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

A risk analyst builds a feed-forward neural network to predict loan default. The network has an input layer, two hidden layers and an output layer. What is the main role of the nonlinear activation function applied in the hidden layers?

The activation function introduces nonlinearity, letting the network model nonlinear relationships. Without it, multiple layers would collapse into one linear mapping, equivalent to linear regression. It does not ensure zero training error, standardize inputs, or eliminate the need for training data.

  1. AIt allows the network to model nonlinear relationships between inputs and the outputCorrect
  2. BIt guarantees that the training error reaches zero
  3. CIt standardizes the input variables to have zero mean
  4. DIt removes the need for a training dataset

Explanation

Without nonlinear activation functions, stacked layers collapse into a single linear transformation, so the network would be no more flexible than linear regression. Nonlinear activations let the network capture complex relationships. Activation functions do not guarantee zero training error, do not standardize inputs, and do not remove the need for training data.

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