Activation functions in ML Python - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is an activation function in a neural network?

An activation function decides if a neuron should be activated or not. It adds non-linearity to the network, helping it learn complex patterns.

beginner

Why do we need non-linear activation functions?

Non-linear activation functions let neural networks learn and model complex data. Without them, the network would behave like a simple linear model.

beginner

Name three common activation functions used in neural networks.

Three common activation functions are: Sigmoid, ReLU (Rectified Linear Unit), and Tanh (Hyperbolic Tangent).

beginner

What is the output range of the Sigmoid activation function?

The Sigmoid function outputs values between 0 and 1, making it useful for probabilities.

beginner

How does the ReLU activation function work?

ReLU outputs the input directly if it is positive; otherwise, it outputs zero. This helps the network learn faster and reduces the chance of vanishing gradients.

What does an activation function add to a neural network?

A More layers

B Non-linearity

C Data normalization

D Weight initialization

Activation functions add non-linearity, allowing the network to learn complex patterns.

Which activation function outputs values between -1 and 1?

A ReLU

B Sigmoid

C Tanh

D Softmax

Tanh outputs values between -1 and 1, centering data around zero.

What is a key advantage of ReLU over Sigmoid?

A ReLU outputs probabilities

B ReLU is non-differentiable

C ReLU outputs values between 0 and 1

D ReLU helps reduce vanishing gradients

ReLU helps reduce the vanishing gradient problem, allowing faster training.

Which activation function is best for the output layer in binary classification?

A Sigmoid

B Tanh

C ReLU

D Linear

Sigmoid outputs values between 0 and 1, suitable for binary classification probabilities.

What happens to negative inputs in the ReLU function?

A They become zero

B They are passed through unchanged

C They become one

D They become negative one

ReLU outputs zero for any negative input.

Explain what an activation function is and why it is important in neural networks.

Think about how neurons decide to 'fire' or not.

Describe the differences between Sigmoid, Tanh, and ReLU activation functions.

Consider their output values and where they are commonly used.

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