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FRM Part I · FRM Exam Part I · Machine Learning and Prediction

A single neuron receives inputs x1 = 2 and x2 = -1 with weights w1 = 0.5 and w2 = 1.5 and bias b = 0.5. It uses a ReLU activation, f(z) = max(0, z). What is the neuron's output?

The output is 0. The weighted sum is 0.5×2 + 1.5×(-1) + 0.5 = 0, and ReLU returns max(0, 0) = 0. A result of -0.5 would ignore the activation function, and 1.0 would ignore the negative second input.

  1. A0Correct
  2. B-0.5
  3. C1.0
  4. D0.0 only if the bias is removed, otherwise 1.5

Explanation

z = 0.5(2) + 1.5(-1) + 0.5 = 1 - 1.5 + 0.5 = 0. ReLU of 0 equals 0. Dropping the bias would give z = -0.5 and still output 0, so the final option is wrong. A negative output of -0.5 would ignore the ReLU, and 1.0 omits the second input's contribution.

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