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

View Explanation

Log in for full answers

Similar Questions

What of the following are commonly used activation functions for neural networks? I Exponential function. II Rectified Linear Unit (ReLU) function. III Sigmoid function. IV Logarithm function.

哪个激活函数保持恒定的导数？ Which activation function maintains constant derivatives?

Which of these plots represents a ReLU activation function?

Question at position 22 What is the purpose of the activation function in an MLP?It determines the loss function used in the MLP. It controls the learning rate of the MLP algorithm.It provides the non-linearity of the MLP network. It determines the number of hidden layers in the MLP.

Question at position 7 What activation functions are commonly used in hidden layers of neural networks? (Select all possible answers)SigmoidReLUSoftmaxTanhLinearUnit Step

Which of the following is the advantage of Leaky ReLU compared to ReLU?

What does the ReLU activation function do?

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler