activation.py

import warnings
from typing import Optional, Tuple

import torch
from torch import Tensor
from .linear import NonDynamicallyQuantizableLinear
from torch.nn.init import constant_, xavier_normal_, xavier_uniform_
from torch.nn.parameter import Parameter
from .module import Module
from .. import functional as F

__all__ = ['Threshold', 'ReLU', 'RReLU', 'Hardtanh', 'ReLU6', 'Sigmoid', 'Hardsigmoid', 'Tanh',
           'SiLU', 'Mish', 'Hardswish', 'ELU', 'CELU', 'SELU', 'GLU', 'GELU', 'Hardshrink', 'LeakyReLU',
           'LogSigmoid', 'Softplus', 'Softshrink', 'MultiheadAttention', 'PReLU', 'Softsign', 'Tanhshrink',
           'Softmin', 'Softmax', 'Softmax2d', 'LogSoftmax']


class Threshold(Module):
    r"""Thresholds each element of the input Tensor.

    Threshold is defined as:

    .. math::
        y =
        \begin{cases}
        x, &\text{ if } x > \text{threshold} \\
        \text{value}, &\text{ otherwise }
        \end{cases}

    Args:
        threshold: The value to threshold at
        value: The value to replace with
        inplace: can optionally do the operation in-place. Default: ``False``

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    Examples::

        >>> m = nn.Threshold(0.1, 20)
        >>> input = torch.randn(2)
        >>> output = m(input)
    """
    __constants__ = ['threshold', 'value', 'inplace']

    threshold: float
    value: float
    inplace: bool

    def __init__(self, threshold: float, value: float, inplace: bool = False) -> None:
        super().__init__()
        self.threshold = threshold
        self.value = value
        self.inplace = inplace
        # TODO: check in THNN (if inplace == True, then assert value <= threshold)

    def forward(self, input: Tensor) -> Tensor:
        return F.threshold(input, self.threshold, self.value, self.inplace)

    def extra_repr(self):
        inplace_str = ', inplace=True' if self.inplace else ''
        return f'threshold={self.threshold}, value={self.value}{inplace_str}'


class ReLU(Module):
    r"""Applies the rectified linear unit function element-wise:

    :math:`\text{ReLU}(x) = (x)^+ = \max(0, x)`

    Args:
        inplace: can optionally do the operation in-place. Default: ``False``

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/ReLU.png

    Examples::

        >>> m = nn.ReLU()
        >>> input = torch.randn(2)
        >>> output = m(input)


      An implementation of CReLU - https://arxiv.org/abs/1603.05201

        >>> m = nn.ReLU()
        >>> input = torch.randn(2).unsqueeze(0)
        >>> output = torch.cat((m(input), m(-input)))
    """
    __constants__ = ['inplace']
    inplace: bool

    def __init__(self, inplace: bool = False):
        super().__init__()
        self.inplace = inplace

    def forward(self, input: Tensor) -> Tensor:
        return F.relu(input, inplace=self.inplace)

    def extra_repr(self) -> str:
        inplace_str = 'inplace=True' if self.inplace else ''
        return inplace_str


class RReLU(Module):
    r"""Applies the randomized leaky rectified linear unit function, element-wise,
    as described in the paper:

    `Empirical Evaluation of Rectified Activations in Convolutional Network`_.

    The function is defined as:

    .. math::
        \text{RReLU}(x) =
        \begin{cases}
            x & \text{if } x \geq 0 \\
            ax & \text{ otherwise }
        \end{cases}

    where :math:`a` is randomly sampled from uniform distribution
    :math:`\mathcal{U}(\text{lower}, \text{upper})` during training while during
    evaluation :math:`a` is fixed with :math:`a = \frac{\text{lower} + \text{upper}}{2}`.

     See: https://arxiv.org/pdf/1505.00853.pdf

    Args:
        lower: lower bound of the uniform distribution. Default: :math:`\frac{1}{8}`
        upper: upper bound of the uniform distribution. Default: :math:`\frac{1}{3}`
        inplace: can optionally do the operation in-place. Default: ``False``

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/RReLU.png

    Examples::

        >>> m = nn.RReLU(0.1, 0.3)
        >>> input = torch.randn(2)
        >>> output = m(input)

    .. _`Empirical Evaluation of Rectified Activations in Convolutional Network`:
        https://arxiv.org/abs/1505.00853
    """
    __constants__ = ['lower', 'upper', 'inplace']

    lower: float
    upper: float
    inplace: bool

    def __init__(
        self,
        lower: float = 1. / 8,
        upper: float = 1. / 3,
        inplace: bool = False
    ):
        super().__init__()
        self.lower = lower
        self.upper = upper
        self.inplace = inplace

    def forward(self, input: Tensor) -> Tensor:
        return F.rrelu(input, self.lower, self.upper, self.training, self.inplace)

    def extra_repr(self):
        inplace_str = ', inplace=True' if self.inplace else ''
        return f'lower={self.lower}, upper={self.upper}{inplace_str}'


class Hardtanh(Module):
    r"""Applies the HardTanh function element-wise.

    HardTanh is defined as:

    .. math::
        \text{HardTanh}(x) = \begin{cases}
            \text{max\_val} & \text{ if } x > \text{ max\_val } \\
            \text{min\_val} & \text{ if } x < \text{ min\_val } \\
            x & \text{ otherwise } \\
        \end{cases}

    Args:
        min_val: minimum value of the linear region range. Default: -1
        max_val: maximum value of the linear region range. Default: 1
        inplace: can optionally do the operation in-place. Default: ``False``

    Keyword arguments :attr:`min_value` and :attr:`max_value`
    have been deprecated in favor of :attr:`min_val` and :attr:`max_val`.

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/Hardtanh.png

    Examples::

        >>> m = nn.Hardtanh(-2, 2)
        >>> input = torch.randn(2)
        >>> output = m(input)
    """
    __constants__ = ['min_val', 'max_val', 'inplace']

    min_val: float
    max_val: float
    inplace: bool

    def __init__(
        self,
        min_val: float = -1.,
        max_val: float = 1.,
        inplace: bool = False,
        min_value: Optional[float] = None,
        max_value: Optional[float] = None
    ) -> None:
        super().__init__()
        if min_value is not None:
            warnings.warn("keyword argument min_value is deprecated and rename to min_val")
            min_val = min_value
        if max_value is not None:
            warnings.warn("keyword argument max_value is deprecated and rename to max_val")
            max_val = max_value

        self.min_val = min_val
        self.max_val = max_val
        self.inplace = inplace
        assert self.max_val > self.min_val

    def forward(self, input: Tensor) -> Tensor:
        return F.hardtanh(input, self.min_val, self.max_val, self.inplace)

    def extra_repr(self) -> str:
        inplace_str = ', inplace=True' if self.inplace else ''
        return f'min_val={self.min_val}, max_val={self.max_val}{inplace_str}'


class ReLU6(Hardtanh):
    r"""Applies the element-wise function:

    .. math::
        \text{ReLU6}(x) = \min(\max(0,x), 6)

    Args:
        inplace: can optionally do the operation in-place. Default: ``False``

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/ReLU6.png

    Examples::

        >>> m = nn.ReLU6()
        >>> input = torch.randn(2)
        >>> output = m(input)
    """

    def __init__(self, inplace: bool = False):
        super().__init__(0., 6., inplace)

    def extra_repr(self) -> str:
        inplace_str = 'inplace=True' if self.inplace else ''
        return inplace_str


class Sigmoid(Module):
    r"""Applies the element-wise function:

    .. math::
        \text{Sigmoid}(x) = \sigma(x) = \frac{1}{1 + \exp(-x)}


    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/Sigmoid.png

    Examples::

        >>> m = nn.Sigmoid()
        >>> input = torch.randn(2)
        >>> output = m(input)
    """

    def forward(self, input: Tensor) -> Tensor:
        return torch.sigmoid(input)


class Hardsigmoid(Module):
    r"""Applies the Hardsigmoid function element-wise.

    Hardsigmoid is defined as:

    .. math::
        \text{Hardsigmoid}(x) = \begin{cases}
            0 & \text{if~} x \le -3, \\
            1 & \text{if~} x \ge +3, \\
            x / 6 + 1 / 2 & \text{otherwise}
        \end{cases}

    Args:
        inplace: can optionally do the operation in-place. Default: ``False``

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/Hardsigmoid.png

    Examples::

        >>> m = nn.Hardsigmoid()
        >>> input = torch.randn(2)
        >>> output = m(input)
    """
    __constants__ = ['inplace']

    inplace: bool

    def __init__(self, inplace : bool = False) -> None:
        super().__init__()
        self.inplace = inplace

    def forward(self, input: Tensor) -> Tensor:
        return F.hardsigmoid(input, self.inplace)


class Tanh(Module):
    r"""Applies the Hyperbolic Tangent (Tanh) function element-wise.

    Tanh is defined as:

    .. math::
        \text{Tanh}(x) = \tanh(x) = \frac{\exp(x) - \exp(-x)} {\exp(x) + \exp(-x)}

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/Tanh.png

    Examples::

        >>> m = nn.Tanh()
        >>> input = torch.randn(2)
        >>> output = m(input)
    """

    def forward(self, input: Tensor) -> Tensor:
        return torch.tanh(input)

class SiLU(Module):
    r"""Applies the Sigmoid Linear Unit (SiLU) function, element-wise.
    The SiLU function is also known as the swish function.

    .. math::
        \text{silu}(x) = x * \sigma(x), \text{where } \sigma(x) \text{ is the logistic sigmoid.}

    .. note::
        See `Gaussian Error Linear Units (GELUs) <https://arxiv.org/abs/1606.08415>`_
        where the SiLU (Sigmoid Linear Unit) was originally coined, and see
        `Sigmoid-Weighted Linear Units for Neural Network Function Approximation
        in Reinforcement Learning <https://arxiv.org/abs/1702.03118>`_ and `Swish:
        a Self-Gated Activation Function <https://arxiv.org/abs/1710.05941v1>`_
        where the SiLU was experimented with later.

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/SiLU.png

    Examples::

        >>> m = nn.SiLU()
        >>> input = torch.randn(2)
        >>> output = m(input)
    """
    __constants__ = ['inplace']
    inplace: bool

    def __init__(self, inplace: bool = False):
        super().__init__()
        self.inplace = inplace

    def forward(self, input: Tensor) -> Tensor:
        return F.silu(input, inplace=self.inplace)

    def extra_repr(self) -> str:
        inplace_str = 'inplace=True' if self.inplace else ''
        return inplace_str

class Mish(Module):
    r"""Applies the Mish function, element-wise.
    Mish: A Self Regularized Non-Monotonic Neural Activation Function.

    .. math::
        \text{Mish}(x) = x * \text{Tanh}(\text{Softplus}(x))

    .. note::
        See `Mish: A Self Regularized Non-Monotonic Neural Activation Function <https://arxiv.org/abs/1908.08681>`_

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/Mish.png

    Examples::

        >>> m = nn.Mish()
        >>> input = torch.randn(2)
        >>> output = m(input)
    """
    __constants__ = ['inplace']
    inplace: bool

    def __init__(self, inplace: bool = False):
        super().__init__()
        self.inplace = inplace

    def forward(self, input: Tensor) -> Tensor:
        return F.mish(input, inplace=self.inplace)

    def extra_repr(self) -> str:
        inplace_str = 'inplace=True' if self.inplace else ''
        return inplace_str

class Hardswish(Module):
    r"""Applies the Hardswish function, element-wise, as described in the paper:
    `Searching for MobileNetV3 <https://arxiv.org/abs/1905.02244>`_.

    Hardswish is defined as:

    .. math::
        \text{Hardswish}(x) = \begin{cases}
            0 & \text{if~} x \le -3, \\
            x & \text{if~} x \ge +3, \\
            x \cdot (x + 3) /6 & \text{otherwise}
        \end{cases}

    Args:
        inplace: can optionally do the operation in-place. Default: ``False``

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/Hardswish.png

    Examples::

        >>> m = nn.Hardswish()
        >>> input = torch.randn(2)
        >>> output = m(input)
    """
    __constants__ = ['inplace']

    inplace: bool

    def __init__(self, inplace : bool = False) -> None:
        super().__init__()
        self.inplace = inplace

    def forward(self, input: Tensor) -> Tensor:
        return F.hardswish(input, self.inplace)


class ELU(Module):
    r"""Applies the Exponential Linear Unit (ELU) function, element-wise, as described
    in the paper: `Fast and Accurate Deep Network Learning by Exponential Linear
    Units (ELUs) <https://arxiv.org/abs/1511.07289>`__.

    ELU is defined as:

    .. math::
        \text{ELU}(x) = \begin{cases}
        x, & \text{ if } x > 0\\
        \alpha * (\exp(x) - 1), & \text{ if } x \leq 0
        \end{cases}

    Args:
        alpha: the :math:`\alpha` value for the ELU formulation. Default: 1.0
        inplace: can optionally do the operation in-place. Default: ``False``

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/ELU.png

    Examples::

        >>> m = nn.ELU()
        >>> input = torch.randn(2)
        >>> output = m(input)
    """
    __constants__ = ['alpha', 'inplace']
    alpha: float
    inplace: bool

    def __init__(self, alpha: float = 1., inplace: bool = False) -> None:
        super().__init__()
        self.alpha = alpha
        self.inplace = inplace

    def forward(self, input: Tensor) -> Tensor:
        return F.elu(input, self.alpha, self.inplace)

    def extra_repr(self) -> str:
        inplace_str = ', inplace=True' if self.inplace else ''
        return f'alpha={self.alpha}{inplace_str}'


class CELU(Module):
    r"""Applies the element-wise function:

    .. math::
        \text{CELU}(x) = \max(0,x) + \min(0, \alpha * (\exp(x/\alpha) - 1))

    More details can be found in the paper `Continuously Differentiable Exponential Linear Units`_ .

    Args:
        alpha: the :math:`\alpha` value for the CELU formulation. Default: 1.0
        inplace: can optionally do the operation in-place. Default: ``False``

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/CELU.png

    Examples::

        >>> m = nn.CELU()
        >>> input = torch.randn(2)
        >>> output = m(input)

    .. _`Continuously Differentiable Exponential Linear Units`:
        https://arxiv.org/abs/1704.07483
    """
    __constants__ = ['alpha', 'inplace']
    alpha: float
    inplace: bool

    def __init__(self, alpha: float = 1., inplace: bool = False) -> None:
        super().__init__()
        self.alpha = alpha
        self.inplace = inplace

    def forward(self, input: Tensor) -> Tensor:
        return F.celu(input, self.alpha, self.inplace)

    def extra_repr(self) -> str:
        inplace_str = ', inplace=True' if self.inplace else ''
        return f'alpha={self.alpha}{inplace_str}'


class SELU(Module):
    r"""Applied element-wise, as:

    .. math::
        \text{SELU}(x) = \text{scale} * (\max(0,x) + \min(0, \alpha * (\exp(x) - 1)))

    with :math:`\alpha = 1.6732632423543772848170429916717` and
    :math:`\text{scale} = 1.0507009873554804934193349852946`.

    .. warning::
        When using ``kaiming_normal`` or ``kaiming_normal_`` for initialisation,
        ``nonlinearity='linear'`` should be used instead of ``nonlinearity='selu'``
        in order to get `Self-Normalizing Neural Networks`_.
        See :func:`torch.nn.init.calculate_gain` for more information.

    More details can be found in the paper `Self-Normalizing Neural Networks`_ .

    Args:
        inplace (bool, optional): can optionally do the operation in-place. Default: ``False``

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/SELU.png

    Examples::

        >>> m = nn.SELU()
        >>> input = torch.randn(2)
        >>> output = m(input)

    .. _Self-Normalizing Neural Networks: https://arxiv.org/abs/1706.02515
    """
    __constants__ = ['inplace']
    inplace: bool

    def __init__(self, inplace: bool = False) -> None:
        super().__init__()
        self.inplace = inplace

    def forward(self, input: Tensor) -> Tensor:
        return F.selu(input, self.inplace)

    def extra_repr(self) -> str:
        inplace_str = 'inplace=True' if self.inplace else ''
        return inplace_str


class GLU(Module):
    r"""Applies the gated linear unit function
    :math:`{GLU}(a, b)= a \otimes \sigma(b)` where :math:`a` is the first half
    of the input matrices and :math:`b` is the second half.

    Args:
        dim (int): the dimension on which to split the input. Default: -1

    Shape:
        - Input: :math:`(\ast_1, N, \ast_2)` where `*` means, any number of additional
          dimensions
        - Output: :math:`(\ast_1, M, \ast_2)` where :math:`M=N/2`

    Examples::

        >>> m = nn.GLU()
        >>> input = torch.randn(4, 2)
        >>> output = m(input)
    """
    __constants__ = ['dim']
    dim: int

    def __init__(self, dim: int = -1) -> None:
        super().__init__()
        self.dim = dim

    def forward(self, input: Tensor) -> Tensor:
        return F.glu(input, self.dim)

    def extra_repr(self) -> str:
        return f'dim={self.dim}'


class GELU(Module):
    r"""Applies the Gaussian Error Linear Units function:

    .. math:: \text{GELU}(x) = x * \Phi(x)

    where :math:`\Phi(x)` is the Cumulative Distribution Function for Gaussian Distribution.

    When the approximate argument is 'tanh', Gelu is estimated with:

    .. math:: \text{GELU}(x) = 0.5 * x * (1 + \text{Tanh}(\sqrt{2 / \pi} * (x + 0.044715 * x^3)))

    Args:
        approximate (str, optional): the gelu approximation algorithm to use:
            ``'none'`` | ``'tanh'``. Default: ``'none'``

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/GELU.png

    Examples::

        >>> m = nn.GELU()
        >>> input = torch.randn(2)
        >>> output = m(input)
    """
    __constants__ = ['approximate']
    approximate: str

    def __init__(self, approximate: str = 'none') -> None:
        super().__init__()
        self.approximate = approximate

    def forward(self, input: Tensor) -> Tensor:
        return F.gelu(input, approximate=self.approximate)

    def extra_repr(self) -> str:
        return f'approximate={repr(self.approximate)}'


class Hardshrink(Module):
    r"""Applies the Hard Shrinkage (Hardshrink) function element-wise.

    Hardshrink is defined as:

    .. math::
        \text{HardShrink}(x) =
        \begin{cases}
        x, & \text{ if } x > \lambda \\
        x, & \text{ if } x < -\lambda \\
        0, & \text{ otherwise }
        \end{cases}

    Args:
        lambd: the :math:`\lambda` value for the Hardshrink formulation. Default: 0.5

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/Hardshrink.png

    Examples::

        >>> m = nn.Hardshrink()
        >>> input = torch.randn(2)
        >>> output = m(input)
    """
    __constants__ = ['lambd']
    lambd: float

    def __init__(self, lambd: float = 0.5) -> None:
        super().__init__()
        self.lambd = lambd

    def forward(self, input: Tensor) -> Tensor:
        return F.hardshrink(input, self.lambd)

    def extra_repr(self) -> str:
        return f'{self.lambd}'


class LeakyReLU(Module):
    r"""Applies the element-wise function:

    .. math::
        \text{LeakyReLU}(x) = \max(0, x) + \text{negative\_slope} * \min(0, x)


    or

    .. math::
        \text{LeakyReLU}(x) =
        \begin{cases}
        x, & \text{ if } x \geq 0 \\
        \text{negative\_slope} \times x, & \text{ otherwise }
        \end{cases}

    Args:
        negative_slope: Controls the angle of the negative slope (which is used for
          negative input values). Default: 1e-2
        inplace: can optionally do the operation in-place. Default: ``False``

    Shape:
        - Input: :math:`(*)` where `*` means, any number of additional
          dimensions
        - Output: :math:`(*)`, same shape as the input

    .. image:: ../scripts/activation_images/LeakyReLU.png

    Examples::

        >>> m = nn.LeakyReLU(0.1)
        >>> input = torch.randn(2)
        >>> output = m(input)
    """
    __constants__ = ['inplace', 'negative_slope']
    inplace: bool
    negative_slope: float

    def __init__(self, negative_slope: float = 1e-2, inplace: bool = False) -> None:
        super().__init__()
        self.negative_slope = negative_slope
        self.inplace = inplace

    def forward(self, input: Tensor) -> Tensor:
        return F.leaky_relu(input, self.negative_slope, self.inplace)

    def extra_repr(self) -> str:
        inplace_str = ', inplace=True' if self.inplace else ''
        return f'negative_slope={self.negative_slope}{inplace_str}'


class LogSigmoid(Module):
    r"""Applies the element-wise function:

    .. math::
        \text{LogSigmoid}(x) = \log\left(\frac{ 1 }{ 1 + \exp(-x)}\right)

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/LogSigmoid.png

    Examples::

        >>> m = nn.LogSigmoid()
        >>> input = torch.randn(2)
        >>> output = m(input)
    """

    def forward(self, input: Tensor) -> Tensor:
        return F.logsigmoid(input)


class Softplus(Module):
    r"""Applies the Softplus function :math:`\text{Softplus}(x) = \frac{1}{\beta} *
    \log(1 + \exp(\beta * x))` element-wise.

    SoftPlus is a smooth approximation to the ReLU function and can be used
    to constrain the output of a machine to always be positive.

    For numerical stability the implementation reverts to the linear function
    when :math:`input \times \beta > threshold`.

    Args:
        beta: the :math:`\beta` value for the Softplus formulation. Default: 1
        threshold: values above this revert to a linear function. Default: 20

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/Softplus.png

    Examples::

        >>> m = nn.Softplus()
        >>> input = torch.randn(2)
        >>> output = m(input)
    """
    __constants__ = ['beta', 'threshold']
    beta: int
    threshold: int

    def __init__(self, beta: int = 1, threshold: int = 20) -> None:
        super().__init__()
        self.beta = beta
        self.threshold = threshold

    def forward(self, input: Tensor) -> Tensor:
        return F.softplus(input, self.beta, self.threshold)

    def extra_repr(self) -> str:
        return f'beta={self.beta}, threshold={self.threshold}'


class Softshrink(Module):
    r"""Applies the soft shrinkage function elementwise:

    .. math::
        \text{SoftShrinkage}(x) =
        \begin{cases}
        x - \lambda, & \text{ if } x > \lambda \\
        x + \lambda, & \text{ if } x < -\lambda \\
        0, & \text{ otherwise }
        \end{cases}

    Args:
        lambd: the :math:`\lambda` (must be no less than zero) value for the Softshrink formulation. Default: 0.5

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/Softshrink.png

    Examples::

        >>> m = nn.Softshrink()
        >>> input = torch.randn(2)
        >>> output = m(input)
    """
    __constants__ = ['lambd']
    lambd: float

    def __init__(self, lambd: float = 0.5) -> None:
        super().__init__()
        self.lambd = lambd

    def forward(self, input: Tensor) -> Tensor:
        return F.softshrink(input, self.lambd)

    def extra_repr(self) -> str:
        return str(self.lambd)


def _check_arg_device(x: Optional[torch.Tensor]) -> bool:
    if x is not None:
        return x.device.type in ["cpu", "cuda", torch.utils.backend_registration._privateuse1_backend_name]
    return True


def _arg_requires_grad(x: Optional[torch.Tensor]) -> bool:
    if x is not None:
        return x.requires_grad
    return False


def _is_make_fx_tracing():
    if not torch.jit.is_scripting():
        torch_dispatch_mode_stack = torch.utils._python_dispatch._get_current_dispatch_mode_stack()
        return any(type(x) == torch.fx.experimental.proxy_tensor.ProxyTorchDispatchMode for x in torch_dispatch_mode_stack)
    else:
        return False


class MultiheadAttention(Module):
    r"""Allows the model to jointly attend to information
    from different representation subspaces as described in the paper:
    `Attention Is All You Need <https://arxiv.org/abs/1706.03762>`_.

    Multi-Head Attention is defined as:

    .. math::
        \text{MultiHead}(Q, K, V) = \text{Concat}(head_1,\dots,head_h)W^O

    where :math:`head_i = \text{Attention}(QW_i^Q, KW_i^K, VW_i^V)`.

    ``nn.MultiHeadAttention`` will use the optimized implementations of
    ``scaled_dot_product_attention()`` when possible.

    In addition to support for the new ``scaled_dot_product_attention()``
    function, for speeding up Inference, MHA will use
    fastpath inference with support for Nested Tensors, iff:

    - self attention is being computed (i.e., ``query``, ``key``, and ``value`` are the same tensor).
    - inputs are batched (3D) with ``batch_first==True``
    - Either autograd is disabled (using ``torch.inference_mode`` or ``torch.no_grad``) or no tensor argument ``requires_grad``
    - training is disabled (using ``.eval()``)
    - ``add_bias_kv`` is ``False``
    - ``add_zero_attn`` is ``False``
    - ``batch_first`` is ``True`` and the input is batched
    - ``kdim`` and ``vdim`` are equal to ``embed_dim``
    - if a `NestedTensor <https://pytorch.org/docs/stable/nested.html>`_ is passed, neither ``key_padding_mask``
      nor ``attn_mask`` is passed
    - autocast is disabled

    If the optimized inference fastpath implementation is in use, a
    `NestedTensor <https://pytorch.org/docs/stable/nested.html>`_ can be passed for
    ``query``/``key``/``value`` to represent padding more efficiently than using a
    padding mask. In this case, a `NestedTensor <https://pytorch.org/docs/stable/nested.html>`_
    will be returned, and an additional speedup proportional to the fraction of the input
    that is padding can be expected.

    Args:
        embed_dim: Total dimension of the model.
        num_heads: Number of parallel attention heads. Note that ``embed_dim`` will be split
            across ``num_heads`` (i.e. each head will have dimension ``embed_dim // num_heads``).
        dropout: Dropout probability on ``attn_output_weights``. Default: ``0.0`` (no dropout).
        bias: If specified, adds bias to input / output projection layers. Default: ``True``.
        add_bias_kv: If specified, adds bias to the key and value sequences at dim=0. Default: ``False``.
        add_zero_attn: If specified, adds a new batch of zeros to the key and value sequences at dim=1.
            Default: ``False``.
        kdim: Total number of features for keys. Default: ``None`` (uses ``kdim=embed_dim``).
        vdim: Total number of features for values. Default: ``None`` (uses ``vdim=embed_dim``).
        batch_first: If ``True``, then the input and output tensors are provided
            as (batch, seq, feature). Default: ``False`` (seq, batch, feature).

    Examples::

        >>> # xdoctest: +SKIP
        >>> multihead_attn = nn.MultiheadAttention(embed_dim, num_heads)
        >>> attn_output, attn_output_weights = multihead_attn(query, key, value)

    .. _`FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness`:
         https://arxiv.org/abs/2205.14135

    """

    __constants__ = ['batch_first']
    bias_k: Optional[torch.Tensor]
    bias_v: Optional[torch.Tensor]

    def __init__(self, embed_dim, num_heads, dropout=0., bias=True, add_bias_kv=False, add_zero_attn=False,
                 kdim=None, vdim=None, batch_first=False, device=None, dtype=None) -> None:
        if embed_dim <= 0 or num_heads <= 0:
            raise ValueError(
                f"embed_dim and num_heads must be greater than 0,"
                f" got embed_dim={embed_dim} and num_heads={num_heads} instead"
            )
        factory_kwargs = {'device': device, 'dtype': dtype}
        super().__init__()
        self.embed_dim = embed_dim
        self.kdim = kdim if kdim is not None else embed_dim
        self.vdim = vdim if vdim is not None else embed_dim
        self._qkv_same_embed_dim = self.kdim == embed_dim and self.vdim == embed_dim

        self.num_heads = num_heads
        self.dropout = dropout
        self.batch_first = batch_first
        self.head_dim = embed_dim // num_heads
        assert self.head_dim * num_heads == self.embed_dim, "embed_dim must be divisible by num_heads"

        if not self._qkv_same_embed_dim:
            self.q_proj_weight = Parameter(torch.empty((embed_dim, embed_dim), **factory_kwargs))
            self.k_proj_weight = Parameter(torch.empty((embed_dim, self.kdim), **factory_kwargs))
            self.v_proj_weight = Parameter(torch.empty((embed_dim, self.vdim), **factory_kwargs))
            self.register_parameter('in_proj_weight', None)
        else:
            self.in_proj_weight = Parameter(torch.empty((3 * embed_dim, embed_dim), **factory_kwargs))
            self.register_parameter('q_proj_weight', None)
            self.register_parameter('k_proj_weight', None)
            self.register_parameter('v_proj_weight', None)

        if bias:
            self.in_proj_bias = Parameter(torch.empty(3 * embed_dim, **factory_kwargs))
        else:
            self.register_parameter('in_proj_bias', None)
        self.out_proj = NonDynamicallyQuantizableLinear(embed_dim, embed_dim, bias=bias, **factory_kwargs)

        if add_bias_kv:
            self.bias_k = Parameter(torch.empty((1, 1, embed_dim), **factory_kwargs))
            self.bias_v = Parameter(torch.empty((1, 1, embed_dim), **factory_kwargs))
        else:
            self.bias_k = self.bias_v = None

        self.add_zero_attn = add_zero_attn

        self._reset_parameters()

    def _reset_parameters(self):
        if self._qkv_same_embed_dim:
            xavier_uniform_(self.in_proj_weight)
        else:
            xavier_uniform_(self.q_proj_weight)
            xavier_uniform_(self.k_proj_weight)
            xavier_uniform_(self.v_proj_weight)

        if self.in_proj_bias is not None:
            constant_(self.in_proj_bias, 0.)
            constant_(self.out_proj.bias, 0.)
        if self.bias_k is not None:
            xavier_normal_(self.bias_k)
        if self.bias_v is not None:
            xavier_normal_(self.bias_v)

    def __setstate__(self, state):
        # Support loading old MultiheadAttention checkpoints generated by v1.1.0
        if '_qkv_same_embed_dim' not in state:
            state['_qkv_same_embed_dim'] = True

        super().__setstate__(state)

    def forward(
            self,
            query: Tensor,
            key: Tensor,
            value: Tensor,
            key_padding_mask: Optional[Tensor] = None,
            need_weights: bool = True,
            attn_mask: Optional[Tensor] = None,
            average_attn_weights: bool = True,
            is_causal : bool = False) -> Tuple[Tensor, Optional[Tensor]]:
        r"""
    Args:
        query: Query embeddings of shape :math:`(L, E_q)` for unbatched input, :math:`(L, N, E_q)` when ``batch_first=False``
            or :math:`(N, L, E_q)` when ``batch_first=True``, where :math:`L` is the target sequence length,
            :math:`N` is the batch size, and :math:`E_q` is the query embedding dimension ``embed_dim``.
            Queries are compared against key-value pairs to produce the output.
            See "Attention Is All You Need" for more details.
        key: Key embeddings of shape :math:`(S, E_k)` for unbatched input, :math:`(S, N, E_k)` when ``batch_first=False``
            or :math:`(N, S, E_k)` when ``batch_first=True``, where :math:`S` is the source sequence length,
            :math:`N` is the batch size, and :math:`E_k` is the key embedding dimension ``kdim``.
            See "Attention Is All You Need" for more details.
        value: Value embeddings of shape :math:`(S, E_v)` for unbatched input, :math:`(S, N, E_v)` when
            ``batch_first=False`` or :math:`(N, S, E_v)` when ``batch_first=True``, where :math:`S` is the source
            sequence length, :math:`N` is the batch size, and :math:`E_v` is the value embedding dimension ``vdim``.
            See "Attention Is All You Need" for more details.
        key_padding_mask: If specified, a mask of shape :math:`(N, S)` indicating which elements within ``key``
            to ignore for the purpose of attention (i.e. treat as "padding"). For unbatched `query`, shape should be :math:`(S)`.
            Binary and float masks are supported.
            For a binary mask, a ``True`` value indicates that the corresponding ``key`` value will be ignored for
            the purpose of attention. For a float mask, it will be directly added to the corresponding ``key`` value.
        need_weights: If specified, returns ``attn_output_weights`` in addition to ``attn_outputs``.
            Set ``need_weights=False`` to use the optimized ``scaled_dot_product_attention``
            and achieve the best performance for MHA.
            Default: ``True``.
        attn_mask: If specified, a 2D or 3D mask preventing attention to certain positions. Must be of shape
            :math:`(L, S)` or :math:`(N\cdot\text{num\_heads}, L, S)`, where :math:`N` is the batch size,
            :math:`L` is the target sequence length, and :math:`S` is the source sequence length. A 2D mask will be
            broadcasted across the batch while a 3D mask allows for a different mask for each entry in the batch.
            Binary and float masks are supported. For a binary mask, a ``True`` value indicates that the
            corresponding position is not allowed to attend. For a float mask, the mask values will be added to
            the attention weight.
            If both attn_mask and key_padding_mask are supplied, their types should match.
        average_attn_weights: If true, indicates that the returned ``attn_weights`` should be averaged across
            heads. Otherwise, ``attn_weights`` are provided separately per head. Note that this flag only has an
            effect when ``need_weights=True``. Default: ``True`` (i.e. average weights across heads)
        is_causal: If specified, applies a causal mask as attention mask.
            Default: ``False``.
            Warning:
            ``is_causal`` provides a hint that ``attn_mask`` is the
            causal mask. Providing incorrect hints can result in
            incorrect execution, including forward and backward
            compatibility.

    Outputs:
        - **attn_output** - Attention outputs of shape :math:`(L, E)` when input is unbatched,
          :math:`(L, N, E)` when ``batch_first=False`` or :math:`(N, L, E)` when ``batch_first=True``,
          where :math:`L` is the target sequence length, :math:`N` is the batch size, and :math:`E` is the
          embedding dimension ``embed_dim``.
        - **attn_output_weights** - Only returned when ``need_weights=True``. If ``average_attn_weights=True``,
          returns attention weights averaged across heads of shape :math:`(L, S)` when input is unbatched or
          :math:`(N, L, S)`, where :math:`N` is the batch size, :math:`L` is the target sequence length, and
          :math:`S` is the source sequence length. If ``average_attn_weights=False``, returns attention weights per
          head of shape :math:`(\text{num\_heads}, L, S)` when input is unbatched or :math:`(N, \text{num\_heads}, L, S)`.

        .. note::
            `batch_first` argument is ignored for unbatched inputs.
        """

        why_not_fast_path = ''
        if ((attn_mask is not None and torch.is_floating_point(attn_mask))
           or (key_padding_mask is not None) and torch.is_floating_point(key_padding_mask)):
            why_not_fast_path = "floating-point masks are not supported for fast path."

        is_batched = query.dim() == 3

        key_padding_mask = F._canonical_mask(
            mask=key_padding_mask,
            mask_name="key_padding_mask",
            other_type=F._none_or_dtype(attn_mask),
            other_name="attn_mask",
            target_type=query.dtype
        )

        attn_mask = F._canonical_mask(
            mask=attn_mask,
            mask_name="attn_mask",
            other_type=None,
            other_name="",
            target_type=query.dtype,
            check_other=False,
        )


        if not is_batched:
            why_not_fast_path = f"input not batched; expected query.dim() of 3 but got {query.dim()}"
        elif query is not key or key is not value:
            # When lifting this restriction, don't forget to either
            # enforce that the dtypes all match or test cases where
            # they don't!
            why_not_fast_path = "non-self attention was used (query, key, and value are not the same Tensor)"
        elif self.in_proj_bias is not None and query.dtype != self.in_proj_bias.dtype:
            why_not_fast_path = f"dtypes of query ({query.dtype}) and self.in_proj_bias ({self.in_proj_bias.dtype}) don't match"
        elif self.in_proj_weight is None:
            why_not_fast_path = "in_proj_weight was None"
        elif query.dtype != self.in_proj_weight.dtype:
            # this case will fail anyway, but at least they'll get a useful error message.
            why_not_fast_path = f"dtypes of query ({query.dtype}) and self.in_proj_weight ({self.in_proj_weight.dtype}) don't match"
        elif self.training:
            why_not_fast_path = "training is enabled"
        elif (self.num_heads % 2) != 0:
            why_not_fast_path = "self.num_heads is not even"
        elif not self.batch_first:
            why_not_fast_path = "batch_first was not True"
        elif self.bias_k is not None:
            why_not_fast_path = "self.bias_k was not None"
        elif self.bias_v is not None:
            why_not_fast_path = "self.bias_v was not None"
        elif self.add_zero_attn:
            why_not_fast_path = "add_zero_attn was enabled"
        elif not self._qkv_same_embed_dim:
            why_not_fast_path = "_qkv_same_embed_dim was not True"
        elif query.is_nested and (key_padding_mask is not None or attn_mask is not None):
            why_not_fast_path = "supplying both src_key_padding_mask and src_mask at the same time \
                                 is not supported with NestedTensor input"
        elif torch.is_autocast_enabled():
            why_not_fast_path = "autocast is enabled"

        if not why_not_fast_path:
            tensor_args = (
                query,
                key,
                value,
                self.in_proj_weight,
                self.in_proj_bias,
                self.out_proj.weight,
                self.out_proj.bias,
            )
            # We have to use list comprehensions below because TorchScript does not support
            # generator expressions.
            if torch.overrides.has_torch_function(tensor_args):
                why_not_fast_path = "some Tensor argument has_torch_function"
            elif _is_make_fx_tracing():
                why_not_fast_path = "we are running make_fx tracing"
            elif not all(_check_arg_device(x) for x in tensor_args):
                why_not_fast_path = ("some Tensor argument's device is neither one of "
                                     f"cpu, cuda or {torch.utils.backend_registration._privateuse1_backend_name}")
            elif torch.is_grad_enabled() and any(_arg_requires_grad(x) for x in tensor_args):
                why_not_fast_path = ("grad is enabled and at least one of query or the "
                                     "input/output projection weights or biases requires_grad")
            if not why_not_fast_path:
                merged_mask, mask_type = self.merge_masks(attn_mask, key_padding_mask, query)

                if self.in_proj_bias is not None and self.in_proj_weight is not None:
                    return torch._native_multi_head_attention(
                        query,
                        key,
                        value,
                        self.embed_dim,
                        self.num_heads,
                        self.in_proj_weight,
                        self.in_proj_bias,
                        self.out_proj.weight,
                        self.out_proj.bias,
                        merged_mask,
                        need_weights,
                        average_attn_weights,
                        mask_type)

        any_nested = query.is_nested or key.is_nested or value.is_nested
        assert not any_nested, ("MultiheadAttention does not support NestedTensor outside of its fast path. " +
                                f"The fast path was not hit because {why_not_fast_path}")

        if self.batch_first and is_batched:
            # make sure that the transpose op does not affect the "is" property
            if key is value:
                if query is key:
                    query = key = value = query.transpose(1, 0)
                else:
                    query, key = (x.transpose(1, 0) for x in (query, key))
                    value = key
            else:
                query, key, value = (x.transpose(1, 0) for x in (query, key, value))

        if not self._qkv_same_embed_dim:
            attn_output, attn_output_weights = F.multi_head_attention_forward(
                query, key, value, self.embed_dim, self.num_heads,
                self.in_proj_weight, self.in_proj_bias,
                self.bias_k, self.bias_v, self.add_zero_attn,
                self.dropout, self.out_proj.weight, self.out_proj.bias,
                training=self.training,
                key_padding_mask=key_padding_mask, need_weights=need_weights,
                attn_mask=attn_mask,
                use_separate_proj_weight=True,
                q_proj_weight=self.q_proj_weight, k_proj_weight=self.k_proj_weight,
                v_proj_weight=self.v_proj_weight,
                average_attn_weights=average_attn_weights,
                is_causal=is_causal)
        else:
            attn_output, attn_output_weights = F.multi_head_attention_forward(
                query, key, value, self.embed_dim, self.num_heads,
                self.in_proj_weight, self.in_proj_bias,
                self.bias_k, self.bias_v, self.add_zero_attn,
                self.dropout, self.out_proj.weight, self.out_proj.bias,
                training=self.training,
                key_padding_mask=key_padding_mask,
                need_weights=need_weights,
                attn_mask=attn_mask,
                average_attn_weights=average_attn_weights,
                is_causal=is_causal)
        if self.batch_first and is_batched:
            return attn_output.transpose(1, 0), attn_output_weights
        else:
            return attn_output, attn_output_weights

    def merge_masks(self, attn_mask: Optional[Tensor], key_padding_mask: Optional[Tensor],
                    query: Tensor) -> Tuple[Optional[Tensor], Optional[int]]:
        r"""
        Determine mask type and combine masks if necessary. If only one mask is provided, that mask
        and the corresponding mask type will be returned. If both masks are provided, they will be both
        expanded to shape ``(batch_size, num_heads, seq_len, seq_len)``, combined with logical ``or``
        and mask type 2 will be returned
        Args:
            attn_mask: attention mask of shape ``(seq_len, seq_len)``, mask type 0
            key_padding_mask: padding mask of shape ``(batch_size, seq_len)``, mask type 1
            query: query embeddings of shape ``(batch_size, seq_len, embed_dim)``
        Returns:
            merged_mask: merged mask
            mask_type: merged mask type (0, 1, or 2)
        """
        mask_type: Optional[int] = None
        merged_mask: Optional[Tensor] = None

        if key_padding_mask is not None:
            mask_type = 1
            merged_mask = key_padding_mask

        if attn_mask is not None:
            # In this branch query can't be a nested tensor, so it has a shape
            batch_size, seq_len, _ = query.shape
            mask_type = 2

            # Always expands attn_mask to 4D
            if attn_mask.dim() == 3:
                attn_mask_expanded = attn_mask.view(batch_size, -1, seq_len, seq_len)
            else:  # attn_mask.dim() == 2:
                attn_mask_expanded = attn_mask.view(1, 1, seq_len, seq_len).expand(batch_size, self.num_heads, -1, -1)
            merged_mask = attn_mask_expanded

            if key_padding_mask is not None:
                key_padding_mask_expanded = key_padding_mask.view(batch_size, 1, 1, seq_len).expand(-1, self.num_heads, -1, -1)
                merged_mask = attn_mask_expanded + key_padding_mask_expanded

        # no attn_mask and no key_padding_mask, returns None, None
        return merged_mask, mask_type


class PReLU(Module):
    r"""Applies the element-wise function:

    .. math::
        \text{PReLU}(x) = \max(0,x) + a * \min(0,x)

    or

    .. math::
        \text{PReLU}(x) =
        \begin{cases}
        x, & \text{ if } x \geq 0 \\
        ax, & \text{ otherwise }
        \end{cases}

    Here :math:`a` is a learnable parameter. When called without arguments, `nn.PReLU()` uses a single
    parameter :math:`a` across all input channels. If called with `nn.PReLU(nChannels)`,
    a separate :math:`a` is used for each input channel.


    .. note::
        weight decay should not be used when learning :math:`a` for good performance.

    .. note::
        Channel dim is the 2nd dim of input. When input has dims < 2, then there is
        no channel dim and the number of channels = 1.

    Args:
        num_parameters (int): number of :math:`a` to learn.
            Although it takes an int as input, there is only two values are legitimate:
            1, or the number of channels at input. Default: 1
        init (float): the initial value of :math:`a`. Default: 0.25

    Shape:
        - Input: :math:`( *)` where `*` means, any number of additional
          dimensions.
        - Output: :math:`(*)`, same shape as the input.

    Attributes:
        weight (Tensor): the learnable weights of shape (:attr:`num_parameters`).

    .. image:: ../scripts/activation_images/PReLU.png

    Examples::

        >>> m = nn.PReLU()
        >>> input = torch.randn(2)
        >>> output = m(input)
    """
    __constants__ = ['num_parameters']
    num_parameters: int

    def __init__(self, num_parameters: int = 1, init: float = 0.25,
                 device=None, dtype=None) -> None:
        factory_kwargs = {'device': device, 'dtype': dtype}
        self.num_parameters = num_parameters
        super().__init__()
        self.init = init
        self.weight = Parameter(torch.empty(num_parameters, **factory_kwargs))
        self.reset_parameters()

    def reset_parameters(self):
        torch.nn.init.constant_(self.weight, self.init)

    def forward(self, input: Tensor) -> Tensor:
        return F.prelu(input, self.weight)

    def extra_repr(self) -> str:
        return f'num_parameters={self.num_parameters}'


class Softsign(Module):
    r"""Applies the element-wise function:

    .. math::
        \text{SoftSign}(x) = \frac{x}{ 1 + |x|}

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/Softsign.png

    Examples::

        >>> m = nn.Softsign()
        >>> input = torch.randn(2)
        >>> output = m(input)
    """

    def forward(self, input: Tensor) -> Tensor:
        return F.softsign(input)


class Tanhshrink(Module):
    r"""Applies the element-wise function:

    .. math::
        \text{Tanhshrink}(x) = x - \tanh(x)

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/Tanhshrink.png

    Examples::

        >>> m = nn.Tanhshrink()
        >>> input = torch.randn(2)
        >>> output = m(input)
    """

    def forward(self, input: Tensor) -> Tensor:
        return F.tanhshrink(input)


class Softmin(Module):
    r"""Applies the Softmin function to an n-dimensional input Tensor
    rescaling them so that the elements of the n-dimensional output Tensor
    lie in the range `[0, 1]` and sum to 1.

    Softmin is defined as:

    .. math::
        \text{Softmin}(x_{i}) = \frac{\exp(-x_i)}{\sum_j \exp(-x_j)}

    Shape:
        - Input: :math:`(*)` where `*` means, any number of additional
          dimensions
        - Output: :math:`(*)`, same shape as the input

    Args:
        dim (int): A dimension along which Softmin will be computed (so every slice
            along dim will sum to 1).

    Returns:
        a Tensor of the same dimension and shape as the input, with
        values in the range [0, 1]

    Examples::

        >>> m = nn.Softmin(dim=1)
        >>> input = torch.randn(2, 3)
        >>> output = m(input)
    """
    __constants__ = ['dim']
    dim: Optional[int]

    def __init__(self, dim: Optional[int] = None) -> None:
        super().__init__()
        self.dim = dim

    def __setstate__(self, state):
        super().__setstate__(state)
        if not hasattr(self, 'dim'):
            self.dim = None

    def forward(self, input: Tensor) -> Tensor:
        return F.softmin(input, self.dim, _stacklevel=5)

    def extra_repr(self):
        return f'dim={self.dim}'

class Softmax(Module):
    r"""Applies the Softmax function to an n-dimensional input Tensor
    rescaling them so that the elements of the n-dimensional output Tensor
    lie in the range [0,1] and sum to 1.

    Softmax is defined as:

    .. math::
        \text{Softmax}(x_{i}) = \frac{\exp(x_i)}{\sum_j \exp(x_j)}

    When the input Tensor is a sparse tensor then the unspecified
    values are treated as ``-inf``.

    Shape:
        - Input: :math:`(*)` where `*` means, any number of additional
          dimensions
        - Output: :math:`(*)`, same shape as the input

    Returns:
        a Tensor of the same dimension and shape as the input with
        values in the range [0, 1]

    Args:
        dim (int): A dimension along which Softmax will be computed (so every slice
            along dim will sum to 1).

    .. note::
        This module doesn't work directly with NLLLoss,
        which expects the Log to be computed between the Softmax and itself.
        Use `LogSoftmax` instead (it's faster and has better numerical properties).

    Examples::

        >>> m = nn.Softmax(dim=1)
        >>> input = torch.randn(2, 3)
        >>> output = m(input)

    """
    __constants__ = ['dim']
    dim: Optional[int]

    def __init__(self, dim: Optional[int] = None) -> None:
        super().__init__()
        self.dim = dim

    def __setstate__(self, state):
        super().__setstate__(state)
        if not hasattr(self, 'dim'):
            self.dim = None

    def forward(self, input: Tensor) -> Tensor:
        return F.softmax(input, self.dim, _stacklevel=5)

    def extra_repr(self) -> str:
        return f'dim={self.dim}'


class Softmax2d(Module):
    r"""Applies SoftMax over features to each spatial location.

    When given an image of ``Channels x Height x Width``, it will
    apply `Softmax` to each location :math:`(Channels, h_i, w_j)`

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

    Returns:
        a Tensor of the same dimension and shape as the input with
        values in the range [0, 1]

    Examples::

        >>> m = nn.Softmax2d()
        >>> # you softmax over the 2nd dimension
        >>> input = torch.randn(2, 3, 12, 13)
        >>> output = m(input)
    """

    def forward(self, input: Tensor) -> Tensor:
        if input.dim() not in (3, 4):
            raise ValueError(
                f"Softmax2d: expected input to be 3D or 4D, got {input.dim()}D instead"
            )
        return F.softmax(input, -3, _stacklevel=5)


class LogSoftmax(Module):
    r"""Applies the :math:`\log(\text{Softmax}(x))` function to an n-dimensional
    input Tensor. The LogSoftmax formulation can be simplified as:

    .. math::
        \text{LogSoftmax}(x_{i}) = \log\left(\frac{\exp(x_i) }{ \sum_j \exp(x_j)} \right)

    Shape:
        - Input: :math:`(*)` where `*` means, any number of additional
          dimensions
        - Output: :math:`(*)`, same shape as the input

    Args:
        dim (int): A dimension along which LogSoftmax will be computed.

    Returns:
        a Tensor of the same dimension and shape as the input with
        values in the range [-inf, 0)

    Examples::

        >>> m = nn.LogSoftmax(dim=1)
        >>> input = torch.randn(2, 3)
        >>> output = m(input)
    """
    __constants__ = ['dim']
    dim: Optional[int]

    def __init__(self, dim: Optional[int] = None) -> None:
        super().__init__()
        self.dim = dim

    def __setstate__(self, state):
        super().__setstate__(state)
        if not hasattr(self, 'dim'):
            self.dim = None

    def forward(self, input: Tensor) -> Tensor:
        return F.log_softmax(input, self.dim, _stacklevel=5)

    def extra_repr(self):
        return f'dim={self.dim}'