Regarding the role of activation functions in neural networks, which of the following statements is correct?

I Activation functions introduce non-linearity, allowing neural networks to model complex relationships in data.
II Without activation functions, a neural network with one hidden layer can only discover linear functions of the inputs.
III Activation functions are applied component-wise to all neurons of a layer.
IV An activation function is always required at the output layer level.

Question

Regarding the role of activation functions in neural networks, which of the following statements is correct?

I	Activation functions introduce non-linearity, allowing neural networks to model complex relationships in data.
II	Without activation functions, a neural network with one hidden layer can only discover linear functions of the inputs.
III	Activation functions are applied component-wise to all neurons of a layer.
IV	An activation function is always required at the output layer level.

BlackTom AI · Accepted Answer

Question: Regarding the role of activation functions in neural networks, which of the following statements is correct?

I	Activation functions introduce non-linearity, allowing neural networks to model complex relationships in data.
II	Without activation functions, a neural network with one hidden layer can only discover linear functions of the inputs.
III	Activation functions are applied component-wise to all neurons of a layer.
IV	An activation function is always required at the output layer level.

Option 1: II and IV
- This option claims that only II and IV are correct. Regarding II, the statement is true: if there are no activation functions anywhere in the network (including hidden layers), the entire network collapses to a linear function of the inputs, regardless of the number of layers. Therefore II being selected would imply that the network can only model linear functions, which is accurate in that restricted case.
- Regarding IV, the claim that an activation function is always required at the output layer is not universal. Some tasks (e.g., regression) use a linear (identity) activation at the output, and in other cases (classification with softmax or sigmoid) the output layer uses a non-linear activation. Thus IV is not universally required and makes this option incorrect.
- Overall, since IV is incorrect, Option 1 cannot be entirely correct.

Option 2: I, II, III and IV
- This option asserts that I, II, III, and IV are all correct. We already noted IV is not universally required, which makes this option incorrect. The inclusion of IV undermines the claim that all four statements are correct.

Option 3: I, II and III
- Statement I is true: activation functions introduce non-linearity, enabling the network to capture complex relationships that linear mappings alone cannot express.
- Statement II is true: without activation functions, even a network with hidden layers behaves as a single linear transformation, so it cannot model non-linear relationships.
- Statement III is true: activation functions are typically applied element-wise (component-wise) to the pre-activation outputs of each neuron in a layer, producing the post-activation outputs that form the layer’s activations.
- Since I, II, and III are all accurate, this option aligns with the correct understanding of activation functions.

Option 4: III and IV
- Statement III is true, as explained above.
- Statement IV, however, is not universally true, since some networks use linear activation at the output or omit an explicit activation in certain regression or specialized architectures. Therefore this option is not correct overall.

Summary:
- Options 1, 2, and 4 each contain at least one incorrect claim (primarily about IV or about the combination of truths).
- Option 3 correctly identifies I, II, and III as true statements about activation functions, with IV being the exception where applicable. The reasoning hinges on understanding non-linearity, the consequence of removing activations, and the per-neuron application of activations.

FINTECH 540.01.Fa25 Quiz 6 - Feedforward Neural Networks

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