional): If ``True``, adds a learnable bias to the output. Default: ``True``
            dilation (int or tuple, optional): Spacing between kernel elements. Default: 1
        """.format(**reproducibility_notes, **convolution_notes) + r"""

        Shape:
            - Input: :math:`(N, C_{in}, H_{in}, W_{in})` or :math:`(C_{in}, H_{in}, W_{in})`
            - Output: :math:`(N, C_{out}, H_{out}, W_{out})` or :math:`(C_{out}, H_{out}, W_{out})`, where

            .. math::
                  H_{out} = (H_{in} - 1) \times \text{stride}[0] - 2 \times \text{padding}[0] + \text{dilation}[0]
                            \times (\text{kernel\_size}[0] - 1) + \text{output\_padding}[0] + 1
            .. math::
                  W_{out} = (W_{in} - 1) \times \text{stride}[1] - 2 \times \text{padding}[1] + \text{dilation}[1]
                            \times (\text{kernel\_size}[1] - 1) + \text{output\_padding}[1] + 1

        Attributes:
            weight (Tensor): the learnable weights of the module of shape
                             :math:`(\text{in\_channels}, \frac{\text{out\_channels}}{\text{groups}},`
                             :math:`\text{kernel\_size[0]}, \text{kernel\_size[1]})`.
                             The values of these weights are sampled from
                             :math:`\mathcal{U}(-\sqrt{k}, \sqrt{k})` where
                             :math:`k = \frac{groups}{C_\text{out} * \prod_{i=0}^{1}\text{kernel\_size}[i]}`
            bias (Tensor):   the learnable bias of the module of shape (out_channels)
                             If :attr:`bias` is ``True``, then the values of these weights are
                             sampled from :math:`\mathcal{U}(-\sqrt{k}, \sqrt{k})` where
                             :math:`k = \frac{groups}{C_\text{out} * \prod_{i=0}^{1}\text{kernel\_size}[i]}`

        Examples::

            >>> # With square kernels and equal stride
            >>> m = nn.ConvTranspose2d(16, 33, 3, stride=2)
            >>> # non-square kernels and unequal stride and with padding
            >>> m = nn.ConvTranspose2d(16, 33, (3, 5), stride=(2, 1), padding=(4, 2))
            >>> input = torch.randn(20, 16, 50, 100)
            >>> output = m(input)
            >>> # exact output size can be also specified as an argument
            >>> input = torch.randn(1, 16, 12, 12)
            >>> downsample = nn.Conv2d(16, 16, 3, stride=2, padding=1)
            >>> upsample = nn.ConvTranspose2d(16, 16, 3, stride=2, padding=1)
            >>> h = downsample(input)
            >>> h.size()
            torch.Size([1, 16, 6, 6])
            >>> output = upsample(h, output_size=input.size())
            >>> output.size()
            torch.Size([1, 16, 12, 12])

        .. _`here`:
            https://github.com/vdumoulin/conv_arithmetic/blob/master/README.md

        .. _`Deconvolutional Networks`:
            https://www.matthewzeiler.com/mattzeiler/deconvolutionalnetworks.pdf
        """

        def __init__(
            self,
            in_channels: int,
            out_channels: int,
            kernel_size: _size_2_t,
            stride: _size_2_t = 1,
            padding: _size_2_t = 0,
            output_padding: _size_2_t = 0,
            groups: int = 1,
            bias: bool = True,
            dilation: _size_2_t = 1,
            padding_mode: str = 'zeros',
            device=None,
            dtype=None
        ) -> None:
            factory_kwargs = {'device': device, 'dtype': dtype}
            kernel_size = _pair(kernel_size)
            stride = _pair(stride)
            padding = _pair(padding)
            dilation = _pair(dilation)
            output_padding = _pair(output_padding)
            super().__init__(
                in_channels, out_channels, kernel_size, stride, padding, dilation,
                True, output_padding, groups, bias, padding_mode, **factory_kwargs)

        def forward(self, input: Tensor, output_size: Optional[List[int]] = None) -> Tensor:
            if self.padding_mode != 'zeros':
                raise ValueError('Only `zeros` padding mode is supported for ConvTranspose2d')

            assert isinstance(self.padding, tuple)
            # One cannot replace List by Tuple or Sequence in "_output_padding" because
            # TorchScript does not support `Sequence[T]` or `Tuple[T, ...]`.
            num_spatial_dims = 2
            output_padding = self._output_padding(
                input, output_size, self.stride, self.padding, self.kernel_size,  # type: ignore[arg-type]
                num_spatial_dims, self.dilation)  # type: ignore[arg-type]

            return F.conv_transpose2d(
                input, self.weight, self.bias, self.stride, self.padding,
                output_padding, self.groups, self.dilation)

    class ConvTranspose3d(_ConvTransposeNd):
        __doc__ = r"""Applies a 3D transposed convolution operator over an input image composed of several input
        planes.
        The transposed convolution operator multiplies each input value element-wise by a learnable kernel,
        and sums over the outputs from all input feature planes.

        This module can be seen as the gradient of Conv3d with respect to its input.
        It is also known as a fractionally-strided convolution or
        a deconvolution (although it is not an actual deconvolution operation as it does
        not compute a true inverse of convolution). For more information, see the visualizations
        `here`_ and the `Deconvolutional Networks`_ paper.

        This module supports :ref:`TensorFloat32<tf32_on_ampere>`.

        On certain ROCm devices, when using float16 inputs this module will use :ref:`different precision<fp16_on_mi200>` for backward.

        * :attr:`stride` controls the stride for the cross-correlation.

        * :attr:`padding` controls the amount of implicit zero padding on both
          sides for ``dilation * (kernel_size - 1) - padding`` number of points. See note
          below for details.

        * :attr:`output_padding` controls the additional size added to one side
          of the output shape. See note below for details.

        * :attr:`dilation` controls the spacing between the kernel points; also known as the à trous algorithm.
          It is harder to describe, but the link `here`_ has a nice visualization of what :attr:`dilation` does.

        {groups_note}

        The parameters :attr:`kernel_size`, :attr:`stride`, :attr:`padding`, :attr:`output_padding`
        can either be:

            - a single ``int`` -- in which case the same value is used for the depth, height and width dimensions
            - a ``tuple`` of three ints -- in which case, the first `int` is used for the depth dimension,
              the second `int` for the height dimension and the third `int` for the width dimension

        Note:
            The :attr:`padding` argument effectively adds ``dilation * (kernel_size - 1) - padding``
            amount of zero padding to both sizes of the input. This is set so that
            when a :class:`~torch.nn.Conv3d` and a :class:`~torch.nn.ConvTranspose3d`
            are initialized with same parameters, they are inverses of each other in
            regard to the input and output shapes. However, when ``stride > 1``,
            :class:`~torch.nn.Conv3d` maps multiple input shapes to the same output
            shape. :attr:`output_padding` is provided to resolve this ambiguity by
            effectively increasing the calculated output shape on one side. Note
            that :attr:`output_padding` is only used to find output shape, but does
            not actually add zero-padding to output.

        Note:
            {cudnn_reproducibility_note}

        Args:
            in_channels (int): Number of channels in the input image
            out_channels (int): Number of channels produced by the convolution
            kernel_size (int or tuple): Size of the convolving kernel
            stride (int or tuple, optional): Stride of the convolution. Default: 1
            padding (int or tuple, optional): ``dilation * (kernel_size - 1) - padding`` zero-padding
                will be added to both sides of each dimension in the input. Default: 0
            output_padding (int or tuple, optional): Additional size added to one side
                of each dimension in the output shape. Default: 0
            groups (int, optional): Number of blocked connections from input channels to output channels. Default: 1
            bias (bool, optional): If ``True``, adds a learnable bias to the output. Default: ``True``
            dilation (int or tuple, optional): Spacing between kernel elements. Default: 1
        """.format(**reproducibility_notes, **convolution_notes) + r"""

        Shape:
            - Input: :math:`(N, C_{in}, D_{in}, H_{in}, W_{in})` or :math:`(C_{in}, D_{in}, H_{in}, W_{in})`
            - Output: :math:`(N, C_{out}, D_{out}, H_{out}, W_{out})` or
              :math:`(C_{out}, D_{out}, H_{out}, W_{out})`, where

            .. math::
                  D_{out} = (D_{in} - 1) \times \text{stride}[0] - 2 \times \text{padding}[0] + \text{dilation}[0]
                            \times (\text{kernel\_size}[0] - 1) + \text{output\_padding}[0] + 1
            .. math::
                  H_{out} = (H_{in} - 1) \times \text{stride}[1] - 2 \times \text{padding}[1] + \text{dilation}[1]
                            \times (\text{kernel\_size}[1] - 1) + \text{output\_padding}[1] + 1
            .. math::
                  W_{out} = (W_{in} - 1) \times \text{stride}[2] - 2 \times \text{padding}[2] + \text{dilation}[2]
                            \times (\text{kernel\_size}[2] - 1) + \text{output\_padding}[2] + 1

        Attributes:
            weight (Tensor): the learnable weights of the module of shape
                             :math:`(\text{in\_channels}, \frac{\text{out\_channels}}{\text{groups}},`
                             :math:`\text{kernel\_size[0]}, \text{kernel\_size[1]}, \text{kernel\_size[2]})`.
                             The values of these weights are sampled from
                             :math:`\mathcal{U}(-\sqrt{k}, \sqrt{k})` where
                             :math:`k = \frac{groups}{C_\text{out} * \prod_{i=0}^{2}\text{kernel\_size}[i]}`
            bias (Tensor):   the learnable bias of the module of shape (out_channels)
                             If :attr:`bias` is ``True``, then the values of these weights are
                             sampled from :math:`\mathcal{U}(-\sqrt{k}, \sqrt{k})` where
                             :math:`k = \frac{groups}{C_\text{out} * \prod_{i=0}^{2}\text{kernel\_size}[i]}`

        Examples::

            >>> # With square kernels and equal stride
            >>> m = nn.ConvTranspose3d(16, 33, 3, stride=2)
            >>> # non-square kernels and unequal stride and with padding
            >>> m = nn.ConvTranspose3d(16, 33, (3, 5, 2), stride=(2, 1, 1), padding=(0, 4, 2))
            >>> input = torch.randn(20, 16, 10, 50, 100)
            >>> output = m(input)

        .. _`here`:
            https://github.com/vdumoulin/conv_arithmetic/blob/master/README.md

        .. _`Deconvolutional Networks`:
            https://www.matthewzeiler.com/mattzeiler/deconvolutionalnetworks.pdf
        """

        def __init__(
            self,
            in_channels: int,
            out_channels: int,
            kernel_size: _size_3_t,
            stride: _size_3_t = 1,
            padding: _size_3_t = 0,
            output_padding: _size_3_t = 0,
            groups: int = 1,
            bias: bool = True,
            dilation: _size_3_t = 1,
            padding_mode: str = 'zeros',
            device=None,
            dtype=None
        ) -> None:
            factory_kwargs = {'device': device, 'dtype': dtype}
            kernel_size = _triple(kernel_size)
            stride = _triple(stride)
            padding = _triple(padding)
            dilation = _triple(dilation)
            output_padding = _triple(output_padding)
            super().__init__(
                in_channels, out_channels, kernel_size, stride, padding, dilation,
                True, output_padding, groups, bias, padding_mode, **factory_kwargs)

        def forward(self, input: Tensor, output_size: Optional[List[int]] = None) -> Tensor:
            if self.padding_mode != 'zeros':
                raise ValueError('Only `zeros` padding mode is supported for ConvTranspose3d')

            assert isinstance(self.padding, tuple)
            # One cannot replace List by Tuple or Sequence in "_output_padding" because
            # TorchScript does not support `Sequence[T]` or `Tuple[T, ...]`.
            num_spatial_dims = 3
            output_padding = self._output_padding(
                input, output_size, self.stride, self.padding, self.kernel_size,  # type: ignore[arg-type]
                num_spatial_dims, self.dilation)  # type: ignore[arg-type]

            return F.conv_transpose3d(
                input, self.weight, self.bias, self.stride, self.padding,
                output_padding, self.groups, self.dilation)

    # TODO: Deprecate and remove the following alias `_ConvTransposeMixin`.
    #
    # `_ConvTransposeMixin` was a mixin that was removed.  It is meant to be used
    # with `_ConvNd` to construct actual module classes that implements conv
    # transpose ops:
    #
    #   class MyConvTranspose(_ConvNd, _ConvTransposeMixin):
    #       ...
    #
    # In PyTorch, it has been replaced by `_ConvTransposeNd`, which is a proper
    # subclass of `_ConvNd`.  However, some user code in the wild still (incorrectly)
    # use the internal class `_ConvTransposeMixin`.  Hence, we provide this alias
    # for BC, because it is cheap and easy for us to do so, even though that
    # `_ConvTransposeNd` is really not a mixin anymore (but multiple inheritance as
    # above would still work).
    class _ConvTransposeMixin(_ConvTransposeNd):
        def __init__(self, *args, **kwargs):
            warnings.warn(
                "_ConvTransposeMixin is a deprecated internal class. "
                "Please consider using public APIs.")
            super().__init__(*args, **kwargs)

    # TODO: Conv2dLocal
    # TODO: Conv2dMap
    # TODO: ConvTranspose2dMap

    class _LazyConvXdMixin(LazyModuleMixin):
        groups: int
        transposed: bool
        in_channels: int
        out_channels: int
        kernel_size: Tuple[int, ...]
        weight: UninitializedParameter
        bias: UninitializedParameter

        def reset_parameters(self) -> None:
            # has_uninitialized_params is defined in parent class and it is using a protocol on self
            if not self.has_uninitialized_params() and self.in_channels != 0:  # type: ignore[misc]
                # "type:ignore[..]" is required because mypy thinks that "reset_parameters" is undefined
                # in super class. Turns out that it is defined in _ConvND which is inherited by any class
                # that also inherits _LazyConvXdMixin
                super().reset_parameters()  # type: ignore[misc]

        # Signature of "initialize_parameters" is incompatible with the definition in supertype LazyModuleMixin
        def initialize_parameters(self, input) -> None:  # type: ignore[override]
            # defined by parent class but using a protocol
            if self.has_uninitialized_params():  # type: ignore[misc]
                self.in_channels = self._get_in_channels(input)
                if self.in_channels % self.groups != 0:
                    raise ValueError('in_channels must be divisible by groups')
                assert isinstance(self.weight, UninitializedParameter)
                if self.transposed:
                    self.weight.materialize((
                        self.in_channels, self.out_channels // self.groups, *self.kernel_size))
                else:
                    self.weight.materialize((
                        self.out_channels, self.in_channels // self.groups, *self.kernel_size))
                if self.bias is not None:
                    assert isinstance(self.bias, UninitializedParameter)
                    self.bias.materialize((self.out_channels,))
                self.reset_parameters()

        # Function to extract in_channels from first input.
        def _get_in_channels(self, input: Tensor) -> int:
            num_spatial_dims = self._get_num_spatial_dims()
            num_dims_no_batch = num_spatial_dims + 1  # +1 for channels dim
            num_dims_batch = num_dims_no_batch + 1
            if input.dim() not in (num_dims_no_batch, num_dims_batch):
                raise RuntimeError("Expected {}D (unbatched) or {}D (batched) input to {}, but "
                                   "got input of size: {}".format(num_dims_no_batch, num_dims_batch,
                                                                  self.__class__.__name__, input.shape))
            return input.shape[1] if input.dim() == num_dims_batch else input.shape[0]

        # Function to return the number of spatial dims expected for inputs to the module.
        # This is expected to be implemented by subclasses.
        def _get_num_spatial_dims(self) -> int:
            raise NotImplementedError()

    # LazyConv1d defines weight as a Tensor but derived class defines it as UnitializeParameter
    class LazyConv1d(_LazyConvXdMixin, Conv1d):  # type: ignore[misc]
        r"""A :class:`torch.nn.Conv1d` module with lazy initialization of
        the ``in_channels`` argument of the :class:`Conv1d` that is inferred from
        the ``input.size(1)``.
        The attributes that will be lazily initialized are `weight` and `bias`.

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

        Args:
            out_channels (int): Number of channels produced by the convolution
            kernel_size (int or tuple): Size of the convolving kernel
            stride (int or tuple, optional): Stride of the convolution. Default: 1
            padding (int or tuple, optional): Zero-padding added to both sides of
                the input. Default: 0
            padding_mode (str, optional): ``'zeros'``, ``'reflect'``,
                ``'replicate'`` or ``'circular'``. Default: ``'zeros'``
            dilation (int or tuple, optional): Spacing between kernel
                elements. Default: 1
            groups (int, optional): Number of blocked connections from input
                channels to output channels. Default: 1
            bias (bool, optional): If ``True``, adds a learnable bias to the
                output. Default: ``True``

        .. seealso:: :class:`torch.nn.Conv1d` and :class:`torch.nn.modules.lazy.LazyModuleMixin`
        """

        # super class define this variable as None. "type: ignore[..] is required
        # since we are redefining the variable.
        cls_to_become = Conv1d  # type: ignore[assignment]

        def __init__(
            self,
            out_channels: int,
            kernel_size: _size_1_t,
            stride: _size_1_t = 1,
            padding: _size_1_t = 0,
            dilation: _size_1_t = 1,
            groups: int = 1,
            bias: bool = True,
            padding_mode: str = 'zeros',
            device=None,
            dtype=None
        ) -> None:
            factory_kwargs = {'device': device, 'dtype': dtype}
            super().__init__(
                0,
                0,
                kernel_size,
                stride,
                padding,
                dilation,
                groups,
                # bias is hardcoded to False to avoid creating tensor
                # that will soon be overwritten.
                False,
                padding_mode,
                **factory_kwargs
            )
            self.weight = UninitializedParameter(**factory_kwargs)
            self.out_channels = out_channels
            if bias:
                self.bias = UninitializedParameter(**factory_kwargs)

        def _get_num_spatial_dims(self) -> int:
            return 1

    # LazyConv2d defines weight as a Tensor but derived class defines it as UnitializeParameter
    class LazyConv2d(_LazyConvXdMixin, Conv2d):  # type: ignore[misc]
        r"""A :class:`torch.nn.Conv2d` module with lazy initialization of
        the ``in_channels`` argument of the :class:`Conv2d` that is inferred from
        the ``input.size(1)``.
        The attributes that will be lazily initialized are `weight` and `bias`.

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

        Args:
            out_channels (int): Number of channels produced by the convolution
            kernel_size (int or tuple): Size of the convolving kernel
            stride (int or tuple, optional): Stride of the convolution. Default: 1
            padding (int or tuple, optional): Zero-padding added to both sides of
                the input. Default: 0
            padding_mode (str, optional): ``'zeros'``, ``'reflect'``,
                ``'replicate'`` or ``'circular'``. Default: ``'zeros'``
            dilation (int or tuple, optional): Spacing between kernel
                elements. Default: 1
            groups (int, optional): Number of blocked connections from input
                channels to output channels. Default: 1
            bias (bool, optional): If ``True``, adds a learnable bias to the
                output. Default: ``True``

        .. seealso:: :class:`torch.nn.Conv2d` and :class:`torch.nn.modules.lazy.LazyModuleMixin`
        """

        # super class define this variable as None. "type: ignore[..] is required
        # since we are redefining the variable.
        cls_to_become = Conv2d  # type: ignore[assignment]

        def __init__(
            self,
            out_channels: int,
            kernel_size: _size_2_t,
            stride: _size_2_t = 1,
            padding: _size_2_t = 0,
            dilation: _size_2_t = 1,
            groups: int = 1,
            bias: bool = True,
            padding_mode: str = 'zeros',  # TODO: refine this type
            device=None,
            dtype=None
        ) -> None:
            factory_kwargs = {'device': device, 'dtype': dtype}
            super().__init__(
                0,
                0,
                kernel_size,
                stride,
                padding,
                dilation,
                groups,
                # bias is hardcoded to False to avoid creating tensor
                # that will soon be overwritten.
                False,
                padding_mode,
                **factory_kwargs
            )
            self.weight = UninitializedParameter(**factory_kwargs)
            self.out_channels = out_channels
            if bias:
                self.bias = UninitializedParameter(**factory_kwargs)

        def _get_num_spatial_dims(self) -> int:
            return 2

    # LazyConv3d defines weight as a Tensor but derived class defines it as UnitializeParameter
    class LazyConv3d(_LazyConvXdMixin, Conv3d):  # type: ignore[misc]
        r"""A :class:`torch.nn.Conv3d` module with lazy initialization of
        the ``in_channels`` argument of the :class:`Conv3d` that is inferred from
        the ``input.size(1)``.
        The attributes that will be lazily initialized are `weight` and `bias`.

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

        Args:
            out_channels (int): Number of channels produced by the convolution
            kernel_size (int or tuple): Size of the convolving kernel
            stride (int or tuple, optional): Stride of the convolution. Default: 1
            padding (int or tuple, optional): Zero-padding added to both sides of
                the input. Default: 0
            padding_mode (str, optional): ``'zeros'``, ``'reflect'``,
                ``'replicate'`` or ``'circular'``. Default: ``'zeros'``
            dilation (int or tuple, optional): Spacing between kernel
                elements. Default: 1
            groups (int, optional): Number of blocked connections from input
                channels to output channels. Default: 1
            bias (bool, optional): If ``True``, adds a learnable bias to the
                output. Default: ``True``

        .. seealso:: :class:`torch.nn.Conv3d` and :class:`torch.nn.modules.lazy.LazyModuleMixin`
        """

        # super class define this variable as None. "type: ignore[..] is required
        # since we are redefining the variable.
        cls_to_become = Conv3d  # type: ignore[assignment]

        def __init__(
            self,
            out_channels: int,
            kernel_size: _size_3_t,
            stride: _size_3_t = 1,
            padding: _size_3_t = 0,
            dilation: _size_3_t = 1,
            groups: int = 1,
            bias: bool = True,
            padding_mode: str = 'zeros',
            device=None,
            dtype=None
        ) -> None:
            factory_kwargs = {'device': device, 'dtype': dtype}
            super().__init__(
                0,
                0,
                kernel_size,
                stride,
                padding,
                dilation,
                groups,
                # bias is hardcoded to False to avoid creating tensor
                # that will soon be overwritten.
                False,
                padding_mode,
                **factory_kwargs
            )
            self.weight = UninitializedParameter(**factory_kwargs)
            self.out_channels = out_channels
            if bias:
                self.bias = UninitializedParameter(**factory_kwargs)

        def _get_num_spatial_dims(self) -> int:
            return 3

    # LazyConvTranspose1d defines weight as a Tensor but derived class defines it as UnitializeParameter
    class LazyConvTranspose1d(_LazyConvXdMixin, ConvTranspose1d):  # type: ignore[misc]
        r"""A :class:`torch.nn.ConvTranspose1d` module with lazy initialization of
        the ``in_channels`` argument of the :class:`ConvTranspose1d` that is inferred from
        the ``input.size(1)``.
        The attributes that will be lazily initialized are `weight` and `bias`.

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

        Args:
            out_channels (int): Number of channels produced by the convolution
            kernel_size (int or tuple): Size of the convolving kernel
            stride (int or tuple, optional): Stride of the convolution. Default: 1
            padding (int or tuple, optional): ``dilation * (kernel_size - 1) - padding`` zero-padding
                will be added to both sides of the input. Default: 0
            output_padding (int or tuple, optional): Additional size added to one side
                of the output shape. Default: 0
            groups (int, optional): Number of blocked connections from input channels to output channels. Default: 1
            bias (bool, optional): If ``True``, adds a learnable bias to the output. Default: ``True``
            dilation (int or tuple, optional): Spacing between kernel elements. Default: 1

        .. seealso:: :class:`torch.nn.ConvTranspose1d` and :class:`torch.nn.modules.lazy.LazyModuleMixin`
        """

        # super class define this variable as None. "type: ignore[..] is required
        # since we are redefining the variable.
        cls_to_become = ConvTranspose1d  # type: ignore[assignment]

        def __init__(
            self,
            out_channels: int,
            kernel_size: _size_1_t,
            stride: _size_1_t = 1,
            padding: _size_1_t = 0,
            output_padding: _size_1_t = 0,
            groups: int = 1,
            bias: bool = True,
            dilation: _size_1_t = 1,
            padding_mode: str = 'zeros',
            device=None,
            dtype=None
        ) -> None:
            factory_kwargs = {'device': device, 'dtype': dtype}
            super().__init__(
                0,
                0,
                kernel_size,
                stride,
                padding,
                output_padding,
                groups,
                # bias is hardcoded to False to avoid creating tensor
                # that will soon be overwritten.
                False,
                dilation,
                padding_mode,
                **factory_kwargs
            )
            self.weight = UninitializedParameter(**factory_kwargs)
            self.out_channels = out_channels
            if bias:
                self.bias = UninitializedParameter(**factory_kwargs)

        def _get_num_spatial_dims(self) -> int:
            return 1

    # LazyConvTranspose2d defines weight as a Tensor but derived class defines it as UnitializeParameter
    class LazyConvTranspose2d(_LazyConvXdMixin, ConvTranspose2d):  # type: ignore[misc]
        r"""A :class:`torch.nn.ConvTranspose2d` module with lazy initialization of
        the ``in_channels`` argument of the :class:`ConvTranspose2d` that is inferred from
        the ``input.size(1)``.
        The attributes that will be lazily initialized are `weight` and `bias`.

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

        Args:
            out_channels (int): Number of channels produced by the convolution
            kernel_size (int or tuple): Size of the convolving kernel
            stride (int or tuple, optional): Stride of the convolution. Default: 1
            padding (int or tuple, optional): ``dilation * (kernel_size - 1) - padding`` zero-padding
                will be added to both sides of each dimension in the input. Default: 0
            output_padding (int or tuple, optional): Additional size added to one side
                of each dimension in the output shape. Default: 0
            groups (int, optional): Number of blocked connections from input channels to output channels. Default: 1
            bias (bool, optional): If ``True``, adds a learnable bias to the output. Default: ``True``
            dilation (int or tuple, optional): Spacing between kernel elements. Default: 1

        .. seealso:: :class:`torch.nn.ConvTranspose2d` and :class:`torch.nn.modules.lazy.LazyModuleMixin`
        """

        # super class define this variable as None. "type: ignore[..] is required
        # since we are redefining the variable.
        cls_to_become = ConvTranspose2d  # type: ignore[assignment]

        def __init__(
            self,
            out_channels: int,
            kernel_size: _size_2_t,
            stride: _size_2_t = 1,
            padding: _size_2_t = 0,
            output_padding: _size_2_t = 0,
            groups: int = 1,
            bias: bool = True,
            dilation: int = 1,
            padding_mode: str = 'zeros',
            device=None,
            dtype=None
        ) -> None:
            factory_kwargs = {'device': device, 'dtype': dtype}
            super().__init__(
                0,
                0,
                kernel_size,
                stride,
                padding,
                output_padding,
                groups,
                # bias is hardcoded to False to avoid creating tensor
                # that will soon be overwritten.
                False,
                dilation,
                padding_mode,
                **factory_kwargs
            )
            self.weight = UninitializedParameter(**factory_kwargs)
            self.out_channels = out_channels
            if bias:
                self.bias = UninitializedParameter(**factory_kwargs)

        def _get_num_spatial_dims(self) -> int:
            return 2

    # LazyConvTranspose3d defines weight as a Tensor but derived class defines it as UnitializeParameter
    class LazyConvTranspose3d(_LazyConvXdMixin, ConvTranspose3d):  # type: ignore[misc]
        r"""A :class:`torch.nn.ConvTranspose3d` module with lazy initialization of
        the ``in_channels`` argument of the :class:`ConvTranspose3d` that is inferred from
        the ``input.size(1)``.
        The attributes that will be lazily initialized are `weight` and `bias`.

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

        Args:
            out_channels (int): Number of channels produced by the convolution
            kernel_size (int or tuple): Size of the convolving kernel
            stride (int or tuple, optional): Stride of the convolution. Default: 1
            padding (int or tuple, optional): ``dilation * (kernel_size - 1) - padding`` zero-padding
                will be added to both sides of each dimension in the input. Default: 0
            output_padding (int or tuple, optional): Additional size added to one side
                of each dimension in the output shape. Default: 0
            groups (int, optional): Number of blocked connections from input channels to output channels. Default: 1
            bias (bool, optional): If ``True``, adds a learnable bias to the output. Default: ``True``
            dilation (int or tuple, optional): Spacing between kernel elements. Default: 1

        .. seealso:: :class:`torch.nn.ConvTranspose3d` and :class:`torch.nn.modules.lazy.LazyModuleMixin`
        """

        # super class define this variable as None. "type: ignore[..] is required
        # since we are redefining the variable.
        cls_to_become = ConvTranspose3d  # type: ignore[assignment]

        def __init__(
            self,
            out_channels: int,
            kernel_size: _size_3_t,
            stride: _size_3_t = 1,
            padding: _size_3_t = 0,
            output_padding: _size_3_t = 0,
            groups: int = 1,
            bias: bool = True,
            dilation: _size_3_t = 1,
            padding_mode: str = 'zeros',
            device=None,
            dtype=None
        ) -> None:
            factory_kwargs = {'device': device, 'dtype': dtype}
            super().__init__(
                0,
                0,
                kernel_size,
                stride,
                padding,
                output_padding,
                groups,
                # bias is hardcoded to False to avoid creating tensor
                # that will soon be overwritten.
                False,
                dilation,
                padding_mode,
                **factory_kwargs
            )
            self.weight = UninitializedParameter(**factory_kwargs)
            self.out_channels = out_channels
            if bias:
                self.bias = UninitializedParameter(**factory_kwargs)

        def _get_num_spatial_dims(self) -> int:
            return 3

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