Write a Python function that computes the output of the sigmoid activation function given an input value z. The function should return the output rounded to four decimal places.
Example
Example:
input: z = 0
output: 0.5
reasoning: The sigmoid function is defined as σ(z) = 1 / (1 + exp(-z)). For z = 0, exp(-0) = 1, hence the output is 1 / (1 + 1) = 0.5.
Understanding the Sigmoid Activation Function
The sigmoid activation function is crucial in neural networks, especially for binary classification tasks. It maps any real-valued number into the (0, 1) interval, making it useful for modeling probability as an output.
Mathematical Definition
The sigmoid function is mathematically defined as:
\[
\sigma(z) = \frac{1}{1 + e^{-z}}
\]
Where \(z\) is the input to the function.
Characteristics
Output Range: The output is always between 0 and 1.
Shape: It has an "S" shaped curve.
Gradient: The function's gradient is highest near \(z = 0\) and decreases toward either end of the z-axis.
This function is particularly useful for turning logits (raw prediction values) into probabilities in binary classification models.
import math
def sigmoid(z: float) -> float:
result = 1 / (1 + math.exp(-z))
return round(result, 4)
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