Class Sigmoid

numpy_ml/neural_nets/activations/activations.py:30–70

class Sigmoid(ActivationBase):
    def __init__(self):
        """A logistic sigmoid activation function."""
        super().__init__()

    def __str__(self):
        """Return a string representation of the activation function"""
        return "Sigmoid"

    def fn(self, z):
        r"""
        Evaluate the logistic sigmoid, :math:`\sigma`, on the elements of input `z`.

        .. math::

            \sigma(x_i) = \frac{1}{1 + e^{-x_i}}
        """
        return 1 / (1 + np.exp(-z))

    def grad(self, x):
        r"""
        Evaluate the first derivative of the logistic sigmoid on the elements of `x`.

        .. math::

            \frac{\partial \sigma}{\partial x_i} = \sigma(x_i) (1 - \sigma(x_i))
        """
        fn_x = self.fn(x)
        return fn_x * (1 - fn_x)

    def grad2(self, x):
        r"""
        Evaluate the second derivative of the logistic sigmoid on the elements of `x`.

        .. math::

            \frac{\partial^2 \sigma}{\partial x_i^2} =
                \frac{\partial \sigma}{\partial x_i} (1 - 2 \sigma(x_i))
        """
        fn_x = self.fn(x)
        return fn_x * (1 - fn_x) * (1 - 2 * fn_x)


class ReLU(ActivationBase):