The Sigmoid activation function π(π‘) is defined as
2017
The Sigmoid activation functionΒ π(π‘)Β is defined as
- A.
\(\dfrac{1}{\text{exp} (t) + \text{exp} (-t)}\) - B.
\(t \text{ exp}(-t)\) - C.
\(\dfrac{1}{1+ \text{exp} (t)}\) - D.
\(\dfrac{1}{1+ \text{exp} (-t)}\)
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Correct answer: D
Correct formula: The Sigmoid activation function is f(t) = 1/(1 + exp(-t)).
Definition: f(t) = 1/(1 + exp(-t)).
Key properties:
Range: outputs values strictly between 0 and 1 (limiting behavior as t β Β±β).
Monotonic: it is strictly increasing in t.
Derivative: f'(t) = f(t)Β·(1 - f(t)), which is useful for gradient-based learning.
Why the other expressions are incorrect:
1/(exp(t) + exp(-t)): This is related to the reciprocal of cosh(t) (hyperbolic functions) and is not the logistic sigmoid; it does not produce the standard 0β1 mapping of the logistic function.
tΒ·exp(-t): This is not a sigmoid function. It is not bounded between 0 and 1 for all real t and lacks the standard logistic form.
1/(1 + exp(t)): This equals the logistic evaluated at -t (i.e., the sigmoid of the negated input). Although closely related, it is not the conventional form f(t) = 1/(1 + exp(-t)).