from __future__ import annotations
import numpy as np
from sklvq.activations._base import ActivationBaseClass
[docs]
class Sigmoid(ActivationBaseClass):
"""Sigmoid function
Class that holds the sigmoid function and gradient as discussed in `[1]`_
Parameters
----------
beta : int or float, optional, default=1
Positive non-zero value that controls the steepness of the Sigmoid function.
See also
--------
Identity, SoftPlus, Swish
References
----------
_`[1]` Villmann, T., Ravichandran, J., Villmann, A., Nebel, D., & Kaden, M. (2019). "Activation
Functions for Generalized Learning Vector Quantization - A Performance Comparison", 2019.
"""
__slots__: tuple[str, ...] = ("beta",)
def __init__(self, beta: float = 1):
if beta <= 0:
msg = f"{type(self).__name__}: Expected beta > 0, but got beta = {beta}"
raise ValueError(msg)
self.beta = beta
[docs]
def __call__(self, x: np.ndarray) -> np.ndarray:
r"""Computes the sigmoid function:
.. math::
f(\mathbf{x}) = \frac{1}{e^{-\beta \cdot \mathbf{x}} + 1}
Parameters
----------
x : ndarray of any shape.
Returns
-------
ndarray of shape (x.shape)
Elementwise evaluation of the sigmoid function.
"""
return np.asarray(1.0 / (np.exp(-self.beta * x) + 1.0))
[docs]
def gradient(self, x: np.ndarray) -> np.ndarray:
r"""Computes the sigmoid function's gradient with respect to x:
.. math::
\frac{\partial f}{\partial \mathbf{x}} = \frac{(\beta \cdot e^{\beta \cdot \mathbf{x})}}{(e^{\beta \cdot \mathbf{x}} + 1)^2}
Parameters
----------
x : ndarray of any shape
Returns
-------
ndarray of shape (x.shape)
Elementwise evaluation of the sigmoid function's gradient.
"""
exp = np.exp(self.beta * x)
return np.asarray((self.beta * exp) / (exp + 1.0) ** 2)