FRM Part I · FRM Exam Part I · Machine Learning and Prediction
A neural network hidden node receives inputs x1 = 2 and x2 = -1. The weights are w1 = 0.5 and w2 = 1.5, and the bias is 0.25. The node uses a ReLU activation, f(z) = max(0, z). What is the node's output?
The output is 0. The pre-activation sum is 0.5×2 + 1.5×(-1) + 0.25 = -0.25, and ReLU sets any negative input to zero. Reporting -0.25 would ignore the activation function.
- A0Correct
- B-0.25
- C1.25
- D-0.5
Explanation
The weighted sum is z = 0.5(2) + 1.5(-1) + 0.25 = 1 - 1.5 + 0.25 = -0.25. ReLU returns max(0, -0.25) = 0. The value -0.25 is wrong because it is the pre-activation sum, ignoring ReLU. 1.25 results from ignoring the sign of x2 (1+1.5... plus bias).
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