Identify the activation function represented by \(\phi(V)=Z+\frac{1}{1+\exp(-XV…
2012
Identify the activation function represented by \(\phi(V)=Z+\frac{1}{1+\exp(-XV+Y)}\), where Z, X, and Y are parameters.
Answer: C. Sigmoid function — ConceptAn activation function maps a neuron input to an output. A sigmoid is a smooth, bounded, S-shaped member of the logistic family. Its standard structure…
- A.
Step function
- B.
Ramp function
- C.
Sigmoid function
- D.
Gaussian function
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Show answer & explanation
Correct answer: C
Concept
An activation function maps a neuron input to an output. A sigmoid is a smooth, bounded, S-shaped member of the logistic family.
Its standard structure is an offset plus a reciprocal term containing 1 plus an exponential of a linear expression.
Application
In the given expression, Z supplies the vertical offset, while X and Y control the slope and horizontal shift of the transition.
As V varies, the reciprocal term changes smoothly between limiting values, so φ(V) changes smoothly between Z and Z + 1.
Cross-check and contrast
Step function: changes discontinuously at a threshold.
Ramp function: is piecewise linear rather than S-shaped.
Gaussian function: is bell-shaped and decreases toward its baseline on both sides of its centre.
Therefore, the expression represents a sigmoid function.