FRM Part I · FRM Exam Part I · Machine-Learning Methods
A neuron has a sigmoid activation, f(z) = 1/(1+e^(-z)). Its inputs are x1 = 1 and x2 = 3, with weights w1 = 2 and w2 = -1, and bias b = 1. What is the output?
The output is 0.50. The weighted sum is 2×1 + (-1)×3 + 1 = 0, and the sigmoid function at zero equals 1/(1+e^0) = 0.5, so the neuron is exactly undecided.
- A0.50Correct
- B0.73
- C0.88
- D0.27
Explanation
z = 2(1) + (-1)(3) + 1 = 0. Sigmoid(0) = 1/(1+1) = 0.50. The value 0.73 is sigmoid(1), which arises from omitting the bias incorrectly; 0.27 is sigmoid(-1), from a sign error on the bias; 0.88 is sigmoid(2), from ignoring the second input.
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