Question at position 11 Which of the following computation adds nonlinearity to an ANN?Performing activation functionTaking weighed sum of inputs单项选择题
A
Performing activation function
B
Taking weighed sum of inputs

Question

Question at position 11 Which of the following computation adds nonlinearity to an ANN?Performing activation functionTaking weighed sum of inputs

BlackTom AI · Accepted Answer

Activation functions introduce nonlinearity into neural networks because they apply a nonlinear mapping to the linear combination produced by a layer.

1. Relevant knowledge points and concepts
- A neuron computes a weighted sum of inputs plus a bias: z = W x + b (a linear operation).
- An activation function φ(z) (e.g., ReLU, sigmoid, tanh) transforms z into a nonlinear output y = φ(z).
- Nonlinearity is necessary so stacked layers can approximate complex, non-linear functions; without it, multiple linear layers collapse to a single linear transformation.

2. Complete reasoning process step by step
- Step A: Compute weighted sum: z = W1 x + b1. This is linear in x.
- Step B: If no activation is applied and a second linear layer follows: y = W2 z + b2 = W2 (W1 x + b1) + b2 = (W2 W1) x + (W2 b1 + b2). This composition is equivalent to one linear mapping from x to y.
- Step C: If an activation φ is applied between layers: y = W2 φ(W1 x + b1) + b2. Because φ is nonlinear, the composition cannot be reduced to a single linear map, enabling the network to learn nonlinear relationships.

3. Calculations and intermediate steps (symbolic)
- Two linear layers without activation:
  z = W1 x + b1
  y = W2 z + b2 = W2 W1 x + W2 b1 + b2
  => single linear mapping y = W' x + b'
- With activation φ:
  y = W2 φ(z) + b2, not reducible to y = W' x + b' unless φ is linear.

4. Why the correct answer is correct
- Performing an activation function applies a non-linear transform φ to the linear sum z, thereby introducing nonlinearity into the network. Common activations (ReLU, sigmoid, tanh) are explicitly nonlinear.

5. Why the other option is incorrect
- Taking the weighted sum of inputs is a linear operation (a linear combination). Alone, it does not introduce nonlinearity; stacked linear operations remain linear and cannot model complex nonlinear functions.

6. Conclusion
- Therefore, "Performing activation function" is the correct choice. This confirms the provided answer: Performing activation function.

Question at position 11 Which of the following computation adds nonlinearity to an ANN?Performing activation functionTaking weighed sum of inputs单项选择题

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