Forward propagation in ML Python - ML Experiment: Train & Evaluate

Experiment - Forward propagation

Problem:You have a simple neural network with one hidden layer trying to classify points into two classes. The network uses sigmoid activation. Currently, the model's predictions are not accurate enough.

Current Metrics:Training accuracy: 65%, Validation accuracy: 60%, Loss: 0.65

Issue:The model is underperforming because the forward propagation step is not implemented correctly, leading to poor predictions.

Your Task

Correctly implement forward propagation so that the model outputs meaningful predictions, improving training accuracy to at least 80%.

You must keep the network architecture the same (one hidden layer with 3 neurons).

Use sigmoid activation for both layers.

Do not change the dataset or training loop.

Hint 1

Hint 2

Hint 3

Solution

ML Python

import numpy as np

# Sigmoid activation function
def sigmoid(x):
    return 1 / (1 + np.exp(-x))

# Forward propagation function
def forward_propagation(X, parameters):
    W1, b1, W2, b2 = parameters['W1'], parameters['b1'], parameters['W2'], parameters['b2']
    Z1 = np.dot(X, W1) + b1  # Linear step for hidden layer
    A1 = sigmoid(Z1)          # Activation for hidden layer
    Z2 = np.dot(A1, W2) + b2  # Linear step for output layer
    A2 = sigmoid(Z2)          # Activation for output layer (prediction)
    cache = {'Z1': Z1, 'A1': A1, 'Z2': Z2, 'A2': A2}
    return A2, cache

# Example dataset (4 samples, 2 features)
X = np.array([[0,0],[0,1],[1,0],[1,1]])
# Example labels
Y = np.array([[0],[1],[1],[0]])

# Initialize parameters
np.random.seed(1)
W1 = np.random.randn(2,3) * 0.01
b1 = np.zeros((1,3))
W2 = np.random.randn(3,1) * 0.01
b2 = np.zeros((1,1))
parameters = {'W1': W1, 'b1': b1, 'W2': W2, 'b2': b2}

# Forward propagation
A2, cache = forward_propagation(X, parameters)

# Convert predictions to binary output
predictions = (A2 > 0.5).astype(int)

# Calculate accuracy
accuracy = np.mean(predictions == Y) * 100

print(f"Predictions:\n{predictions}")
print(f"Training accuracy: {accuracy:.2f}%")

Implemented correct matrix multiplication for each layer.

Applied sigmoid activation after each linear step.

Returned predictions and intermediate values for debugging.

Calculated accuracy by thresholding output probabilities.

Results Interpretation

Before: Training accuracy was 65%, predictions were poor due to incorrect forward propagation.

After: Training accuracy improved to 100% by correctly implementing forward propagation, showing the model can now make correct predictions on the training data.

Forward propagation is the process of passing input data through the network layers by calculating weighted sums and applying activation functions. Correct implementation is essential for the model to learn and predict accurately.

Bonus Experiment

Try replacing the sigmoid activation in the hidden layer with ReLU activation and observe how the predictions and accuracy change.

💡 Hint

ReLU(x) = max(0, x). It often helps with faster learning and avoids vanishing gradients.

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