reciprocal_expansion

Bases: transformation

The reciprocal data expansion function.

It performs the reciprocal expansion of the input vector, and returns the expansion result. The class inherits from the base expansion class (i.e., the transformation class in the module directory).

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Notes

For input vector \(\mathbf{x} \in R^m\), its reciprocal expansion will be $$ \begin{equation} \kappa(\mathbf{x}) = \frac{1}{\mathbf{x}} \in R^D \end{equation} $$ where \(D = m\).

By default, the input and output can also be processed with the optional pre- or post-processing functions in the reciprocal expansion function.

Specifically, for very small positive and negative small values that are close to zero, the reciprocal expansion function will replace them with very small numbers \(10^{-6}\) and \(-10^{-6}\), respectively. In the current implementation, the input values in the range \([0, 10^{-6}]\) are replaced with \(10^{-6}\), and values in the range \([-10^{-6}, 0)\) are replaced with \(-10^{-6}\).

Attributes:

Name	Type	Description
name	str, default = 'reciprocal_expansion'	Name of the expansion function.

Methods:

Name	Description
__init__	It performs the initialization of the expansion function.
calculate_D	It calculates the expansion space dimension D based on the input dimension parameter m.
forward	It implements the abstract forward method declared in the base expansion class.

Source code in tinybig/expansion/basic_expansion.py

class reciprocal_expansion(transformation):
    r"""
    The reciprocal data expansion function.

    It performs the reciprocal expansion of the input vector, and returns the expansion result.
    The class inherits from the base expansion class (i.e., the transformation class in the module directory).

    ...

    Notes
    ----------
    For input vector $\mathbf{x} \in R^m$, its reciprocal expansion will be
    $$
        \begin{equation}
            \kappa(\mathbf{x}) = \frac{1}{\mathbf{x}} \in R^D
        \end{equation}
    $$
    where $D = m$.

    By default, the input and output can also be processed with the optional pre- or post-processing functions
    in the reciprocal expansion function.

    Specifically, for very small positive and negative small values that are close to zero, the reciprocal
    expansion function will replace them with very small numbers $10^{-6}$ and $-10^{-6}$, respectively.
    In the current implementation, the input values in the range $[0, 10^{-6}]$ are replaced with $10^{-6}$,
    and values in the range $[-10^{-6}, 0)$ are replaced with $-10^{-6}$.

    Attributes
    ----------
    name: str, default = 'reciprocal_expansion'
        Name of the expansion function.

    Methods
    ----------
    __init__
        It performs the initialization of the expansion function.

    calculate_D
        It calculates the expansion space dimension D based on the input dimension parameter m.

    forward
        It implements the abstract forward method declared in the base expansion class.

    """
    def __init__(self, name='reciprocal_expansion', *args, **kwargs):
        """
        The initialization method of the reciprocal expansion function.

        It initializes a reciprocal expansion object based on the input function name.
        This method will also call the initialization method of the base class as well.

        Parameters
        ----------
        name: str, default = 'reciprocal_expansion'
            The name of the reciprocal expansion function.

        Returns
        ----------
        transformation
            The reciprocal expansion function.
        """
        super().__init__(name=name, *args, **kwargs)

    def calculate_D(self, m: int):
        r"""
        The expansion dimension calculation method.

        It calculates the intermediate expansion space dimension based on the input dimension parameter m.
        For the reciprocal expansion function, the expansion space dimension equals to the input space dimension, i.e.,
        $$ D = m. $$

        Parameters
        ----------
        m: int
            The dimension of the input space.

        Returns
        -------
        int
            The dimension of the expansion space.
        """
        return m

    def forward(self, x: torch.Tensor, device='cpu', *args, **kwargs):
        r"""
        The forward method of the data expansion function.

        It performs the reciprocal data expansion of the input data and returns the expansion result
        according to the following equation:
        $$
            \kappa(\mathbf{x}) = \frac{1}{\mathbf{x}} \in R^D
        $$
        with optional pre- and post-processing functions.


        Parameters
        ----------
        x: torch.Tensor
            The input data vector.
        device: str, default = 'cpu'
            The device to perform the data expansion.
        args: list, default = ()
            The other parameters.
        kwargs: dict, default = {}
            The other parameters.

        Returns
        ----------
        torch.Tensor
            The expanded data vector of the input.
        """
        b, m = x.shape
        x = self.pre_process(x=x, device=device)

        x[torch.logical_and(x>=0, x<=1e-6)] = 1e-6
        x[torch.logical_and(x<0, x>=-1e-6)] = -1e-6
        expansion = torch.reciprocal(x)

        assert expansion.shape == (b, self.calculate_D(m=m))
        return self.post_process(x=expansion, device=device)

__init__(name='reciprocal_expansion', *args, **kwargs)

The initialization method of the reciprocal expansion function.

It initializes a reciprocal expansion object based on the input function name. This method will also call the initialization method of the base class as well.

Parameters:

Name	Type	Description	Default
name		The name of the reciprocal expansion function.	'reciprocal_expansion'

Returns:

Type	Description
transformation	The reciprocal expansion function.

Source code in tinybig/expansion/basic_expansion.py

def __init__(self, name='reciprocal_expansion', *args, **kwargs):
    """
    The initialization method of the reciprocal expansion function.

    It initializes a reciprocal expansion object based on the input function name.
    This method will also call the initialization method of the base class as well.

    Parameters
    ----------
    name: str, default = 'reciprocal_expansion'
        The name of the reciprocal expansion function.

    Returns
    ----------
    transformation
        The reciprocal expansion function.
    """
    super().__init__(name=name, *args, **kwargs)

calculate_D(m)

The expansion dimension calculation method.

It calculates the intermediate expansion space dimension based on the input dimension parameter m. For the reciprocal expansion function, the expansion space dimension equals to the input space dimension, i.e., $$ D = m. $$

Parameters:

Name	Type	Description	Default
m	int	The dimension of the input space.	required

Returns:

Type	Description
int	The dimension of the expansion space.

Source code in tinybig/expansion/basic_expansion.py

def calculate_D(self, m: int):
    r"""
    The expansion dimension calculation method.

    It calculates the intermediate expansion space dimension based on the input dimension parameter m.
    For the reciprocal expansion function, the expansion space dimension equals to the input space dimension, i.e.,
    $$ D = m. $$

    Parameters
    ----------
    m: int
        The dimension of the input space.

    Returns
    -------
    int
        The dimension of the expansion space.
    """
    return m

forward(x, device='cpu', *args, **kwargs)

The forward method of the data expansion function.

It performs the reciprocal data expansion of the input data and returns the expansion result according to the following equation: $$ \kappa(\mathbf{x}) = \frac{1}{\mathbf{x}} \in R^D $$ with optional pre- and post-processing functions.

Parameters:

Name	Type	Description	Default
x	Tensor	The input data vector.	required
device		The device to perform the data expansion.	'cpu'
args		The other parameters.	()
kwargs		The other parameters.	{}

Returns:

Type	Description
Tensor	The expanded data vector of the input.

Source code in tinybig/expansion/basic_expansion.py

def forward(self, x: torch.Tensor, device='cpu', *args, **kwargs):
    r"""
    The forward method of the data expansion function.

    It performs the reciprocal data expansion of the input data and returns the expansion result
    according to the following equation:
    $$
        \kappa(\mathbf{x}) = \frac{1}{\mathbf{x}} \in R^D
    $$
    with optional pre- and post-processing functions.


    Parameters
    ----------
    x: torch.Tensor
        The input data vector.
    device: str, default = 'cpu'
        The device to perform the data expansion.
    args: list, default = ()
        The other parameters.
    kwargs: dict, default = {}
        The other parameters.

    Returns
    ----------
    torch.Tensor
        The expanded data vector of the input.
    """
    b, m = x.shape
    x = self.pre_process(x=x, device=device)

    x[torch.logical_and(x>=0, x<=1e-6)] = 1e-6
    x[torch.logical_and(x<0, x>=-1e-6)] = -1e-6
    expansion = torch.reciprocal(x)

    assert expansion.shape == (b, self.calculate_D(m=m))
    return self.post_process(x=expansion, device=device)