Backpropagation is the process used to train neural networks by updating weights and biases based on the error of predictions. It works alongside forward propagation and is a cornerstone of deep learning. Understanding backpropagation helps you see how neural networks learn from data.<\/p>\n\n\n\n
Why Backpropagation is Important<\/strong><\/p>\n\n\n\n Step-by-Step Process<\/strong><\/p>\n\n\n\n 1. Forward Propagation<\/strong><\/p>\n\n\n\n 2. Compute Loss<\/strong><\/p>\n\n\n\n 3. Backward Pass (Compute Gradients)<\/strong><\/p>\n\n\n\n 4. Update Weights and Biases<\/strong><\/p>\n\n\n\n 5. Repeat for Multiple Epochs<\/strong><\/p>\n\n\n\n Example: Backpropagation in Python (Simplified)<\/strong><\/p>\n\n\n\n Key Points<\/strong><\/p>\n\n\n\n Applications<\/strong><\/p>\n\n\n\n Lesson Summary<\/strong>\n
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w = w \u2212 learning_rate \u00d7 \u2202Loss\/\u2202w
b = b \u2212 learning_rate \u00d7 \u2202Loss\/\u2202b<\/li>\n\n\n\n\n
import numpy as np# Sample input and output
X = np.array([1, 2])
y_true = 1# Initialize weights and bias
weights = np.array([0.5, -0.5])
bias = 0.1
learning_rate = 0.1# Forward pass
z = np.dot(X, weights) + bias
output = 1 \/ (1 + np.exp(-z)) # Sigmoid activation# Compute error (Binary cross-entropy derivative simplified)
error = output - y_true# Gradients for weights and bias
grad_w = error * X
grad_b = error# Update weights and bias
weights -= learning_rate * grad_w
bias -= learning_rate * grad_bprint(\"Updated weights:\", weights)
print(\"Updated bias:\", bias)<\/pre>\n\n\n\n\n
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Backpropagation is the process of updating weights and biases in a neural network to reduce prediction error. By combining forward propagation, loss computation, gradient calculation, and weight updates, the network learns iteratively. Understanding this process is crucial for mastering neural network training and deep learning.<\/p>\n\n\n