Forward propagation in ML Python - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate the weighted sum in forward propagation.

ML Python

weighted_sum = sum(inputs[i] * weights[i] for i in range(len(inputs))) + [1]

Drag options to blanks, or click blank then click option'

Abias

Bactivation

Coutput

Dloss

Attempts:

3 left

💡 Hint

Common Mistakes

Using activation instead of bias in the weighted sum.

Forgetting to add bias at all.

The weighted sum includes the bias term added to the sum of inputs times weights.

2fill in blank

medium

Complete the code to apply the activation function in forward propagation.

ML Python

output = [1](weighted_sum)

Drag options to blanks, or click blank then click option'

Aactivation_function

Blen

Cprint

Dsum

Attempts:

3 left

💡 Hint

Common Mistakes

Using sum instead of activation_function.

Trying to print the weighted sum instead of applying activation.

The activation function is applied to the weighted sum to produce the output.

3fill in blank

hard

Fix the error in the code to correctly compute the output of a neuron.

ML Python

output = activation_function([1])

Drag options to blanks, or click blank then click option'

Ainputs

Bweighted_sum

Cweights

Dbias

Attempts:

3 left

💡 Hint

Common Mistakes

Applying activation function directly to inputs or weights.

Using bias alone as input to activation.

The activation function should be applied to the weighted sum, not directly to inputs or weights.

4fill in blank

hard

Fill both blanks to complete the forward propagation step for one neuron.

ML Python

weighted_sum = sum([1][i] * [2][i] for i in range(len(inputs))) + bias

Drag options to blanks, or click blank then click option'

Ainputs

Bweights

Cbias

Doutput

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping inputs and weights in multiplication.

Including bias inside the loop.

Inputs and weights are multiplied element-wise and summed to get the weighted sum.

5fill in blank

hard

Fill all three blanks to complete the forward propagation for a layer of neurons.

ML Python

outputs = [activation_function(sum([1][i] * [2][j][i] for i in range(len([3]))) + biases[j]) for j in range(len(weights))]

Drag options to blanks, or click blank then click option'

Ainputs

Bweights

Dbiases

Attempts:

3 left

💡 Hint

Common Mistakes

Using biases instead of inputs in the sum.

Mixing up weights and biases indices.

For each neuron j, multiply inputs by weights[j], sum, add bias, then apply activation.

Practice

1. What is the main purpose of forward propagation in a neural network?

easy

A. To pass input data through the network to get predictions

B. To update the weights using gradients

C. To split data into training and testing sets

D. To initialize the weights randomly

Solution

1. Step 1: Understand forward propagation role

   Forward propagation is the process where input data moves through the network layers to produce output predictions.

2. Step 2: Differentiate from other processes

   Updating weights and splitting data are separate steps, not part of forward propagation.

3. Final Answer:

   To pass input data through the network to get predictions -> Option A

4. Quick Check:

   Forward propagation = prediction step [OK]

Hint: Forward propagation = input to output prediction [OK]

Common Mistakes:

• Confusing forward propagation with training steps
• Thinking it updates weights
• Mixing it with data preparation

2. Which of the following is the correct formula for calculating the output of a neuron during forward propagation?

easy

A. output = input / weight - bias

B. output = weight + input * bias

C. output = activation(input - weight + bias)

D. output = activation(weight * input + bias)

Solution

1. Step 1: Recall neuron output formula

   The neuron output is calculated by multiplying input by weight, adding bias, then applying activation.

2. Step 2: Match formula to options

   output = activation(weight * input + bias) correctly shows output = activation(weight * input + bias).

3. Final Answer:

   output = activation(weight * input + bias) -> Option D

4. Quick Check:

   Neuron output = weighted sum + bias, then activation [OK]

Hint: Neuron output = activation(weight x input + bias) [OK]

Common Mistakes:

• Mixing order of operations
• Forgetting to apply activation function
• Using addition instead of multiplication for weights

3. Given a single neuron with weight = 0.5, bias = 1, input = 4, and activation function f(x) = x (identity), what is the output after forward propagation?

medium

A. 3.5

B. 3.0

C. 4.0

D. 2.0

Solution

1. Step 1: Calculate weighted sum

   Weighted sum = weight * input + bias = 0.5 * 4 + 1 = 2 + 1 = 3.

2. Step 2: Apply activation function

   Activation is identity, so output = 3.

3. Final Answer:

   3.0 -> Option B

4. Quick Check:

   Output = 0.5x4 + 1 = 3.0 [OK]

Hint: Multiply weight and input, add bias, then activate [OK]

Common Mistakes:

• Adding weight and input instead of multiplying
• Forgetting bias
• Misapplying activation function

4. Consider this Python code for forward propagation of a single neuron:

def forward(input, weight, bias):
    return input * weight + bias

output = forward(3, 2, 1)
print(output)

What is the error in this code if the activation function is missing?

medium

A. The code misses applying the activation function, so output is not transformed

B. The multiplication operator is wrong, should be '+' instead of '*'

C. The bias should be multiplied, not added

D. The function should return input + weight + bias instead

Solution

1. Step 1: Analyze the function output

   The function returns weighted sum without applying any activation function.

2. Step 2: Understand activation role

   Activation function adds non-linearity; missing it means output is raw sum, which is incomplete forward propagation.

3. Final Answer:

   The code misses applying the activation function, so output is not transformed -> Option A

4. Quick Check:

   Activation missing = incomplete forward propagation [OK]

Hint: Always apply activation after weighted sum [OK]

Common Mistakes:

• Thinking bias should be multiplied
• Confusing operators
• Ignoring activation importance

5. You have a 2-layer neural network where the first layer outputs [2, 3] and the second layer has weights [[1, -1], [0, 2]] and biases [0, 1]. Using ReLU activation f(x) = max(0, x), what is the output of the second layer after forward propagation?

hard

A. [3, 4]

B. [2, 5]

C. [0, 7]

D. [1, 6]

Solution

1. Step 1: Calculate weighted sums for second layer

   Multiply first layer output by weights and add biases: For first neuron: (2*1) + (3*0) + 0 = 2 + 0 + 0 = 2 For second neuron: (2*(-1)) + (3*2) + 1 = -2 + 6 + 1 = 5

2. Step 2: Apply ReLU activation

   ReLU outputs max(0, x): First neuron: max(0, 2) = 2 Second neuron: max(0, 5) = 5

3. Step 3: Re-check calculations for correctness

   Re-examining weights and biases: Weights matrix: [[1, -1], [0, 2]] means first output neuron weights: [1, -1] Second output neuron weights: [0, 2] Input vector: [2, 3] Calculations: Neuron 1: 2*1 + 3*(-1) + 0 = 2 - 3 + 0 = -1 Neuron 2: 2*0 + 3*2 + 1 = 0 + 6 + 1 = 7 Apply ReLU: Neuron 1: max(0, -1) = 0 Neuron 2: max(0, 7) = 7

4. Final Answer:

   [0, 7] -> Option C

5. Quick Check:

   Weighted sum + bias, then ReLU = [0, 7] [OK]

Hint: Multiply inputs by weights, add bias, apply ReLU [OK]

Common Mistakes:

• Mixing weight matrix rows and columns
• Forgetting to add bias
• Applying activation before weighted sum