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reciprocal_compression

Bases: reciprocal_expansion

The reciprocal data compression function.

It performs the reciprocal compression of the input vector, and returns the compression result. The class inherits from the reciprocal_expansion class, which inherits from the base data transformation class.

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Notes

For input vector \(\mathbf{x} \in R^m\), its reciprocal compression 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 compression function.

Specifically, for very small positive and negative small values that are close to zero, the reciprocal compression 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_compression'

Name of the compression function.

Methods:

Name Description
__init__

It performs the initialization of the compression function.
calculate_D

It calculates the compression space dimension d based on the input dimension parameter m.
forward

It implements the abstract forward method declared in the base compression class.
Source code in tinybig/compression/basic_compression.py 
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class reciprocal_compression(reciprocal_expansion):
    r"""
        The reciprocal data compression function.

        It performs the reciprocal compression of the input vector, and returns the compression result.
        The class inherits from the reciprocal_expansion class, which inherits from the base data transformation class.

        ...

        Notes
        ----------
        For input vector $\mathbf{x} \in R^m$, its reciprocal compression 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 compression function.

        Specifically, for very small positive and negative small values that are close to zero, the reciprocal
        compression 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_compression'
            Name of the compression function.

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

        calculate_D
            It calculates the compression space dimension d based on the input dimension parameter m.

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

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

            It initializes a reciprocal compression 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_compression'
                The name of the reciprocal compression function.

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

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

The initialization method of the reciprocal compression function.

It initializes a reciprocal compression 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 compression function.

 'reciprocal_compression'

Returns:

Type Description
transformation

The reciprocal compression function.
Source code in tinybig/compression/basic_compression.py 
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def __init__(self, name='reciprocal_compression', *args, **kwargs):
    """
        The initialization method of the reciprocal compression function.

        It initializes a reciprocal compression 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_compression'
            The name of the reciprocal compression function.

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