Convolutional Neural Network CNN: What is NOT a Property of the Sigmoid Function?

Learn what is NOT a property of the sigmoid function in neural networks. Understand its behavior, characteristics, and why?

Question

What is NOT the property of sigmoid function?

A. Input is any real number
B. Output is a real number in range between 0 to 1
C. Nearly linear when input is close to zero
D. Slope is close to zero when input is close to zero

Answer

D. Slope is close to zero when input is close to zero

Explanation

The sigmoid function is widely used in machine learning and neural networks due to its smooth, differentiable, and bounded properties.

Why Option D is Incorrect:

The slope (or derivative) of the sigmoid function is not close to zero when the input is near zero. Instead:

At x=0, the sigmoid function outputs 0.5, and its slope reaches its maximum value of 0.25. This means the sigmoid behaves almost linearly around this region.

The slope approaches zero only at extreme values of x (e.g., as x→−∞ or x→+∞), where the function saturates near its asymptotes ( 0 and 1).

Why Other Options are Correct

A. Input is any real number: True. The domain of the sigmoid function includes all real numbers.
B. Output is a real number in range between 0 to 1: True. The sigmoid squashes any input into the range (0,1).
C. Nearly linear when input is close to zero: True. Around x=0, the sigmoid curve approximates a linear function with a slope of 0.25.

Key Takeaway

Option D contradicts the mathematical properties of the sigmoid function because its slope near x=0 is not close to zero; it is at its maximum value instead. Understanding this behavior is crucial for leveraging sigmoid functions effectively in neural networks, especially in tasks like binary classification or as activation functions.

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