Activation functions in ML Python - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Why use activation functions in neural networks?

What is the main reason to use activation functions in neural networks?

A To convert outputs into probabilities only

B To reduce the size of the input data

C To speed up the training by skipping some layers

D To introduce non-linearity so the network can learn complex patterns

💡 Hint

Think about what would happen if the network was just a chain of linear operations.

Activation functions add non-linearity, allowing the network to learn complex patterns beyond simple linear relationships.

❓ Predict Output

intermediate

Output of ReLU activation function

What is the output of the ReLU function for the input array [-2, 0, 3]?

ML Python

import numpy as np
inputs = np.array([-2, 0, 3])
outputs = np.maximum(0, inputs)
print(outputs.tolist())

A [0, 0, 3]

B [-2, 0, 3]

C [0, 0, 0]

D [-2, 0, 0]

💡 Hint

ReLU outputs zero for negative inputs and the input itself if positive.

ReLU returns 0 for negative inputs and the input value for zero or positive inputs.

❓ Hyperparameter

advanced

Choosing activation function for hidden layers

Which activation function is generally preferred for hidden layers in deep neural networks to avoid vanishing gradients?

A ReLU

B Tanh

C Sigmoid

D Linear

💡 Hint

Consider which function keeps gradients strong during backpropagation.

ReLU helps avoid vanishing gradients by outputting zero or positive values, keeping gradients alive during training.

❓ Metrics

advanced

Effect of activation function on model accuracy

A model trained with sigmoid activation in hidden layers achieves 70% accuracy. After switching to ReLU, accuracy improves to 85%. What is the most likely reason?

A ReLU reduces the number of model parameters

B ReLU allows faster training and better gradient flow, improving accuracy

C Sigmoid activation always produces lower accuracy regardless of data

D Sigmoid causes the model to overfit the training data

💡 Hint

Think about how activation functions affect training dynamics and gradients.

ReLU improves gradient flow and speeds up training, often leading to better accuracy compared to sigmoid in hidden layers.

🔧 Debug

expert

Identifying error in activation function usage

What does this code output when applying the sigmoid function incorrectly?

import numpy as np
def sigmoid(x):
    return 1 / (1 + np.exp(x))
print(sigmoid(1))

A Outputs 0.0

B Outputs 1.0

C Outputs approximately 0.268

D Outputs 0.5

💡 Hint

Check the formula for sigmoid and the sign inside the exponent.

The sigmoid function is defined incorrectly: it should be 1 / (1 + np.exp(-x)). For x=1, the correct output is ~0.731, but this code outputs ~0.268.

Practice

1. What is the main purpose of an activation function in a neural network?

easy

A. To split data into training and testing sets

B. To initialize the weights of the network

C. To reduce the size of the dataset

D. To add non-linearity so the network can learn complex patterns

Solution

1. Step 1: Understand the role of activation functions

   Activation functions introduce non-linearity to the network, allowing it to learn complex patterns beyond simple straight lines.

2. Step 2: Compare with other options

   Weight initialization, data splitting, and dataset size reduction are unrelated to activation functions.

3. Final Answer:

   To add non-linearity so the network can learn complex patterns -> Option D

4. Quick Check:

   Activation function purpose = Add non-linearity [OK]

Hint: Activation functions make models learn complex patterns [OK]

Common Mistakes:

• Confusing activation functions with weight initialization
• Thinking activation functions reduce dataset size
• Believing activation functions split data

2. Which of the following is the correct Python syntax to apply the ReLU activation function on a variable x using NumPy?

easy

A. relu_x = np.maximum(0, x)

B. relu_x = np.min(0, x)

C. relu_x = np.exp(x)

D. relu_x = np.log(x)

Solution

1. Step 1: Recall ReLU function definition

   ReLU returns the maximum between 0 and the input value, so np.maximum(0, x) is correct.

2. Step 2: Check other options

   np.min(0, x) returns the minimum, which is incorrect. np.exp(x) and np.log(x) are exponential and logarithm functions, not ReLU.

3. Final Answer:

   relu_x = np.maximum(0, x) -> Option A

4. Quick Check:

   ReLU = max(0, x) [OK]

Hint: ReLU = max between zero and input [OK]

Common Mistakes:

• Using np.min instead of np.maximum
• Confusing ReLU with exponential or log functions
• Forgetting to import numpy as np

3. Given the following Python code using NumPy, what is the output of print(output)?

import numpy as np
x = np.array([-2, 0, 3])
output = 1 / (1 + np.exp(-x))
print(output)

medium

A. [0 0 3]

B. [0.11920292 0.5 0.95257413]

C. [-2 0 3]

D. [1 1 1]

Solution

1. Step 1: Identify the activation function used

   The code applies the sigmoid function: 1 / (1 + exp(-x)) on each element of x.

2. Step 2: Calculate sigmoid values for each element

   For x = -2: sigmoid ≈ 0.1192; for 0: sigmoid = 0.5; for 3: sigmoid ≈ 0.9526.

3. Final Answer:

   [0.11920292 0.5 0.95257413] -> Option B

4. Quick Check:

   Sigmoid([-2,0,3]) = [0.119,0.5,0.953] [OK]

Hint: Sigmoid outputs values between 0 and 1 [OK]

Common Mistakes:

• Confusing sigmoid with identity function
• Expecting original input as output
• Miscomputing exponential values

4. The following code attempts to implement the Tanh activation function but has an error. What is the error?

import numpy as np
def tanh(x):
    return (np.exp(x) - np.exp(-x)) / (np.exp(x) + np.exp(x))

print(tanh(1))

medium

A. The denominator should be (np.exp(x) + np.exp(-x)) instead of (np.exp(x) + np.exp(x))

B. The numerator should be (np.exp(x) + np.exp(-x))

C. The function should use np.tanh(x) directly

D. The function is missing a return statement

Solution

1. Step 1: Review the Tanh formula

   Tanh(x) = (exp(x) - exp(-x)) / (exp(x) + exp(-x)). The denominator in the code is incorrect.

2. Step 2: Identify the error in denominator

   The code uses (np.exp(x) + np.exp(x)) which doubles exp(x) instead of adding exp(-x).

3. Final Answer:

   The denominator should be (np.exp(x) + np.exp(-x)) instead of (np.exp(x) + np.exp(x)) -> Option A

4. Quick Check:

   Tanh denominator = exp(x)+exp(-x) [OK]

Hint: Check denominator carefully for plus and minus signs [OK]

Common Mistakes:

• Copying exp(x) twice in denominator
• Swapping numerator and denominator terms
• Forgetting to return the value

5. You want to design a neural network for a binary classification task. Which activation function should you use in the output layer to get a probability between 0 and 1, and why?

hard

A. Tanh, because it outputs values between -1 and 1

B. ReLU, because it outputs only positive values

C. Sigmoid, because it outputs values between 0 and 1 suitable for probabilities

D. Linear, because it outputs raw scores

Solution

1. Step 1: Understand output layer needs for binary classification

   The output should represent a probability, so it must be between 0 and 1.

2. Step 2: Match activation functions to output range

   Sigmoid outputs between 0 and 1, perfect for probabilities. ReLU outputs 0 or more but unbounded. Tanh outputs between -1 and 1, not suitable for probabilities. Linear outputs any real number.

3. Final Answer:

   Sigmoid, because it outputs values between 0 and 1 suitable for probabilities -> Option C

4. Quick Check:

   Binary output needs sigmoid for probability [OK]

Hint: Use sigmoid for binary output probabilities [OK]

Common Mistakes:

• Using ReLU or Tanh in output layer for probabilities
• Choosing linear activation for classification output
• Not considering output range needed