Sigmoid

SOURCE CODE

The sigmoid function, also known as the logistic function, is a mathematical function that takes a real-valued input and maps it to a value between 0 and 1. The sigmoid function is commonly used in machine learning and neural networks, particularly in the context of binary classification problems.

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Sigmoid.forward()

Applies the Sigmoid function to each element of a PackedFloat32Array.

\[\text{Sigmoid.forward}(x) = \sigma(x) = \frac{1}{1 + e^{-x}}\]

    func forward(xx: PackedFloat32Array) -> PackedFloat32Array:
        self.inputs = xx
        var output: PackedFloat32Array = []

        for x  in xx: output.append( 1 / (1 + exp(-x)) )

        return output

Args
x	A PackedFloat32Array 1D

Return
A PackedFloat32Array with the same shape as x

\[\text{For } x \in (-\infty, \infty)\text{, } \mathrm{sigmoid}(x) \in (0, 1)\]

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Sigmoid.calculate_derivative()

The Sigmoid.calculate_derivative() method computes the derivative of the sigmoid function for each element in the self.input array.

\[\frac{d\sigma(x)}{dx} = \sigma(x)(1 - \sigma(x))\]

func calculate_derivative() -> Tensor:
    var output := Tensor.new()

    for x in self.inputs: output.append(exp(-x) * (1 + exp(-x)) ** -2)

    return  output

Args

Return
A Tensor with the same shape as self.inputs

\[\sigma'(x)\]

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Examples

var x := PackedFloat32Array()

var sigmoid = Sigmoid.new()

func _ready():
    x = sigmoid.forward(x)
    var derivative = sigmoid.calculate_derivative()

    print(derivative.values)